%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP088^2 : 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 08:08:17 AM UTC 2026
% Result : Theorem 2.07s 0.60s
% Output : Refutation 2.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP088^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n005.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 19:52:01 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 Running higher-order theorem proving
% 0.10/0.27 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
% 0.83/0.46 % (2124880)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.83/0.46 % (2124892)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.83/0.46 % (2124892)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
% 0.83/0.46 % (2124892)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=1729128737:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.83/0.46 % (2124887)lrs+10_16_si=on:nwc=1.5:random_seed=3894502924:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.83/0.46 % (2124888)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1207598641:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.83/0.46 % (2124886)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=259211135:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.83/0.46 % (2124891)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=579882179:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.83/0.46 % (2124890)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1335513694:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.83/0.46 % (2124889)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=4026039107: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)
% 0.83/0.46 % (2124888)Instruction limit reached!
% 0.83/0.46 % (2124888)------------------------------
% 0.83/0.46 % (2124888)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.46 % (2124888)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.46 % (2124888)CaDiCaL version: 2.1.3
% 0.83/0.46 % (2124888)Termination reason: Instruction limit
% 0.83/0.46 % (2124888)Termination phase: shuffling
% 0.83/0.46 % (2124888)Time elapsed: 0.004 s
% 0.83/0.46 % (2124888)Peak memory usage: 10 MB
% 0.83/0.46 % (2124888)Instructions burned: 4 (million)
% 0.83/0.46 % (2124887)Instruction limit reached!
% 0.83/0.46 % (2124887)------------------------------
% 0.83/0.46 % (2124887)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.46 % (2124887)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.46 % (2124887)CaDiCaL version: 2.1.3
% 0.83/0.46 % (2124887)Termination reason: Instruction limit
% 0.83/0.46 % (2124887)Termination phase: shuffling
% 0.83/0.46 % (2124887)Time elapsed: 0.016 s
% 0.83/0.46 % (2124887)Peak memory usage: 10 MB
% 0.83/0.46 % (2124887)Instructions burned: 19 (million)
% 0.83/0.46 % (2124908)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2093333192:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.83/0.46 % (2124890)Instruction limit reached!
% 0.83/0.46 % (2124890)------------------------------
% 0.83/0.46 % (2124890)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.46 % (2124890)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.46 % (2124890)CaDiCaL version: 2.1.3
% 0.83/0.46 % (2124890)Termination reason: Instruction limit
% 0.83/0.46 % (2124890)Termination phase: shuffling
% 0.83/0.46 % (2124890)Time elapsed: 0.029 s
% 0.83/0.46 % (2124890)Peak memory usage: 10 MB
% 0.83/0.46 % (2124890)Instructions burned: 25 (million)
% 0.83/0.46 % (2124908)Instruction limit reached!
% 0.83/0.46 % (2124908)------------------------------
% 0.83/0.46 % (2124908)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.46 % (2124908)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.46 % (2124908)CaDiCaL version: 2.1.3
% 0.83/0.46 % (2124908)Termination reason: Instruction limit
% 0.83/0.46 % (2124908)Termination phase: shuffling
% 0.83/0.46 % (2124908)Time elapsed: 0.002 s
% 0.83/0.46 % (2124908)Peak memory usage: 10 MB
% 0.83/0.46 % (2124908)Instructions burned: 3 (million)
% 0.83/0.46 % (2124918)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.83/0.51 % (2124914)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2906966166:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.83/0.51 % (2124918)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=842187520:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.83/0.51 % (2124892)Instruction limit reached!
% 0.83/0.51 % (2124892)------------------------------
% 0.83/0.51 % (2124892)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.51 % (2124892)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.51 % (2124892)CaDiCaL version: 2.1.3
% 0.83/0.51 % (2124892)Termination reason: Instruction limit
% 0.83/0.51 % (2124892)Termination phase: Saturation
% 0.83/0.51 % (2124892)Time elapsed: 0.067 s
% 0.83/0.51 % (2124892)Peak memory usage: 14 MB
% 0.83/0.51 % (2124892)Instructions burned: 157 (million)
% 0.83/0.51 % (2124914)Instruction limit reached!
% 0.83/0.51 % (2124914)------------------------------
% 0.83/0.51 % (2124914)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.51 % (2124914)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.51 % (2124914)CaDiCaL version: 2.1.3
% 0.83/0.51 % (2124914)Termination reason: Instruction limit
% 0.83/0.51 % (2124914)Termination phase: shuffling
% 0.83/0.51 % (2124914)Time elapsed: 0.005 s
% 0.83/0.51 % (2124914)Peak memory usage: 10 MB
% 0.83/0.51 % (2124914)Instructions burned: 5 (million)
% 0.83/0.51 % (2124918)Instruction limit reached!
% 0.83/0.51 % (2124918)------------------------------
% 0.83/0.51 % (2124918)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.51 % (2124918)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.51 % (2124918)CaDiCaL version: 2.1.3
% 0.83/0.51 % (2124918)Termination reason: Instruction limit
% 0.83/0.51 % (2124918)Termination phase: shuffling
% 0.83/0.51 % (2124918)Time elapsed: 0.005 s
% 0.83/0.51 % (2124918)Peak memory usage: 10 MB
% 0.83/0.51 % (2124918)Instructions burned: 8 (million)
% 0.83/0.51 % (2124891)Instruction limit reached!
% 0.83/0.51 % (2124891)------------------------------
% 0.83/0.51 % (2124891)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.51 % (2124891)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.51 % (2124891)CaDiCaL version: 2.1.3
% 0.83/0.51 % (2124891)Termination reason: Instruction limit
% 0.83/0.51 % (2124891)Termination phase: Property scanning
% 0.83/0.51 % (2124891)Time elapsed: 0.065 s
% 0.83/0.51 % (2124891)Peak memory usage: 12 MB
% 0.83/0.51 % (2124891)Instructions burned: 75 (million)
% 0.83/0.51 % (2124920)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2005532614:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.83/0.51 % (2124886)Instruction limit reached!
% 0.83/0.51 % (2124886)------------------------------
% 0.83/0.51 % (2124886)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.51 % (2124886)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.51 % (2124886)CaDiCaL version: 2.1.3
% 0.83/0.51 % (2124886)Termination reason: Instruction limit
% 0.83/0.51 % (2124886)Termination phase: Property scanning
% 0.83/0.51 % (2124886)Time elapsed: 0.072 s
% 0.83/0.51 % (2124886)Peak memory usage: 12 MB
% 0.83/0.51 % (2124886)Instructions burned: 87 (million)
% 0.83/0.51 % (2124930)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=2193118583:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.83/0.51 % (2124931)lrs+10_1_si=on:cs=on:random_seed=2909477376:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.83/0.51 % (2124920)Instruction limit reached!
% 0.83/0.51 % (2124920)------------------------------
% 0.83/0.51 % (2124920)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.51 % (2124920)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.51 % (2124920)CaDiCaL version: 2.1.3
% 0.83/0.51 % (2124920)Termination reason: Instruction limit
% 0.83/0.51 % (2124920)Termination phase: shuffling
% 0.83/0.51 % (2124920)Time elapsed: 0.011 s
% 0.83/0.51 % (2124920)Peak memory usage: 10 MB
% 0.83/0.51 % (2124920)Instructions burned: 12 (million)
% 0.83/0.51 % (2124929)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 1.55/0.55 % (2124929)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.55/0.55 % (2124929)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=58889902:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 1.55/0.55 % (2124931)Instruction limit reached!
% 1.55/0.55 % (2124931)------------------------------
% 1.55/0.55 % (2124931)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.55/0.55 % (2124931)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.55/0.55 % (2124931)CaDiCaL version: 2.1.3
% 1.55/0.55 % (2124931)Termination reason: Instruction limit
% 1.55/0.55 % (2124931)Termination phase: shuffling
% 1.55/0.55 % (2124931)Time elapsed: 0.008 s
% 1.55/0.55 % (2124931)Peak memory usage: 10 MB
% 1.55/0.55 % (2124931)Instructions burned: 8 (million)
% 1.55/0.55 % (2124933)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.55/0.55 % (2124933)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=2314761026:i=2:add=on:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.55/0.55 % (2124933)Instruction limit reached!
% 1.55/0.55 % (2124933)------------------------------
% 1.55/0.55 % (2124933)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.55/0.55 % (2124933)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.55/0.55 % (2124933)CaDiCaL version: 2.1.3
% 1.55/0.55 % (2124933)Termination reason: Instruction limit
% 1.55/0.55 % (2124933)Termination phase: shuffling
% 1.55/0.55 % (2124933)Time elapsed: 0.003 s
% 1.55/0.55 % (2124933)Peak memory usage: 10 MB
% 1.55/0.55 % (2124933)Instructions burned: 3 (million)
% 1.55/0.55 % (2124938)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=4022754662:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 1.55/0.55 % (2124930)Instruction limit reached!
% 1.55/0.55 % (2124930)------------------------------
% 1.55/0.55 % (2124930)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.55/0.55 % (2124930)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.55/0.55 % (2124930)CaDiCaL version: 2.1.3
% 1.55/0.55 % (2124930)Termination reason: Instruction limit
% 1.55/0.55 % (2124930)Termination phase: Preprocessing 3
% 1.55/0.55 % (2124930)Time elapsed: 0.034 s
% 1.55/0.55 % (2124930)Peak memory usage: 11 MB
% 1.55/0.55 % (2124930)Instructions burned: 88 (million)
% 1.55/0.55 % (2124941)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=1859763310:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 1.55/0.55 % (2124929)Instruction limit reached!
% 1.55/0.55 % (2124929)------------------------------
% 1.55/0.55 % (2124929)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.55/0.55 % (2124929)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.55/0.55 % (2124929)CaDiCaL version: 2.1.3
% 1.55/0.56 % (2124929)Termination reason: Instruction limit
% 1.55/0.56 % (2124929)Termination phase: shuffling
% 1.55/0.56 % (2124929)Time elapsed: 0.025 s
% 1.55/0.56 % (2124929)Peak memory usage: 10 MB
% 1.55/0.56 % (2124929)Instructions burned: 29 (million)
% 1.55/0.56 % (2124945)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=1098803192:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.55/0.56 % (2124954)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1709728502:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.55/0.56 % (2124948)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=3956534710:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.55/0.56 % (2124938)Instruction limit reached!
% 1.55/0.56 % (2124938)------------------------------
% 1.55/0.56 % (2124938)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.55/0.56 % (2124938)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.07/0.59 % (2124938)CaDiCaL version: 2.1.3
% 2.07/0.59 % (2124938)Termination reason: Instruction limit
% 2.07/0.59 % (2124938)Termination phase: Property scanning
% 2.07/0.59 % (2124938)Time elapsed: 0.031 s
% 2.07/0.59 % (2124938)Peak memory usage: 10 MB
% 2.07/0.59 % (2124938)Instructions burned: 39 (million)
% 2.07/0.59 % (2124945)Instruction limit reached!
% 2.07/0.59 % (2124945)------------------------------
% 2.07/0.59 % (2124945)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.07/0.59 % (2124945)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.07/0.59 % (2124945)CaDiCaL version: 2.1.3
% 2.07/0.59 % (2124945)Termination reason: Instruction limit
% 2.07/0.59 % (2124945)Termination phase: shuffling
% 2.07/0.59 % (2124945)Time elapsed: 0.022 s
% 2.07/0.59 % (2124945)Peak memory usage: 10 MB
% 2.07/0.59 % (2124945)Instructions burned: 26 (million)
% 2.07/0.59 % (2124957)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=2758574920:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 2.07/0.59 % (2124948)Instruction limit reached!
% 2.07/0.59 % (2124948)------------------------------
% 2.07/0.59 % (2124948)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.07/0.59 % (2124948)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.07/0.59 % (2124948)CaDiCaL version: 2.1.3
% 2.07/0.59 % (2124948)Termination reason: Instruction limit
% 2.07/0.59 % (2124948)Termination phase: shuffling
% 2.07/0.59 % (2124948)Time elapsed: 0.013 s
% 2.07/0.59 % (2124948)Peak memory usage: 10 MB
% 2.07/0.59 % (2124948)Instructions burned: 14 (million)
% 2.07/0.59 % (2124941)Refutation not found, incomplete strategy
% 2.07/0.59 % (2124941)------------------------------
% 2.07/0.59 % (2124941)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.07/0.59 % (2124941)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.07/0.59 % (2124941)CaDiCaL version: 2.1.3
% 2.07/0.59 % (2124941)Termination reason: Refutation not found, incomplete strategy
% 2.07/0.59 % (2124941)Time elapsed: 0.038 s
% 2.07/0.59 % (2124941)Peak memory usage: 13 MB
% 2.07/0.59 % (2124941)Instructions burned: 62 (million)
% 2.07/0.59 % (2124941)------------------------------
% 2.07/0.59 % (2124941)------------------------------
% 2.07/0.59 % (2124957)Instruction limit reached!
% 2.07/0.59 % (2124957)------------------------------
% 2.07/0.59 % (2124957)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.07/0.59 % (2124957)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.07/0.59 % (2124957)CaDiCaL version: 2.1.3
% 2.07/0.59 % (2124957)Termination reason: Instruction limit
% 2.07/0.59 % (2124957)Termination phase: shuffling
% 2.07/0.59 % (2124957)Time elapsed: 0.013 s
% 2.07/0.59 % (2124957)Peak memory usage: 10 MB
% 2.07/0.59 % (2124957)Instructions burned: 15 (million)
% 2.07/0.59 % (2124964)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=2904746385:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 2.07/0.59 % (2124964)Instruction limit reached!
% 2.07/0.59 % (2124964)------------------------------
% 2.07/0.59 % (2124964)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.07/0.59 % (2124964)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.07/0.59 % (2124964)CaDiCaL version: 2.1.3
% 2.07/0.59 % (2124964)Termination reason: Instruction limit
% 2.07/0.59 % (2124964)Termination phase: shuffling
% 2.07/0.59 % (2124964)Time elapsed: 0.003 s
% 2.07/0.59 % (2124964)Peak memory usage: 10 MB
% 2.07/0.59 % (2124964)Instructions burned: 3 (million)
% 2.07/0.59 % (2124969)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2822849747:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 2.07/0.59 % (2124972)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=1030766550:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 2.07/0.59 % (2124970)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=3900486710:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 2.07/0.59 % (2124973)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) 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
% 2.07/0.59 % (2124973)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 2.07/0.60 % (2124973)ott+21_1_to=kbo:sil=128000:cnfonf=lazy_gen:bsd=on:si=on:sp=const_frequency:lma=off:uwa=off:foolp=on:s2agt=10:lwlo=on:random_seed=4197939009:i=14:add=off:nm=40:rtra=on:rawr=on_2997 on theBenchmark for (2997ds/14Mi)
% 2.07/0.60 % (2124969)Instruction limit reached!
% 2.07/0.60 % (2124969)------------------------------
% 2.07/0.60 % (2124969)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.07/0.60 % (2124969)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.07/0.60 % (2124969)CaDiCaL version: 2.1.3
% 2.07/0.60 % (2124969)Termination reason: Instruction limit
% 2.07/0.60 % (2124969)Termination phase: shuffling
% 2.07/0.60 % (2124969)Time elapsed: 0.020 s
% 2.07/0.60 % (2124969)Peak memory usage: 10 MB
% 2.07/0.60 % (2124969)Instructions burned: 26 (million)
% 2.07/0.60 % (2124981)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 2.07/0.60 % (2124970)Instruction limit reached!
% 2.07/0.60 % (2124970)------------------------------
% 2.07/0.60 % (2124970)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.07/0.60 % (2124970)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.07/0.60 % (2124970)CaDiCaL version: 2.1.3
% 2.07/0.60 % (2124970)Termination reason: Instruction limit
% 2.07/0.60 % (2124970)Termination phase: shuffling
% 2.07/0.60 % (2124970)Time elapsed: 0.018 s
% 2.07/0.60 % (2124970)Peak memory usage: 10 MB
% 2.07/0.60 % (2124970)Instructions burned: 23 (million)
% 2.07/0.60 % (2124973)Instruction limit reached!
% 2.07/0.60 % (2124973)------------------------------
% 2.07/0.60 % (2124973)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.07/0.60 % (2124973)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.07/0.60 % (2124973)CaDiCaL version: 2.1.3
% 2.07/0.60 % (2124973)Termination reason: Instruction limit
% 2.07/0.60 % (2124973)Termination phase: shuffling
% 2.07/0.60 % (2124973)Time elapsed: 0.009 s
% 2.07/0.60 % (2124973)Peak memory usage: 10 MB
% 2.07/0.60 % (2124973)Instructions burned: 16 (million)
% 2.07/0.60 % (2124981)lrs+1010_4:1_slsqr=8,1:to=kbo:cha=on:drc=off:si=on:sp=arity:lcm=predicate:uwa=off:fd=preordered:gs=on:nwc=5:s2agt=32:slsqc=1:kmz=on:updr=off:chr=on:pe=on:slsq=on:random_seed=4215760358:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2997 on theBenchmark for (2997ds/8Mi)
% 2.07/0.60 % (2124981)Instruction limit reached!
% 2.07/0.60 % (2124981)------------------------------
% 2.07/0.60 % (2124981)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.07/0.60 % (2124981)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.07/0.60 % (2124981)CaDiCaL version: 2.1.3
% 2.07/0.60 % (2124981)Termination reason: Instruction limit
% 2.07/0.60 % (2124981)Termination phase: shuffling
% 2.07/0.60 % (2124981)Time elapsed: 0.004 s
% 2.07/0.60 % (2124981)Peak memory usage: 10 MB
% 2.07/0.60 % (2124981)Instructions burned: 8 (million)
% 2.07/0.60 % (2124990)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=4010091848:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2997 on theBenchmark for (2997ds/31Mi)
% 2.07/0.60 % (2124972)Instruction limit reached!
% 2.07/0.60 % (2124972)------------------------------
% 2.07/0.60 % (2124972)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.07/0.60 % (2124972)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.07/0.60 % (2124972)CaDiCaL version: 2.1.3
% 2.07/0.60 % (2124972)Termination reason: Instruction limit
% 2.07/0.60 % (2124972)Termination phase: Preprocessing 3
% 2.07/0.60 % (2124972)Time elapsed: 0.037 s
% 2.07/0.60 % (2124972)Peak memory usage: 11 MB
% 2.07/0.60 % (2124972)Instructions burned: 60 (million)
% 2.07/0.60 % (2124993)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=4113642148:i=23:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/23Mi)
% 2.07/0.60 % (2124992)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=3602814080:i=7:hud=5:bd=preordered:rtra=on:bet=on_2997 on theBenchmark for (2997ds/7Mi)
% 2.07/0.60 % (2124995)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=2371141179:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2997 on theBenchmark for (2997ds/20Mi)
% 2.07/0.60 % (2124992)Instruction limit reached!
% 2.07/0.60 % (2124992)------------------------------
% 2.07/0.60 % (2124992)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.07/0.60 % (2124992)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.07/0.60 % (2124992)CaDiCaL version: 2.1.3
% 2.07/0.60 % (2124992)Termination reason: Instruction limit
% 2.07/0.60 % (2124992)Termination phase: shuffling
% 2.07/0.60 % (2124992)Time elapsed: 0.004 s
% 2.07/0.60 % (2124992)Peak memory usage: 10 MB
% 2.07/0.60 % (2124992)Instructions burned: 8 (million)
% 2.07/0.60 % (2124990)Instruction limit reached!
% 2.07/0.60 % (2124990)------------------------------
% 2.07/0.60 % (2124990)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.07/0.60 % (2124990)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.07/0.60 % (2124990)CaDiCaL version: 2.1.3
% 2.07/0.60 % (2124990)Termination reason: Instruction limit
% 2.07/0.60 % (2124990)Termination phase: shuffling
% 2.07/0.60 % (2124990)Time elapsed: 0.015 s
% 2.07/0.60 % (2124990)Peak memory usage: 10 MB
% 2.07/0.60 % (2124990)Instructions burned: 33 (million)
% 2.07/0.60 % (2124993)Instruction limit reached!
% 2.07/0.60 % (2124993)------------------------------
% 2.07/0.60 % (2124993)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.07/0.60 % (2124993)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.07/0.60 % (2124993)CaDiCaL version: 2.1.3
% 2.07/0.60 % (2124993)Termination reason: Instruction limit
% 2.07/0.60 % (2124993)Termination phase: shuffling
% 2.07/0.60 % (2124993)Time elapsed: 0.011 s
% 2.07/0.60 % (2124993)Peak memory usage: 10 MB
% 2.07/0.60 % (2124993)Instructions burned: 25 (million)
% 2.07/0.60 % (2124995)Instruction limit reached!
% 2.07/0.60 % (2124995)------------------------------
% 2.07/0.60 % (2124995)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.07/0.60 % (2124995)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.07/0.60 % (2124995)CaDiCaL version: 2.1.3
% 2.07/0.60 % (2124995)Termination reason: Instruction limit
% 2.07/0.60 % (2124995)Termination phase: shuffling
% 2.07/0.60 % (2124995)Time elapsed: 0.010 s
% 2.07/0.60 % (2124995)Peak memory usage: 10 MB
% 2.07/0.60 % (2124995)Instructions burned: 22 (million)
% 2.07/0.60 % (2124997)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=405106250:i=1240:rtra=on:ixr=off_2997 on theBenchmark for (2997ds/1240Mi)
% 2.07/0.60 % (2124954)Instruction limit reached!
% 2.07/0.60 % (2124954)------------------------------
% 2.07/0.60 % (2124954)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.07/0.60 % (2124954)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.07/0.60 % (2124954)CaDiCaL version: 2.1.3
% 2.07/0.60 % (2124954)Termination reason: Instruction limit
% 2.07/0.60 % (2124954)Termination phase: Saturation
% 2.07/0.60 % (2124954)Time elapsed: 0.118 s
% 2.07/0.60 % (2124954)Peak memory usage: 14 MB
% 2.07/0.60 % (2124954)Instructions burned: 327 (million)
% 2.07/0.60 % (2125001)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=2990037620:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/143Mi)
% 2.07/0.60 % (2125002)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=3253052259:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 2.07/0.60 % (2125006)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=1259055741:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 2.07/0.60 % (2125004)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 2.07/0.60 % (2125003)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2224939664:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 2.07/0.60 % (2125004)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3986646971:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 2.07/0.60 % (2125004)Instruction limit reached!
% 2.07/0.60 % (2125004)------------------------------
% 2.07/0.60 % (2125004)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.07/0.60 % (2125004)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.07/0.60 % (2125004)CaDiCaL version: 2.1.3
% 2.07/0.60 % (2125004)Termination reason: Instruction limit
% 2.07/0.60 % (2125004)Termination phase: shuffling
% 2.07/0.60 % (2125004)Time elapsed: 0.004 s
% 2.07/0.60 % (2125004)Peak memory usage: 10 MB
% 2.07/0.60 % (2125004)Instructions burned: 9 (million)
% 2.07/0.60 % (2124889) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2124880-2124889"...
% 2.07/0.60 % (2124889)...printing done.
% 2.07/0.60 % (2125003)Instruction limit reached!
% 2.07/0.60 % (2125003)------------------------------
% 2.07/0.60 % (2125003)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.07/0.60 % (2125003)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.07/0.60 % (2125003)CaDiCaL version: 2.1.3
% 2.07/0.60 % (2125003)Termination reason: Instruction limit
% 2.07/0.60 % (2125003)Termination phase: Property scanning
% 2.07/0.60 % (2125003)Time elapsed: 0.019 s
% 2.07/0.60 % (2125003)Peak memory usage: 10 MB
% 2.07/0.60 % (2125003)Instructions burned: 43 (million)
% 2.07/0.60 % (2124889)Refutation found. Thanks to Tanya!
% 2.07/0.60 % SZS status Theorem for theBenchmark
% 2.07/0.60 % SZS output start Proof for theBenchmark
% 2.07/0.60 thf(type_def_5, type, secrecy_Expression: $tType).
% 2.07/0.60 thf(type_def_6, type, secrecy_Secrets: $tType).
% 2.07/0.60 thf(type_def_7, type, secrecy_specID: $tType).
% 2.07/0.60 thf(type_def_8, type, secrecy_chanID: $tType).
% 2.07/0.60 thf(type_def_9, type, secrecy_Keys: $tType).
% 2.07/0.60 thf(type_def_10, type, secrecy_KS: $tType).
% 2.07/0.60 thf(type_def_11, type, list: $tType > $tType).
% 2.07/0.60 thf(type_def_12, type, set: $tType > $tType).
% 2.07/0.60 thf(type_def_13, type, nat: $tType).
% 2.07/0.60 thf(type_def_14, type, sTfun: ($tType * $tType) > $tType).
% 2.07/0.60 thf(func_def_0, type, bounded_lattice: !>[X0: $tType]:($o)).
% 2.07/0.60 thf(func_def_1, type, type: !>[X0: $tType]:($o)).
% 2.07/0.60 thf(func_def_2, type, bot: !>[X0: $tType]:($o)).
% 2.07/0.60 thf(func_def_3, type, ord: !>[X0: $tType]:($o)).
% 2.07/0.60 thf(func_def_4, type, order: !>[X0: $tType]:($o)).
% 2.07/0.60 thf(func_def_5, type, linorder: !>[X0: $tType]:($o)).
% 2.07/0.60 thf(func_def_6, type, preorder: !>[X0: $tType]:($o)).
% 2.07/0.60 thf(func_def_7, type, bounde1808546759up_bot: !>[X0: $tType]:($o)).
% 2.07/0.60 thf(func_def_8, type, localSecrets: (secrecy_specID > set @ secrecy_KS)).
% 2.07/0.60 thf(func_def_9, type, knowle1667810483orrect: (secrecy_specID > secrecy_KS > $o)).
% 2.07/0.60 thf(func_def_10, type, knowle1437066798e_know: (secrecy_specID > secrecy_KS > $o)).
% 2.07/0.60 thf(func_def_11, type, sup_sup: !>[X0: $tType]:((X0 > X0 > X0))).
% 2.07/0.60 thf(func_def_12, type, mem: !>[X0: $tType]:((X0 > list @ X0 > $o))).
% 2.07/0.60 thf(func_def_13, type, bot_bot: !>[X0: $tType]:(X0)).
% 2.07/0.60 thf(func_def_14, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 2.07/0.60 thf(func_def_15, type, correctCompositionKS: (secrecy_specID > $o)).
% 2.07/0.60 thf(func_def_16, type, eout: (secrecy_specID > secrecy_Expression > $o)).
% 2.07/0.60 thf(func_def_17, type, eoutM: (secrecy_specID > set @ secrecy_chanID > secrecy_Expression > $o)).
% 2.07/0.60 thf(func_def_18, type, exprChannel: (secrecy_chanID > secrecy_Expression > $o)).
% 2.07/0.60 thf(func_def_19, type, ine: (secrecy_specID > secrecy_Expression > $o)).
% 2.07/0.60 thf(func_def_20, type, ineM: (secrecy_specID > set @ secrecy_chanID > secrecy_Expression > $o)).
% 2.07/0.60 thf(func_def_21, type, ine_exprChannelSet: (secrecy_specID > set @ secrecy_chanID > secrecy_Expression > $o)).
% 2.07/0.60 thf(func_def_22, type, ine_ex1303305700Single: (secrecy_specID > secrecy_chanID > secrecy_Expression > $o)).
% 2.07/0.60 thf(func_def_23, type, notSpe1586871396tsExpr: (secrecy_specID > list @ secrecy_Expression > $o)).
% 2.07/0.60 thf(func_def_24, type, out_exprChannelSet: (secrecy_specID > set @ secrecy_chanID > secrecy_Expression > $o)).
% 2.07/0.60 thf(func_def_25, type, out_ex985543062Single: (secrecy_specID > secrecy_chanID > secrecy_Expression > $o)).
% 2.07/0.60 thf(func_def_26, type, specKeys: (secrecy_specID > set @ secrecy_Keys)).
% 2.07/0.60 thf(func_def_27, type, specKeysSecrets: (secrecy_specID > set @ secrecy_KS)).
% 2.07/0.60 thf(func_def_28, type, specSecrets: (secrecy_specID > set @ secrecy_Secrets)).
% 2.07/0.60 thf(func_def_29, type, secrec487562139ession: !>[X0: $tType]:(((secrecy_Keys > X0) > (secrecy_Secrets > X0) > (nat > X0) > (secrecy_specID > X0) > secrecy_Expression > X0))).
% 2.07/0.60 thf(func_def_30, type, secrecy_dE: (nat > secrecy_Expression)).
% 2.07/0.60 thf(func_def_31, type, secrecy_idE: (secrecy_specID > secrecy_Expression)).
% 2.07/0.60 thf(func_def_32, type, secrecy_kE: (secrecy_Keys > secrecy_Expression)).
% 2.07/0.60 thf(func_def_33, type, secrec1231112373ession: !>[X0: $tType]:(((secrecy_Keys > X0) > (secrecy_Secrets > X0) > (nat > X0) > (secrecy_specID > X0) > secrecy_Expression > X0))).
% 2.07/0.60 thf(func_def_34, type, secrecy_sE: (secrecy_Secrets > secrecy_Expression)).
% 2.07/0.60 thf(func_def_35, type, secrec1016742679ession: (secrecy_KS > secrecy_Expression)).
% 2.07/0.60 thf(func_def_36, type, secrecy_kKS: (secrecy_Keys > secrecy_KS)).
% 2.07/0.60 thf(func_def_37, type, secrecy_sKS: (secrecy_Secrets > secrecy_KS)).
% 2.07/0.60 thf(func_def_38, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 2.07/0.60 thf(func_def_39, type, insert: !>[X0: $tType]:((X0 > set @ X0 > set @ X0))).
% 2.07/0.60 thf(func_def_40, type, is_empty: !>[X0: $tType]:((set @ X0 > $o))).
% 2.07/0.60 thf(func_def_41, type, is_singleton: !>[X0: $tType]:((set @ X0 > $o))).
% 2.07/0.60 thf(func_def_42, type, the_elem: !>[X0: $tType]:((set @ X0 > X0))).
% 2.07/0.60 thf(func_def_43, type, correctCompositionIn: (secrecy_specID > $o)).
% 2.07/0.60 thf(func_def_44, type, correc965049635ionLoc: (secrecy_specID > $o)).
% 2.07/0.60 thf(func_def_45, type, correc990227761ionOut: (secrecy_specID > $o)).
% 2.07/0.60 thf(func_def_46, type, inStream: (secrecy_specID > set @ secrecy_chanID > $o)).
% 2.07/0.60 thf(func_def_47, type, ins: (secrecy_specID > set @ secrecy_chanID)).
% 2.07/0.60 thf(func_def_48, type, loc: (secrecy_specID > set @ secrecy_chanID)).
% 2.07/0.60 thf(func_def_49, type, locStream: (secrecy_specID > set @ secrecy_chanID > $o)).
% 2.07/0.60 thf(func_def_50, type, out: (secrecy_specID > set @ secrecy_chanID)).
% 2.07/0.60 thf(func_def_51, type, outStream: (secrecy_specID > set @ secrecy_chanID > $o)).
% 2.07/0.60 thf(func_def_52, type, subcomponents: (secrecy_specID > set @ secrecy_specID)).
% 2.07/0.60 thf(func_def_53, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 2.07/0.60 thf(func_def_54, type, p: secrecy_specID).
% 2.07/0.60 thf(func_def_55, type, pq: secrecy_specID).
% 2.07/0.60 thf(func_def_56, type, q: secrecy_specID).
% 2.07/0.60 thf(func_def_57, type, key: secrecy_Keys).
% 2.07/0.60 thf(func_def_61, type, db0: !>[X0: $tType]:(X0)).
% 2.07/0.60 thf(func_def_62, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 2.07/0.60 thf(func_def_63, type, db1: !>[X0: $tType]:(X0)).
% 2.07/0.60 thf(func_def_64, type, vAND: ($o > $o > $o)).
% 2.07/0.60 thf(func_def_65, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 2.07/0.60 thf(func_def_66, type, vIMP: ($o > $o > $o)).
% 2.07/0.60 thf(func_def_67, type, vNOT: ($o > $o)).
% 2.07/0.60 thf(func_def_68, type, db2: !>[X0: $tType]:(X0)).
% 2.07/0.60 thf(func_def_69, type, db3: !>[X0: $tType]:(X0)).
% 2.07/0.60 thf(func_def_70, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 2.07/0.60 thf(func_def_71, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 2.07/0.60 thf(func_def_72, type, sP0: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 2.07/0.60 thf(func_def_73, type, sP1: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 2.07/0.60 thf(func_def_74, type, sK2: !>[X0: $tType]:((set @ X0 > X0))).
% 2.07/0.60 thf(func_def_75, type, sK3: (secrecy_specID > secrecy_Secrets > secrecy_chanID)).
% 2.07/0.60 thf(func_def_76, type, sK4: (secrecy_specID > secrecy_KS > secrecy_specID > secrecy_Keys)).
% 2.07/0.60 thf(func_def_77, type, sK5: (secrecy_specID > secrecy_KS > secrecy_specID > secrecy_Secrets)).
% 2.07/0.60 thf(func_def_78, type, sK6: !>[X0: $tType]:((set @ X0 > X0))).
% 2.07/0.60 thf(func_def_79, type, sK7: !>[X0: $tType]:((set @ X0 > X0))).
% 2.07/0.60 thf(func_def_80, type, sK8: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 2.07/0.60 thf(func_def_81, type, sK9: !>[X0: $tType]:(((X0 > $o) > X0))).
% 2.07/0.60 thf(func_def_82, type, sK10: !>[X0: $tType]:((set @ X0 > (X0 > $o) > set @ X0 > X0))).
% 2.07/0.60 thf(func_def_83, type, sK11: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 2.07/0.60 thf(func_def_84, type, sK12: !>[X0: $tType]:(((X0 > $o) > set @ X0 > X0))).
% 2.07/0.60 thf(func_def_85, type, sK13: (set @ secrecy_chanID > secrecy_specID > secrecy_chanID)).
% 2.07/0.60 thf(func_def_86, type, sK14: (secrecy_KS > secrecy_Secrets)).
% 2.07/0.60 thf(func_def_87, type, sK15: (secrecy_KS > secrecy_Keys)).
% 2.07/0.60 thf(func_def_88, type, sK16: !>[X0: $tType]:((set @ X0 > X0 > set @ X0))).
% 2.07/0.60 thf(func_def_89, type, sK17: (set @ secrecy_chanID > secrecy_specID > secrecy_chanID)).
% 2.07/0.60 thf(func_def_90, type, sK18: (set @ secrecy_chanID > secrecy_specID > secrecy_chanID)).
% 2.07/0.60 thf(func_def_91, type, sK19: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 2.07/0.60 thf(func_def_92, type, sK20: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 2.07/0.60 thf(func_def_93, type, sK21: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 2.07/0.60 thf(func_def_94, type, sK22: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 2.07/0.60 thf(func_def_95, type, sK23: !>[X0: $tType]:(((X0 > $o) > X0))).
% 2.07/0.60 thf(func_def_96, type, sK24: ((secrecy_KS > $o) > secrecy_Secrets)).
% 2.07/0.60 thf(func_def_97, type, sK25: ((secrecy_KS > $o) > secrecy_Keys)).
% 2.07/0.60 thf(func_def_98, type, sK26: !>[X0: $tType]:((set @ X0 > X0 > set @ X0))).
% 2.07/0.60 thf(func_def_99, type, sK27: (secrecy_specID > secrecy_specID > secrecy_KS > secrecy_Keys)).
% 2.07/0.60 thf(func_def_100, type, sK28: (secrecy_specID > secrecy_specID > secrecy_KS > secrecy_Secrets)).
% 2.07/0.60 thf(func_def_101, type, sK29: (secrecy_Keys > secrecy_specID > secrecy_chanID)).
% 2.07/0.60 thf(func_def_102, type, sK30: (set @ secrecy_chanID > secrecy_specID > secrecy_chanID)).
% 2.07/0.60 thf(func_def_103, type, sK31: (set @ secrecy_chanID > secrecy_specID > secrecy_chanID)).
% 2.07/0.60 thf(func_def_104, type, sK32: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 2.07/0.60 thf(func_def_105, type, sK33: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 2.07/0.60 thf(func_def_106, type, sK34: !>[X0: $tType]:((set @ X0 > X0))).
% 2.07/0.60 thf(func_def_107, type, sK35: !>[X0: $tType]:(((X0 > $o) > set @ X0 > set @ X0 > X0))).
% 2.07/0.60 thf(func_def_108, type, sK36: !>[X0: $tType]:(((X0 > $o) > set @ X0 > X0))).
% 2.07/0.60 thf(func_def_109, type, sK37: !>[X0: $tType]:(((X0 > $o) > set @ X0 > X0))).
% 2.07/0.60 thf(func_def_110, type, sK38: (secrecy_specID > secrecy_Keys > secrecy_chanID)).
% 2.07/0.60 thf(func_def_111, type, sK39: !>[X0: $tType]:((set @ X0 > X0))).
% 2.07/0.60 thf(func_def_112, type, sK40: (set @ secrecy_chanID > secrecy_specID > secrecy_chanID)).
% 2.07/0.60 thf(func_def_113, type, sK41: (set @ secrecy_chanID > secrecy_specID > secrecy_chanID)).
% 2.07/0.60 thf(func_def_114, type, sK42: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 2.07/0.60 thf(func_def_115, type, sK43: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 2.07/0.60 thf(func_def_116, type, sK44: !>[X0: $tType]:((set @ X0 > X0))).
% 2.07/0.60 thf(func_def_117, type, sK45: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.07/0.60 thf(func_def_118, type, sK46: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.07/0.60 thf(func_def_119, type, sK47: (secrecy_specID > set @ secrecy_chanID > secrecy_chanID)).
% 2.07/0.60 thf(func_def_120, type, sK48: (secrecy_Expression > secrecy_Secrets)).
% 2.07/0.60 thf(func_def_121, type, sK49: (secrecy_Expression > nat)).
% 2.07/0.60 thf(func_def_122, type, sK50: (secrecy_Expression > secrecy_specID)).
% 2.07/0.60 thf(func_def_123, type, sK51: (secrecy_Expression > secrecy_Keys)).
% 2.07/0.60 thf(func_def_124, type, sK52: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 2.07/0.60 thf(func_def_125, type, sK53: (secrecy_specID > secrecy_Secrets > secrecy_specID)).
% 2.07/0.60 thf(func_def_126, type, sK54: ((secrecy_Expression > $o) > secrecy_Keys)).
% 2.07/0.60 thf(func_def_127, type, sK55: ((secrecy_Expression > $o) > nat)).
% 2.07/0.60 thf(func_def_128, type, sK56: ((secrecy_Expression > $o) > secrecy_Secrets)).
% 2.07/0.60 thf(func_def_129, type, sK57: ((secrecy_Expression > $o) > secrecy_specID)).
% 2.07/0.60 thf(func_def_130, type, sK58: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 2.07/0.60 thf(func_def_131, type, sK59: !>[X0: $tType]:((set @ X0 > set @ X0 > set @ X0 > set @ X0))).
% 2.07/0.60 thf(func_def_132, type, sK60: !>[X0: $tType]:((set @ X0 > set @ X0 > set @ X0 > set @ X0))).
% 2.07/0.60 thf(func_def_133, type, sK61: (secrecy_specID > secrecy_Secrets > secrecy_chanID)).
% 2.07/0.60 thf(func_def_134, type, sK62: !>[X0: $tType]:((set @ X0 > set @ X0 > X0 > X0 > set @ X0))).
% 2.07/0.60 thf(func_def_135, type, sK63: (secrecy_specID > secrecy_Keys > secrecy_specID)).
% 2.07/0.60 thf(func_def_136, type, sK64: (set @ secrecy_chanID > secrecy_specID > secrecy_chanID)).
% 2.07/0.60 thf(func_def_137, type, sK65: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > X0))).
% 2.07/0.60 thf(func_def_138, type, sK66: (set @ secrecy_chanID > secrecy_specID > secrecy_chanID)).
% 2.07/0.60 thf(func_def_139, type, sK67: (set @ secrecy_chanID > secrecy_specID > secrecy_chanID)).
% 2.07/0.60 thf(func_def_140, type, sK68: (secrecy_specID > set @ secrecy_chanID > secrecy_chanID)).
% 2.07/0.60 thf(func_def_141, type, sK69: (secrecy_specID > secrecy_Expression > secrecy_chanID)).
% 2.07/0.60 thf(func_def_142, type, sK70: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 2.07/0.60 thf(func_def_143, type, sK71: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 2.07/0.60 thf(func_def_144, type, sK72: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 2.07/0.60 thf(func_def_145, type, sK73: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 2.07/0.60 thf(func_def_147, type, inv_secrecy_kE_75: (secrecy_Expression > secrecy_Keys)).
% 2.07/0.60 thf(func_def_148, type, inv_secrecy_sE_76: (secrecy_Expression > secrecy_Secrets)).
% 2.07/0.60 thf(func_def_149, type, inv_secrecy_idE_77: (secrecy_Expression > secrecy_specID)).
% 2.07/0.60 thf(func_def_150, type, inv_secrecy_kKS_78: (secrecy_KS > secrecy_Keys)).
% 2.07/0.60 thf(func_def_151, type, inv_secrecy_sKS_79: (secrecy_KS > secrecy_Secrets)).
% 2.07/0.60 thf(func_def_152, type, inv_secrecy_dE_80: (secrecy_Expression > nat)).
% 2.07/0.60 thf(f1,axiom,(
% 2.07/0.60 (correctCompositionIn @ pq)),
% 2.07/0.60 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_assms_I4_J)).
% 2.07/0.60 thf(f2,axiom,(
% 2.07/0.60 ~(knowle1437066798e_know @ q @ (secrecy_kKS @ key))),
% 2.07/0.60 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_assms_I2_J)).
% 2.07/0.60 thf(f3,axiom,(
% 2.07/0.60 ~(knowle1437066798e_know @ p @ (secrecy_kKS @ key))),
% 2.07/0.60 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_assms_I1_J)).
% 2.07/0.60 thf(f4,axiom,(
% 2.07/0.60 (((subcomponents @ pq)) = ((insert @ secrecy_specID @ p @ (insert @ secrecy_specID @ q @ bot_bot @ set @ secrecy_specID))))),
% 2.07/0.60 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_assms_I3_J)).
% 2.07/0.60 thf(f6,axiom,(
% 2.07/0.60 ! [X0 : secrecy_specID,X1 : secrecy_Keys] : (~(knowle1437066798e_know @ X0 @ (secrecy_kKS @ X1)) => ~(ine @ X0 @ (secrecy_kE @ X1)))),
% 2.07/0.60 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_not__know__k__not__ine)).
% 2.07/0.60 thf(f43,axiom,(
% 2.07/0.60 ! [X1 : secrecy_Expression,X2 : secrecy_specID,X3 : secrecy_specID,X0 : secrecy_specID] : (~(ine @ X0 @ X1) => (~(ine @ X2 @ X1) => ((((subcomponents @ X3)) = ((insert @ secrecy_specID @ X0 @ (insert @ secrecy_specID @ X2 @ bot_bot @ set @ secrecy_specID)))) => ((correctCompositionIn @ X3) => ~(ine @ X3 @ X1)))))),
% 2.07/0.60 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_TBtheorem3a)).
% 2.07/0.60 thf(f281,conjecture,(
% 2.07/0.60 ~(ine @ pq @ (secrecy_kE @ key))),
% 2.07/0.60 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 2.07/0.60 thf(f282,negated_conjecture,(
% 2.07/0.60 ~ ~(ine @ pq @ (secrecy_kE @ key))),
% 2.07/0.60 inference(negated_conjecture,[status(cth)],[f281])).
% 2.07/0.60 thf(f334,plain,(
% 2.07/0.60 ~ ~(ine @ pq @ (secrecy_kE @ key))),
% 2.07/0.60 inference(rectify,[],[f282])).
% 2.07/0.60 thf(f335,plain,(
% 2.07/0.60 ~ ~ (((ine @ pq @ (secrecy_kE @ key))) = $true)),
% 2.07/0.60 inference(fool_elimination,[],[f334])).
% 2.07/0.60 thf(f348,plain,(
% 2.07/0.60 ~(knowle1437066798e_know @ q @ (secrecy_kKS @ key))),
% 2.07/0.60 inference(rectify,[],[f2])).
% 2.07/0.60 thf(f349,plain,(
% 2.07/0.60 ~ (((knowle1437066798e_know @ q @ (secrecy_kKS @ key))) = $true)),
% 2.07/0.60 inference(fool_elimination,[],[f348])).
% 2.07/0.60 thf(f377,plain,(
% 2.07/0.60 ! [X0 : secrecy_Expression,X1 : secrecy_specID,X2 : secrecy_specID,X3 : secrecy_specID] : (~(ine @ X3 @ X0) => (~(ine @ X1 @ X0) => ((((subcomponents @ X2)) = ((insert @ secrecy_specID @ X3 @ (insert @ secrecy_specID @ X1 @ bot_bot @ set @ secrecy_specID)))) => ((correctCompositionIn @ X2) => ~(ine @ X2 @ X0)))))),
% 2.07/0.60 inference(rectify,[],[f43])).
% 2.07/0.60 thf(f378,plain,(
% 2.07/0.60 ! [X0 : secrecy_Expression,X1 : secrecy_specID,X2 : secrecy_specID,X3 : secrecy_specID] : (~ (((ine @ X3 @ X0)) = $true) => (~ (((ine @ X1 @ X0)) = $true) => ((((subcomponents @ X2)) = ((insert @ secrecy_specID @ X3 @ (insert @ secrecy_specID @ X1 @ bot_bot @ set @ secrecy_specID)))) => ((((correctCompositionIn @ X2)) = $true) => ~ (((ine @ X2 @ X0)) = $true)))))),
% 2.07/0.60 inference(fool_elimination,[],[f377])).
% 2.07/0.60 thf(f406,plain,(
% 2.07/0.60 (correctCompositionIn @ pq)),
% 2.07/0.60 inference(rectify,[],[f1])).
% 2.07/0.60 thf(f407,plain,(
% 2.07/0.60 (((correctCompositionIn @ pq)) = $true)),
% 2.07/0.60 inference(fool_elimination,[],[f406])).
% 2.07/0.60 thf(f503,plain,(
% 2.07/0.60 ~(knowle1437066798e_know @ p @ (secrecy_kKS @ key))),
% 2.07/0.60 inference(rectify,[],[f3])).
% 2.07/0.60 thf(f504,plain,(
% 2.07/0.60 ~ (((knowle1437066798e_know @ p @ (secrecy_kKS @ key))) = $true)),
% 2.07/0.60 inference(fool_elimination,[],[f503])).
% 2.07/0.60 thf(f550,plain,(
% 2.07/0.60 ! [X0 : secrecy_specID,X1 : secrecy_Keys] : (~(knowle1437066798e_know @ X0 @ (secrecy_kKS @ X1)) => ~(ine @ X0 @ (secrecy_kE @ X1)))),
% 2.07/0.60 inference(rectify,[],[f6])).
% 2.07/0.60 thf(f551,plain,(
% 2.07/0.60 ! [X0 : secrecy_specID,X1 : secrecy_Keys] : (~ (((knowle1437066798e_know @ X0 @ (secrecy_kKS @ X1))) = $true) => ~ (((ine @ X0 @ (secrecy_kE @ X1))) = $true))),
% 2.07/0.60 inference(fool_elimination,[],[f550])).
% 2.07/0.60 thf(f770,plain,(
% 2.07/0.60 (((ine @ pq @ (secrecy_kE @ key))) = $true)),
% 2.07/0.60 inference(flattening,[],[f335])).
% 2.07/0.60 thf(f774,plain,(
% 2.07/0.60 (((knowle1437066798e_know @ q @ (secrecy_kKS @ key))) != $true)),
% 2.07/0.60 inference(flattening,[],[f349])).
% 2.07/0.60 thf(f780,plain,(
% 2.07/0.60 ! [X0 : secrecy_Expression,X3 : secrecy_specID,X1 : secrecy_specID,X2 : secrecy_specID] : ((((ine @ X3 @ X0)) != $true) => ((((ine @ X1 @ X0)) != $true) => ((((subcomponents @ X2)) = ((insert @ secrecy_specID @ X3 @ (insert @ secrecy_specID @ X1 @ bot_bot @ set @ secrecy_specID)))) => ((((correctCompositionIn @ X2)) = $true) => (((ine @ X2 @ X0)) != $true)))))),
% 2.07/0.60 inference(flattening,[],[f378])).
% 2.07/0.60 thf(f800,plain,(
% 2.07/0.60 (((knowle1437066798e_know @ p @ (secrecy_kKS @ key))) != $true)),
% 2.07/0.60 inference(flattening,[],[f504])).
% 2.07/0.60 thf(f808,plain,(
% 2.07/0.60 ! [X1 : secrecy_Keys,X0 : secrecy_specID] : ((((knowle1437066798e_know @ X0 @ (secrecy_kKS @ X1))) != $true) => (((ine @ X0 @ (secrecy_kE @ X1))) != $true))),
% 2.07/0.60 inference(flattening,[],[f551])).
% 2.07/0.60 thf(f859,plain,(
% 2.07/0.60 ! [X0 : secrecy_Expression,X3 : secrecy_specID,X1 : secrecy_specID,X2 : secrecy_specID] : (((((((ine @ X2 @ X0)) != $true) | (((correctCompositionIn @ X2)) != $true)) | (((subcomponents @ X2)) != ((insert @ secrecy_specID @ X3 @ (insert @ secrecy_specID @ X1 @ bot_bot @ set @ secrecy_specID))))) | (((ine @ X1 @ X0)) = $true)) | (((ine @ X3 @ X0)) = $true))),
% 2.07/0.60 inference(ennf_transformation,[],[f780])).
% 2.07/0.60 thf(f860,plain,(
% 2.07/0.60 ! [X3 : secrecy_specID,X2 : secrecy_specID,X0 : secrecy_Expression,X1 : secrecy_specID] : ((((ine @ X1 @ X0)) = $true) | (((correctCompositionIn @ X2)) != $true) | (((ine @ X2 @ X0)) != $true) | (((ine @ X3 @ X0)) = $true) | (((subcomponents @ X2)) != ((insert @ secrecy_specID @ X3 @ (insert @ secrecy_specID @ X1 @ bot_bot @ set @ secrecy_specID)))))),
% 2.07/0.60 inference(flattening,[],[f859])).
% 2.07/0.60 thf(f972,plain,(
% 2.07/0.60 ! [X1 : secrecy_Keys,X0 : secrecy_specID] : ((((knowle1437066798e_know @ X0 @ (secrecy_kKS @ X1))) = $true) | (((ine @ X0 @ (secrecy_kE @ X1))) != $true))),
% 2.07/0.60 inference(ennf_transformation,[],[f808])).
% 2.07/0.60 thf(f1206,plain,(
% 2.07/0.60 ! [X0 : secrecy_specID,X1 : secrecy_specID,X2 : secrecy_Expression,X3 : secrecy_specID] : (($true = ((ine @ X3 @ X2))) | (((correctCompositionIn @ X1)) != $true) | (((ine @ X1 @ X2)) != $true) | (((ine @ X0 @ X2)) = $true) | (((insert @ secrecy_specID @ X0 @ (insert @ secrecy_specID @ X3 @ bot_bot @ set @ secrecy_specID))) != ((subcomponents @ X1))))),
% 2.07/0.60 inference(rectify,[],[f860])).
% 2.07/0.60 thf(f1318,plain,(
% 2.07/0.60 ! [X0 : secrecy_Keys,X1 : secrecy_specID] : ((((knowle1437066798e_know @ X1 @ (secrecy_kKS @ X0))) = $true) | ($true != ((ine @ X1 @ (secrecy_kE @ X0)))))),
% 2.07/0.60 inference(rectify,[],[f972])).
% 2.07/0.60 thf(f1484,plain,(
% 2.07/0.60 (((knowle1437066798e_know @ p @ (secrecy_kKS @ key))) != $true)),
% 2.07/0.60 inference(cnf_transformation,[],[f800])).
% 2.07/0.60 thf(f1529,plain,(
% 2.07/0.60 (((knowle1437066798e_know @ q @ (secrecy_kKS @ key))) != $true)),
% 2.07/0.60 inference(cnf_transformation,[],[f774])).
% 2.07/0.60 thf(f1531,plain,(
% 2.07/0.60 ( ! [X2 : secrecy_Expression,X3 : secrecy_specID,X0 : secrecy_specID,X1 : secrecy_specID] : ((((insert @ secrecy_specID @ X0 @ (insert @ secrecy_specID @ X3 @ bot_bot @ set @ secrecy_specID))) != ((subcomponents @ X1))) | ($true = ((ine @ X3 @ X2))) | (((ine @ X0 @ X2)) = $true) | (((correctCompositionIn @ X1)) != $true) | (((ine @ X1 @ X2)) != $true)) )),
% 2.07/0.60 inference(cnf_transformation,[],[f1206])).
% 2.07/0.60 thf(f1703,plain,(
% 2.07/0.60 (((ine @ pq @ (secrecy_kE @ key))) = $true)),
% 2.07/0.60 inference(cnf_transformation,[],[f770])).
% 2.07/0.60 thf(f1725,plain,(
% 2.07/0.60 ( ! [X0 : secrecy_Keys,X1 : secrecy_specID] : ((((knowle1437066798e_know @ X1 @ (secrecy_kKS @ X0))) = $true) | ($true != ((ine @ X1 @ (secrecy_kE @ X0))))) )),
% 2.07/0.60 inference(cnf_transformation,[],[f1318])).
% 2.07/0.60 thf(f1801,plain,(
% 2.07/0.60 (((subcomponents @ pq)) = ((insert @ secrecy_specID @ p @ (insert @ secrecy_specID @ q @ bot_bot @ set @ secrecy_specID))))),
% 2.07/0.60 inference(cnf_transformation,[],[f4])).
% 2.07/0.60 thf(f1865,plain,(
% 2.07/0.60 (((correctCompositionIn @ pq)) = $true)),
% 2.07/0.60 inference(cnf_transformation,[],[f407])).
% 2.07/0.60 thf(f1995,definition,(
% 2.07/0.60 spl74_6 <=> (((knowle1437066798e_know @ q @ (secrecy_kKS @ key))) = $true)),
% 2.07/0.60 introduced(definition,[new_symbols(definition,[spl74_6])],[avatar_definition])).
% 2.07/0.60 thf(f1997,plain,(
% 2.07/0.60 (((knowle1437066798e_know @ q @ (secrecy_kKS @ key))) != $true) | spl74_6),
% 2.07/0.60 inference(avatar_component_clause,[],[f1995])).
% 2.07/0.60 thf(f1998,plain,(
% 2.07/0.60 ~spl74_6),
% 2.07/0.60 inference(avatar_split_clause,[],[f1529,f1995])).
% 2.07/0.60 thf(f2010,definition,(
% 2.07/0.60 spl74_9 <=> (((subcomponents @ pq)) = ((insert @ secrecy_specID @ p @ (insert @ secrecy_specID @ q @ bot_bot @ set @ secrecy_specID))))),
% 2.07/0.60 introduced(definition,[new_symbols(definition,[spl74_9])],[avatar_definition])).
% 2.07/0.60 thf(f2012,plain,(
% 2.07/0.60 (((subcomponents @ pq)) = ((insert @ secrecy_specID @ p @ (insert @ secrecy_specID @ q @ bot_bot @ set @ secrecy_specID)))) | ~spl74_9),
% 2.07/0.60 inference(avatar_component_clause,[],[f2010])).
% 2.07/0.60 thf(f2013,plain,(
% 2.07/0.60 spl74_9),
% 2.07/0.60 inference(avatar_split_clause,[],[f1801,f2010])).
% 2.07/0.60 thf(f2020,definition,(
% 2.07/0.60 spl74_11 <=> (((knowle1437066798e_know @ p @ (secrecy_kKS @ key))) = $true)),
% 2.07/0.60 introduced(definition,[new_symbols(definition,[spl74_11])],[avatar_definition])).
% 2.07/0.60 thf(f2022,plain,(
% 2.07/0.60 (((knowle1437066798e_know @ p @ (secrecy_kKS @ key))) != $true) | spl74_11),
% 2.07/0.60 inference(avatar_component_clause,[],[f2020])).
% 2.07/0.60 thf(f2023,plain,(
% 2.07/0.60 ~spl74_11),
% 2.07/0.60 inference(avatar_split_clause,[],[f1484,f2020])).
% 2.07/0.60 thf(f2030,definition,(
% 2.07/0.60 spl74_13 <=> (((ine @ pq @ (secrecy_kE @ key))) = $true)),
% 2.07/0.60 introduced(definition,[new_symbols(definition,[spl74_13])],[avatar_definition])).
% 2.07/0.60 thf(f2032,plain,(
% 2.07/0.60 (((ine @ pq @ (secrecy_kE @ key))) = $true) | ~spl74_13),
% 2.07/0.60 inference(avatar_component_clause,[],[f2030])).
% 2.07/0.60 thf(f2033,plain,(
% 2.07/0.60 spl74_13),
% 2.07/0.60 inference(avatar_split_clause,[],[f1703,f2030])).
% 2.07/0.60 thf(f2105,definition,(
% 2.07/0.60 spl74_28 <=> (((correctCompositionIn @ pq)) = $true)),
% 2.07/0.60 introduced(definition,[new_symbols(definition,[spl74_28])],[avatar_definition])).
% 2.07/0.60 thf(f2107,plain,(
% 2.07/0.60 (((correctCompositionIn @ pq)) = $true) | ~spl74_28),
% 2.07/0.60 inference(avatar_component_clause,[],[f2105])).
% 2.07/0.60 thf(f2108,plain,(
% 2.07/0.60 spl74_28),
% 2.07/0.60 inference(avatar_split_clause,[],[f1865,f2105])).
% 2.07/0.60 thf(f2121,plain,(
% 2.07/0.60 ($true != $true) | ($true != ((ine @ q @ (secrecy_kE @ key)))) | spl74_6),
% 2.07/0.60 inference(superposition,[],[f1997,f1725])).
% 2.07/0.60 thf(f2122,plain,(
% 2.07/0.60 ($true != ((ine @ q @ (secrecy_kE @ key)))) | spl74_6),
% 2.07/0.60 inference(trivial_inequality_removal,[],[f2121])).
% 2.07/0.60 thf(f2124,definition,(
% 2.07/0.60 spl74_30 <=> ($true = ((ine @ q @ (secrecy_kE @ key))))),
% 2.07/0.60 introduced(definition,[new_symbols(definition,[spl74_30])],[avatar_definition])).
% 2.07/0.60 thf(f2126,plain,(
% 2.07/0.60 ($true != ((ine @ q @ (secrecy_kE @ key)))) | spl74_30),
% 2.07/0.60 inference(avatar_component_clause,[],[f2124])).
% 2.07/0.60 thf(f2127,plain,(
% 2.07/0.60 ~spl74_30 | spl74_6),
% 2.07/0.60 inference(avatar_split_clause,[],[f2122,f1995,f2124])).
% 2.07/0.60 thf(f2129,plain,(
% 2.07/0.60 ($true != $true) | (((ine @ p @ (secrecy_kE @ key))) != $true) | spl74_11),
% 2.07/0.60 inference(superposition,[],[f2022,f1725])).
% 2.07/0.60 thf(f2130,plain,(
% 2.07/0.60 (((ine @ p @ (secrecy_kE @ key))) != $true) | spl74_11),
% 2.07/0.60 inference(trivial_inequality_removal,[],[f2129])).
% 2.07/0.60 thf(f2132,definition,(
% 2.07/0.60 spl74_31 <=> (((ine @ p @ (secrecy_kE @ key))) = $true)),
% 2.07/0.60 introduced(definition,[new_symbols(definition,[spl74_31])],[avatar_definition])).
% 2.07/0.60 thf(f2134,plain,(
% 2.07/0.60 (((ine @ p @ (secrecy_kE @ key))) != $true) | spl74_31),
% 2.07/0.60 inference(avatar_component_clause,[],[f2132])).
% 2.07/0.60 thf(f2135,plain,(
% 2.07/0.60 ~spl74_31 | spl74_11),
% 2.07/0.60 inference(avatar_split_clause,[],[f2130,f2020,f2132])).
% 2.07/0.60 thf(f2161,plain,(
% 2.07/0.60 ( ! [X0 : secrecy_specID,X1 : secrecy_Expression] : ((((subcomponents @ pq)) != ((subcomponents @ X0))) | (((correctCompositionIn @ X0)) != $true) | (((ine @ X0 @ X1)) != $true) | ($true = ((ine @ q @ X1))) | (((ine @ p @ X1)) = $true)) ) | ~spl74_9),
% 2.07/0.60 inference(superposition,[],[f1531,f2012])).
% 2.07/0.60 thf(f2248,plain,(
% 2.07/0.60 ( ! [X0 : secrecy_Expression] : ((((ine @ q @ X0)) = $true) | (((correctCompositionIn @ pq)) != $true) | (((ine @ pq @ X0)) != $true) | (((ine @ p @ X0)) = $true)) ) | ~spl74_9),
% 2.07/0.60 inference(equality_resolution,[],[f2161])).
% 2.07/0.60 thf(f2249,plain,(
% 2.07/0.60 ( ! [X0 : secrecy_Expression] : ((((ine @ q @ X0)) = $true) | (((ine @ p @ X0)) = $true) | (((ine @ pq @ X0)) != $true)) ) | (~spl74_9 | ~spl74_28)),
% 2.07/0.60 inference(forward_subsumption_resolution,[],[f2248,f2107])).
% 2.07/0.60 thf(f2981,plain,(
% 2.07/0.60 (((ine @ pq @ (secrecy_kE @ key))) != $true) | (((ine @ p @ (secrecy_kE @ key))) = $true) | ($true != $true) | (~spl74_9 | ~spl74_28 | spl74_30)),
% 2.07/0.60 inference(superposition,[],[f2126,f2249])).
% 2.07/0.60 thf(f2984,plain,(
% 2.07/0.60 (((ine @ pq @ (secrecy_kE @ key))) != $true) | (((ine @ p @ (secrecy_kE @ key))) = $true) | (~spl74_9 | ~spl74_28 | spl74_30)),
% 2.07/0.60 inference(trivial_inequality_removal,[],[f2981])).
% 2.07/0.60 thf(f3009,plain,(
% 2.07/0.60 (((ine @ p @ (secrecy_kE @ key))) = $true) | (~spl74_9 | ~spl74_13 | ~spl74_28 | spl74_30)),
% 2.07/0.60 inference(forward_subsumption_resolution,[],[f2984,f2032])).
% 2.07/0.60 thf(f3010,plain,(
% 2.07/0.60 $false | (~spl74_9 | ~spl74_13 | ~spl74_28 | spl74_30 | spl74_31)),
% 2.07/0.60 inference(forward_subsumption_resolution,[],[f3009,f2134])).
% 2.07/0.60 thf(f3011,plain,(
% 2.07/0.60 ~spl74_9 | ~spl74_13 | ~spl74_28 | spl74_30 | spl74_31),
% 2.07/0.60 inference(avatar_contradiction_clause,[],[f3010])).
% 2.07/0.60 cnf(s6, plain, ~spl74_6, inference(sat_conversion,[],[f1998])).
% 2.07/0.60 cnf(s9, plain, spl74_9, inference(sat_conversion,[],[f2013])).
% 2.07/0.60 cnf(s11, plain, ~spl74_11, inference(sat_conversion,[],[f2023])).
% 2.07/0.60 cnf(s13, plain, spl74_13, inference(sat_conversion,[],[f2033])).
% 2.07/0.60 cnf(s28, plain, spl74_28, inference(sat_conversion,[],[f2108])).
% 2.07/0.60 cnf(s30, plain, spl74_6 | ~spl74_30, inference(sat_conversion,[],[f2127])).
% 2.07/0.60 cnf(s31, plain, spl74_11 | ~spl74_31, inference(sat_conversion,[],[f2135])).
% 2.07/0.60 cnf(s40, plain, ~spl74_9 | ~spl74_13 | ~spl74_28 | spl74_30 | spl74_31, inference(sat_conversion,[],[f3011])).
% 2.07/0.60 cnf(s41, plain, ~spl74_31, inference(rat,[],[s31,s11])).
% 2.07/0.60 cnf(s42, plain, spl74_30, inference(rat,[],[s40,s41,s13,s28,s9])).
% 2.07/0.60 cnf(s45, plain, spl74_6, inference(rat,[],[s30,s42])).
% 2.07/0.60 cnf(s46, plain, $false, inference(rat,[],[s6,s45])).
% 2.07/0.60 thf(f3012,plain,(
% 2.07/0.60 $false),
% 2.07/0.60 inference(avatar_sat_refutation,[],[s46])).
% 2.07/0.60 % SZS output end Proof for theBenchmark
% 2.07/0.60 % (2124889)------------------------------
% 2.07/0.60 % (2124889)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.07/0.60 % (2124889)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.07/0.60 % (2124889)CaDiCaL version: 2.1.3
% 2.07/0.60 % (2124889)Termination reason: Refutation
% 2.07/0.60 % (2124889)Time elapsed: 0.273 s
% 2.07/0.60 % (2124889)Peak memory usage: 16 MB
% 2.07/0.60 % (2124889)Instructions burned: 384 (million)
% 2.07/0.60 % (2124880)Success in time 0.321 s
% 2.07/0.60 % Vampire exiting
%------------------------------------------------------------------------------