%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NLP266^23 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 08:16:31 AM UTC 2026
% Result : Theorem 2.68s 0.74s
% Output : Refutation 2.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NLP266^23 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n010.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 11:45:18 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.25 Running higher-order theorem proving
% 0.09/0.28 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
% 0.94/0.47 % (2752094)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.94/0.47 % (2752101)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3420737668:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.94/0.47 % (2752101)Instruction limit reached!
% 0.94/0.47 % (2752101)------------------------------
% 0.94/0.47 % (2752101)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.94/0.47 % (2752101)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.94/0.47 % (2752101)CaDiCaL version: 2.1.3
% 0.94/0.47 % (2752101)Termination reason: Instruction limit
% 0.94/0.47 % (2752101)Termination phase: Function definition elimination
% 0.94/0.47 % (2752101)Time elapsed: 0.002 s
% 0.94/0.47 % (2752101)Peak memory usage: 10 MB
% 0.94/0.47 % (2752101)Instructions burned: 4 (million)
% 0.94/0.47 % (2752105)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.94/0.47 % (2752105)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
% 0.94/0.47 % (2752099)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1698412725:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.94/0.47 % (2752100)lrs+10_16_si=on:nwc=1.5:random_seed=1185825404:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.94/0.47 % (2752103)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2233028736:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.94/0.47 % (2752102)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=2297163707: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)
% 0.94/0.47 % (2752104)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3405149877:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.94/0.47 % (2752105)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=445946107:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.94/0.47 % (2752107)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2049775089:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.94/0.47 % (2752107)Instruction limit reached!
% 0.94/0.47 % (2752107)------------------------------
% 0.94/0.47 % (2752107)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.94/0.47 % (2752107)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.94/0.47 % (2752107)CaDiCaL version: 2.1.3
% 0.94/0.47 % (2752107)Termination reason: Instruction limit
% 0.94/0.47 % (2752107)Termination phase: Property scanning
% 0.94/0.47 % (2752107)Time elapsed: 0.001 s
% 0.94/0.47 % (2752107)Peak memory usage: 10 MB
% 0.94/0.47 % (2752107)Instructions burned: 2 (million)
% 0.94/0.47 % (2752100)Instruction limit reached!
% 0.94/0.47 % (2752100)------------------------------
% 0.94/0.47 % (2752100)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.94/0.47 % (2752100)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.94/0.47 % (2752100)CaDiCaL version: 2.1.3
% 0.94/0.47 % (2752100)Termination reason: Instruction limit
% 0.94/0.47 % (2752100)Termination phase: Saturation
% 0.94/0.47 % (2752100)Time elapsed: 0.016 s
% 0.94/0.47 % (2752100)Peak memory usage: 12 MB
% 0.94/0.47 % (2752100)Instructions burned: 18 (million)
% 0.94/0.47 % (2752103)Instruction limit reached!
% 0.94/0.47 % (2752103)------------------------------
% 0.94/0.47 % (2752103)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.94/0.47 % (2752103)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.94/0.47 % (2752103)CaDiCaL version: 2.1.3
% 0.94/0.47 % (2752103)Termination reason: Instruction limit
% 0.94/0.47 % (2752103)Termination phase: Saturation
% 0.94/0.47 % (2752103)Time elapsed: 0.023 s
% 0.94/0.47 % (2752103)Peak memory usage: 11 MB
% 0.94/0.47 % (2752103)Instructions burned: 25 (million)
% 0.94/0.47 % (2752115)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2531227559:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.94/0.53 % (2752115)Instruction limit reached!
% 0.94/0.53 % (2752115)------------------------------
% 0.94/0.53 % (2752115)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.94/0.53 % (2752115)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.94/0.53 % (2752115)CaDiCaL version: 2.1.3
% 0.94/0.53 % (2752115)Termination reason: Instruction limit
% 0.94/0.53 % (2752115)Termination phase: Saturation
% 0.94/0.53 % (2752115)Time elapsed: 0.003 s
% 0.94/0.53 % (2752115)Peak memory usage: 11 MB
% 0.94/0.53 % (2752115)Instructions burned: 6 (million)
% 0.94/0.53 % (2752116)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.94/0.53 % (2752119)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
% 0.94/0.53 % (2752119)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.94/0.53 % (2752119)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1722075586:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.94/0.53 % (2752116)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2420936120:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.94/0.53 % (2752117)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1595952476:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.94/0.53 % (2752116)Instruction limit reached!
% 0.94/0.53 % (2752116)------------------------------
% 0.94/0.53 % (2752116)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.94/0.53 % (2752116)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.94/0.53 % (2752116)CaDiCaL version: 2.1.3
% 0.94/0.53 % (2752116)Termination reason: Instruction limit
% 0.94/0.53 % (2752116)Termination phase: Saturation
% 0.94/0.53 % (2752116)Time elapsed: 0.006 s
% 0.94/0.53 % (2752116)Peak memory usage: 11 MB
% 0.94/0.53 % (2752116)Instructions burned: 7 (million)
% 0.94/0.53 % (2752119)Instruction limit reached!
% 0.94/0.53 % (2752119)------------------------------
% 0.94/0.53 % (2752119)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.94/0.53 % (2752119)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.94/0.53 % (2752119)CaDiCaL version: 2.1.3
% 0.94/0.53 % (2752119)Termination reason: Instruction limit
% 0.94/0.53 % (2752119)Termination phase: Saturation
% 0.94/0.53 % (2752119)Time elapsed: 0.013 s
% 0.94/0.53 % (2752119)Peak memory usage: 11 MB
% 0.94/0.53 % (2752119)Instructions burned: 28 (million)
% 0.94/0.53 % (2752117)Instruction limit reached!
% 0.94/0.53 % (2752117)------------------------------
% 0.94/0.53 % (2752117)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.94/0.53 % (2752117)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.94/0.53 % (2752117)CaDiCaL version: 2.1.3
% 0.94/0.53 % (2752117)Termination reason: Instruction limit
% 0.94/0.53 % (2752117)Termination phase: Saturation
% 0.94/0.53 % (2752117)Time elapsed: 0.011 s
% 0.94/0.53 % (2752117)Peak memory usage: 11 MB
% 0.94/0.53 % (2752117)Instructions burned: 12 (million)
% 0.94/0.53 % (2752104)Instruction limit reached!
% 0.94/0.53 % (2752104)------------------------------
% 0.94/0.53 % (2752104)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.94/0.53 % (2752104)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.94/0.53 % (2752104)CaDiCaL version: 2.1.3
% 0.94/0.53 % (2752104)Termination reason: Instruction limit
% 0.94/0.53 % (2752104)Termination phase: Saturation
% 0.94/0.53 % (2752104)Time elapsed: 0.067 s
% 0.94/0.53 % (2752104)Peak memory usage: 12 MB
% 0.94/0.53 % (2752104)Instructions burned: 75 (million)
% 0.94/0.53 % (2752099)Instruction limit reached!
% 0.94/0.53 % (2752099)------------------------------
% 0.94/0.53 % (2752099)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.94/0.53 % (2752099)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.94/0.53 % (2752099)CaDiCaL version: 2.1.3
% 0.94/0.53 % (2752099)Termination reason: Instruction limit
% 1.67/0.59 % (2752099)Termination phase: Saturation
% 1.67/0.59 % (2752099)Time elapsed: 0.077 s
% 1.67/0.59 % (2752099)Peak memory usage: 12 MB
% 1.67/0.59 % (2752099)Instructions burned: 88 (million)
% 1.67/0.59 % (2752124)lrs+10_1_si=on:cs=on:random_seed=1154391151:i=8:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.67/0.59 % (2752124)Instruction limit reached!
% 1.67/0.59 % (2752124)------------------------------
% 1.67/0.59 % (2752124)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.67/0.59 % (2752124)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.67/0.59 % (2752124)CaDiCaL version: 2.1.3
% 1.67/0.59 % (2752124)Termination reason: Instruction limit
% 1.67/0.59 % (2752124)Termination phase: Saturation
% 1.67/0.59 % (2752124)Time elapsed: 0.004 s
% 1.67/0.59 % (2752124)Peak memory usage: 11 MB
% 1.67/0.59 % (2752124)Instructions burned: 9 (million)
% 1.67/0.59 % (2752123)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=1500508663:i=86:piset=equals:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/86Mi)
% 1.67/0.59 % (2752125)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.67/0.59 % (2752125)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=1467540091:i=2:add=on:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.67/0.59 % (2752126)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=726394582:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 1.67/0.59 % (2752125)Instruction limit reached!
% 1.67/0.59 % (2752125)------------------------------
% 1.67/0.59 % (2752125)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.67/0.59 % (2752125)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.67/0.59 % (2752125)CaDiCaL version: 2.1.3
% 1.67/0.59 % (2752125)Termination reason: Instruction limit
% 1.67/0.59 % (2752125)Termination phase: Property scanning
% 1.67/0.59 % (2752125)Time elapsed: 0.002 s
% 1.67/0.59 % (2752125)Peak memory usage: 9 MB
% 1.67/0.59 % (2752125)Instructions burned: 2 (million)
% 1.67/0.59 % (2752126)Refutation not found, incomplete strategy
% 1.67/0.59 % (2752126)------------------------------
% 1.67/0.59 % (2752126)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.67/0.59 % (2752126)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.67/0.59 % (2752126)CaDiCaL version: 2.1.3
% 1.67/0.59 % (2752126)Termination reason: Refutation not found, incomplete strategy
% 1.67/0.59 % (2752126)Time elapsed: 0.006 s
% 1.67/0.59 % (2752126)Peak memory usage: 12 MB
% 1.67/0.59 % (2752126)Instructions burned: 6 (million)
% 1.67/0.59 % (2752126)------------------------------
% 1.67/0.59 % (2752126)------------------------------
% 1.67/0.59 % (2752127)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=2526145085:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 1.67/0.59 % (2752129)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=3180449764:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.67/0.59 % (2752127)Refutation not found, incomplete strategy
% 1.67/0.59 % (2752127)------------------------------
% 1.67/0.59 % (2752127)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.67/0.59 % (2752127)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.67/0.59 % (2752127)CaDiCaL version: 2.1.3
% 1.67/0.59 % (2752127)Termination reason: Refutation not found, incomplete strategy
% 1.67/0.59 % (2752127)Time elapsed: 0.010 s
% 1.67/0.59 % (2752127)Peak memory usage: 12 MB
% 1.67/0.59 % (2752127)Instructions burned: 10 (million)
% 1.67/0.59 % (2752133)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=3475473814:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.67/0.59 % (2752127)------------------------------
% 1.67/0.59 % (2752127)------------------------------
% 1.67/0.59 % (2752133)Instruction limit reached!
% 1.67/0.59 % (2752133)------------------------------
% 1.67/0.59 % (2752133)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.67/0.59 % (2752133)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.52/0.68 % (2752133)CaDiCaL version: 2.1.3
% 2.52/0.68 % (2752133)Termination reason: Instruction limit
% 2.52/0.68 % (2752133)Termination phase: Saturation
% 2.52/0.68 % (2752133)Time elapsed: 0.007 s
% 2.52/0.68 % (2752133)Peak memory usage: 11 MB
% 2.52/0.68 % (2752133)Instructions burned: 15 (million)
% 2.52/0.68 % (2752135)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=270393802:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 2.52/0.68 % (2752105)Instruction limit reached!
% 2.52/0.68 % (2752105)------------------------------
% 2.52/0.68 % (2752105)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.52/0.68 % (2752105)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.52/0.68 % (2752105)CaDiCaL version: 2.1.3
% 2.52/0.68 % (2752105)Termination reason: Instruction limit
% 2.52/0.68 % (2752105)Termination phase: Saturation
% 2.52/0.68 % (2752105)Time elapsed: 0.149 s
% 2.52/0.68 % (2752105)Peak memory usage: 12 MB
% 2.52/0.68 % (2752105)Instructions burned: 157 (million)
% 2.52/0.68 % (2752129)Instruction limit reached!
% 2.52/0.68 % (2752129)------------------------------
% 2.52/0.68 % (2752129)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.52/0.68 % (2752129)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.52/0.68 % (2752129)CaDiCaL version: 2.1.3
% 2.52/0.68 % (2752129)Termination reason: Instruction limit
% 2.52/0.68 % (2752129)Termination phase: Saturation
% 2.52/0.68 % (2752129)Time elapsed: 0.031 s
% 2.52/0.68 % (2752129)Peak memory usage: 12 MB
% 2.52/0.68 % (2752129)Instructions burned: 26 (million)
% 2.52/0.68 % (2752138)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=2423550291:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 2.52/0.68 % (2752139)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=1275008505: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)
% 2.52/0.68 % (2752139)Instruction limit reached!
% 2.52/0.68 % (2752139)------------------------------
% 2.52/0.68 % (2752139)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.52/0.68 % (2752139)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.52/0.68 % (2752139)CaDiCaL version: 2.1.3
% 2.52/0.68 % (2752139)Termination reason: Instruction limit
% 2.52/0.68 % (2752139)Termination phase: SInE selection
% 2.52/0.68 % (2752139)Time elapsed: 0.003 s
% 2.52/0.68 % (2752139)Peak memory usage: 10 MB
% 2.52/0.68 % (2752139)Instructions burned: 3 (million)
% 2.52/0.68 % (2752138)Instruction limit reached!
% 2.52/0.68 % (2752138)------------------------------
% 2.52/0.68 % (2752138)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.52/0.68 % (2752138)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.52/0.68 % (2752138)CaDiCaL version: 2.1.3
% 2.52/0.68 % (2752138)Termination reason: Instruction limit
% 2.52/0.68 % (2752138)Termination phase: Saturation
% 2.52/0.68 % (2752138)Time elapsed: 0.014 s
% 2.52/0.68 % (2752138)Peak memory usage: 11 MB
% 2.52/0.68 % (2752138)Instructions burned: 16 (million)
% 2.52/0.68 % (2752123)Instruction limit reached!
% 2.52/0.68 % (2752123)------------------------------
% 2.52/0.68 % (2752123)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.52/0.68 % (2752123)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.52/0.68 % (2752123)CaDiCaL version: 2.1.3
% 2.52/0.68 % (2752123)Termination reason: Instruction limit
% 2.52/0.68 % (2752123)Termination phase: Saturation
% 2.52/0.68 % (2752123)Time elapsed: 0.081 s
% 2.52/0.68 % (2752123)Peak memory usage: 13 MB
% 2.52/0.68 % (2752123)Instructions burned: 86 (million)
% 2.52/0.68 % (2752142)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=4053436743:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 2.52/0.68 % (2752141)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=1559637931:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 2.52/0.68 % (2752142)Instruction limit reached!
% 2.52/0.68 % (2752142)------------------------------
% 2.52/0.68 % (2752142)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.52/0.68 % (2752142)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.52/0.68 % (2752142)CaDiCaL version: 2.1.3
% 2.68/0.74 % (2752142)Termination reason: Instruction limit
% 2.68/0.74 % (2752142)Termination phase: Saturation
% 2.68/0.74 % (2752142)Time elapsed: 0.012 s
% 2.68/0.74 % (2752142)Peak memory usage: 11 MB
% 2.68/0.74 % (2752142)Instructions burned: 24 (million)
% 2.68/0.74 % (2752146)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
% 2.68/0.74 % (2752146)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 2.68/0.74 % (2752147)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 2.68/0.74 % (2752145)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=1115491724:cond=on:i=60:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/60Mi)
% 2.68/0.74 % (2752146)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=3511881944:i=14:add=off:nm=40:rtra=on:rawr=on_2997 on theBenchmark for (2997ds/14Mi)
% 2.68/0.74 % (2752147)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=3650198864:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2997 on theBenchmark for (2997ds/8Mi)
% 2.68/0.74 % (2752141)Instruction limit reached!
% 2.68/0.74 % (2752141)------------------------------
% 2.68/0.74 % (2752141)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.68/0.74 % (2752141)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/0.74 % (2752141)CaDiCaL version: 2.1.3
% 2.68/0.74 % (2752141)Termination reason: Instruction limit
% 2.68/0.74 % (2752141)Termination phase: Saturation
% 2.68/0.74 % (2752141)Time elapsed: 0.024 s
% 2.68/0.74 % (2752141)Peak memory usage: 12 MB
% 2.68/0.74 % (2752141)Instructions burned: 26 (million)
% 2.68/0.74 % (2752150)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=2691011988:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2997 on theBenchmark for (2997ds/31Mi)
% 2.68/0.74 % (2752147)Instruction limit reached!
% 2.68/0.74 % (2752147)------------------------------
% 2.68/0.74 % (2752147)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.68/0.74 % (2752147)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/0.74 % (2752147)CaDiCaL version: 2.1.3
% 2.68/0.74 % (2752147)Termination reason: Instruction limit
% 2.68/0.74 % (2752147)Termination phase: Saturation
% 2.68/0.74 % (2752147)Time elapsed: 0.008 s
% 2.68/0.74 % (2752147)Peak memory usage: 12 MB
% 2.68/0.74 % (2752147)Instructions burned: 8 (million)
% 2.68/0.74 % (2752146)Instruction limit reached!
% 2.68/0.74 % (2752146)------------------------------
% 2.68/0.74 % (2752146)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.68/0.74 % (2752146)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/0.74 % (2752146)CaDiCaL version: 2.1.3
% 2.68/0.74 % (2752146)Termination reason: Instruction limit
% 2.68/0.74 % (2752146)Termination phase: Saturation
% 2.68/0.74 % (2752146)Time elapsed: 0.013 s
% 2.68/0.74 % (2752146)Peak memory usage: 12 MB
% 2.68/0.74 % (2752146)Instructions burned: 14 (million)
% 2.68/0.74 % (2752150)Instruction limit reached!
% 2.68/0.74 % (2752150)------------------------------
% 2.68/0.74 % (2752150)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.68/0.74 % (2752150)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/0.74 % (2752150)CaDiCaL version: 2.1.3
% 2.68/0.74 % (2752150)Termination reason: Instruction limit
% 2.68/0.74 % (2752150)Termination phase: Saturation
% 2.68/0.74 % (2752150)Time elapsed: 0.015 s
% 2.68/0.74 % (2752150)Peak memory usage: 12 MB
% 2.68/0.74 % (2752150)Instructions burned: 31 (million)
% 2.68/0.74 % (2752154)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=850211896:i=7:hud=5:bd=preordered:rtra=on:bet=on_2997 on theBenchmark for (2997ds/7Mi)
% 2.68/0.74 % (2752158)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=372622523:i=1240:rtra=on:ixr=off_2997 on theBenchmark for (2997ds/1240Mi)
% 2.68/0.74 % (2752154)Instruction limit reached!
% 2.68/0.74 % (2752154)------------------------------
% 2.68/0.74 % (2752154)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.68/0.74 % (2752154)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/0.74 % (2752154)CaDiCaL version: 2.1.3
% 2.68/0.74 % (2752154)Termination reason: Instruction limit
% 2.68/0.74 % (2752154)Termination phase: Saturation
% 2.68/0.74 % (2752154)Time elapsed: 0.007 s
% 2.68/0.74 % (2752154)Peak memory usage: 11 MB
% 2.68/0.74 % (2752154)Instructions burned: 8 (million)
% 2.68/0.74 % (2752157)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=611603573:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2997 on theBenchmark for (2997ds/20Mi)
% 2.68/0.74 % (2752145)Instruction limit reached!
% 2.68/0.74 % (2752145)------------------------------
% 2.68/0.74 % (2752145)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.68/0.74 % (2752145)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/0.74 % (2752145)CaDiCaL version: 2.1.3
% 2.68/0.74 % (2752145)Termination reason: Instruction limit
% 2.68/0.74 % (2752145)Termination phase: Saturation
% 2.68/0.74 % (2752145)Time elapsed: 0.057 s
% 2.68/0.74 % (2752145)Peak memory usage: 12 MB
% 2.68/0.74 % (2752145)Instructions burned: 60 (million)
% 2.68/0.74 % (2752156)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=2280053102:i=23:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/23Mi)
% 2.68/0.74 % (2752157)Instruction limit reached!
% 2.68/0.74 % (2752157)------------------------------
% 2.68/0.74 % (2752157)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.68/0.74 % (2752157)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/0.74 % (2752157)CaDiCaL version: 2.1.3
% 2.68/0.74 % (2752157)Termination reason: Instruction limit
% 2.68/0.74 % (2752157)Termination phase: Saturation
% 2.68/0.74 % (2752157)Time elapsed: 0.019 s
% 2.68/0.74 % (2752157)Peak memory usage: 12 MB
% 2.68/0.74 % (2752157)Instructions burned: 20 (million)
% 2.68/0.74 % (2752162)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=2553777250:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/143Mi)
% 2.68/0.74 % (2752156)Instruction limit reached!
% 2.68/0.74 % (2752156)------------------------------
% 2.68/0.74 % (2752156)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.68/0.74 % (2752156)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/0.74 % (2752156)CaDiCaL version: 2.1.3
% 2.68/0.74 % (2752156)Termination reason: Instruction limit
% 2.68/0.74 % (2752156)Termination phase: Saturation
% 2.68/0.74 % (2752156)Time elapsed: 0.028 s
% 2.68/0.74 % (2752156)Peak memory usage: 11 MB
% 2.68/0.74 % (2752156)Instructions burned: 23 (million)
% 2.68/0.74 % (2752163)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=3528464193:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2996 on theBenchmark for (2996ds/193Mi)
% 2.68/0.74 % (2752165)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3983965169:i=42:hud=10:rtra=on_2996 on theBenchmark for (2996ds/42Mi)
% 2.68/0.74 % (2752168)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 2.68/0.74 % (2752168)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1339892878:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2996 on theBenchmark for (2996ds/7Mi)
% 2.68/0.74 % (2752168)Instruction limit reached!
% 2.68/0.74 % (2752168)------------------------------
% 2.68/0.74 % (2752168)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.68/0.74 % (2752168)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/0.74 % (2752168)CaDiCaL version: 2.1.3
% 2.68/0.74 % (2752168)Termination reason: Instruction limit
% 2.68/0.74 % (2752168)Termination phase: Saturation
% 2.68/0.74 % (2752168)Time elapsed: 0.007 s
% 2.68/0.74 % (2752168)Peak memory usage: 12 MB
% 2.68/0.74 % (2752168)Instructions burned: 7 (million)
% 2.68/0.74 % (2752165)Instruction limit reached!
% 2.68/0.74 % (2752165)------------------------------
% 2.68/0.74 % (2752165)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.68/0.74 % (2752165)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/0.74 % (2752165)CaDiCaL version: 2.1.3
% 2.68/0.74 % (2752165)Termination reason: Instruction limit
% 2.68/0.74 % (2752165)Termination phase: Saturation
% 2.68/0.74 % (2752165)Time elapsed: 0.038 s
% 2.68/0.74 % (2752165)Peak memory usage: 12 MB
% 2.68/0.74 % (2752165)Instructions burned: 42 (million)
% 2.68/0.74 % (2752163) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2752094-2752163"...
% 2.68/0.74 % (2752171)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=4061189624:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2996 on theBenchmark for (2996ds/181Mi)
% 2.68/0.74 % (2752172)dis+10_8_sil=128000:plsq=on:plsqc=1:si=on:sp=unary_first:sos=on:lma=off:plsqr=64,1:uwa=interpreted_only:foolp=on:random_seed=3228933835:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2996 on theBenchmark for (2996ds/169Mi)
% 2.68/0.74 % (2752171)Refutation not found, incomplete strategy
% 2.68/0.74 % (2752171)------------------------------
% 2.68/0.74 % (2752171)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.68/0.74 % (2752171)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/0.74 % (2752171)CaDiCaL version: 2.1.3
% 2.68/0.74 % (2752171)Termination reason: Refutation not found, incomplete strategy
% 2.68/0.74 % (2752171)Time elapsed: 0.009 s
% 2.68/0.74 % (2752171)Peak memory usage: 12 MB
% 2.68/0.74 % (2752171)Instructions burned: 8 (million)
% 2.68/0.74 % (2752171)------------------------------
% 2.68/0.74 % (2752171)------------------------------
% 2.68/0.74 % (2752172)Refutation not found, incomplete strategy
% 2.68/0.74 % (2752172)------------------------------
% 2.68/0.74 % (2752172)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.68/0.74 % (2752172)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/0.74 % (2752172)CaDiCaL version: 2.1.3
% 2.68/0.74 % (2752172)Termination reason: Refutation not found, incomplete strategy
% 2.68/0.74 % (2752172)Time elapsed: 0.012 s
% 2.68/0.74 % (2752172)Peak memory usage: 12 MB
% 2.68/0.74 % (2752172)Instructions burned: 13 (million)
% 2.68/0.74 % (2752172)------------------------------
% 2.68/0.74 % (2752172)------------------------------
% 2.68/0.74 % (2752163)...printing done.
% 2.68/0.74 % (2752163)Refutation found. Thanks to Tanya!
% 2.68/0.74 % SZS status Theorem for theBenchmark
% 2.68/0.74 % SZS output start Proof for theBenchmark
% 2.68/0.74 thf(type_def_5, type, mworld: $tType).
% 2.68/0.74 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 2.68/0.74 thf(func_def_0, type, mrel: (mworld > mworld > $o)).
% 2.68/0.74 thf(func_def_1, type, mactual: mworld).
% 2.68/0.74 thf(func_def_2, type, mlocal: ((mworld > $o) > $o)).
% 2.68/0.74 thf(func_def_4, type, mnot: ((mworld > $o) > mworld > $o)).
% 2.68/0.74 thf(func_def_5, type, mand: ((mworld > $o) > (mworld > $o) > mworld > $o)).
% 2.68/0.74 thf(func_def_6, type, mor: ((mworld > $o) > (mworld > $o) > mworld > $o)).
% 2.68/0.74 thf(func_def_7, type, mimplies: ((mworld > $o) > (mworld > $o) > mworld > $o)).
% 2.68/0.74 thf(func_def_8, type, mequiv: ((mworld > $o) > (mworld > $o) > mworld > $o)).
% 2.68/0.74 thf(func_def_9, type, mbox: ((mworld > $o) > mworld > $o)).
% 2.68/0.74 thf(func_def_10, type, mdia: ((mworld > $o) > mworld > $o)).
% 2.68/0.74 thf(func_def_11, type, eiw_di: ($i > mworld > $o)).
% 2.68/0.74 thf(func_def_12, type, mforall_di: (($i > mworld > $o) > mworld > $o)).
% 2.68/0.74 thf(func_def_13, type, mexists_di: (($i > mworld > $o) > mworld > $o)).
% 2.68/0.74 thf(func_def_16, type, number: ($i > $i > mworld > $o)).
% 2.68/0.74 thf(func_def_17, type, string: ($i > mworld > $o)).
% 2.68/0.74 thf(func_def_18, type, in: ($i > $i > $i > mworld > $o)).
% 2.68/0.74 thf(func_def_19, type, do: ($i > $i > $i > mworld > $o)).
% 2.68/0.74 thf(func_def_20, type, entry_box: ($i > mworld > $o)).
% 2.68/0.74 thf(func_def_21, type, userid: ($i > $i > mworld > $o)).
% 2.68/0.74 thf(func_def_22, type, db0: !>[X0: $tType]:(X0)).
% 2.68/0.74 thf(func_def_23, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 2.68/0.74 thf(func_def_26, type, vIMP: ($o > $o > $o)).
% 2.68/0.74 thf(func_def_27, type, db2: !>[X0: $tType]:(X0)).
% 2.68/0.74 thf(func_def_28, type, db1: !>[X0: $tType]:(X0)).
% 2.68/0.74 thf(func_def_29, type, db4: !>[X0: $tType]:(X0)).
% 2.68/0.74 thf(func_def_30, type, db3: !>[X0: $tType]:(X0)).
% 2.68/0.74 thf(func_def_31, type, vAND: ($o > $o > $o)).
% 2.68/0.74 thf(func_def_32, type, vOR: ($o > $o > $o)).
% 2.68/0.74 thf(func_def_33, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 2.68/0.74 thf(func_def_34, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 2.68/0.74 thf(func_def_35, type, vNOT: ($o > $o)).
% 2.68/0.74 thf(func_def_36, type, vIFF: ($o > $o > $o)).
% 2.68/0.74 thf(func_def_37, type, sK0: (mworld > $i)).
% 2.68/0.74 thf(func_def_38, type, db6: !>[X0: $tType]:(X0)).
% 2.68/0.74 thf(func_def_39, type, db5: !>[X0: $tType]:(X0)).
% 2.68/0.74 thf(func_def_40, type, db7: !>[X0: $tType]:(X0)).
% 2.68/0.74 thf(func_def_41, type, sK1: ($i > mworld > $i > $i > $i)).
% 2.68/0.74 thf(func_def_42, type, sK2: (mworld > $i)).
% 2.68/0.74 thf(func_def_43, type, sK3: mworld).
% 2.68/0.74 thf(func_def_44, type, sK4: ($i > $i > mworld)).
% 2.68/0.74 thf(func_def_45, type, sK5: ($i > $i > $i > $i > mworld)).
% 2.68/0.74 thf(func_def_46, type, sK6: ($i > $i > $i > $i > $i)).
% 2.68/0.74 thf(func_def_47, type, sK7: ($i > $i > $i > $i > $i)).
% 2.68/0.74 thf(f1,axiom,(
% 2.68/0.74 ((^[X0 : (mworld > $o)] : ((X0 @ mactual))) = mlocal)),
% 2.68/0.74 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mlocal_def)).
% 2.68/0.74 thf(f3,axiom,(
% 2.68/0.74 ((^[X0 : (mworld > $o), X1 : (mworld > $o), X2 : mworld] : ((X0 @ X2) & (X1 @ X2))) = mand)),
% 2.68/0.74 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand_def)).
% 2.68/0.74 thf(f5,axiom,(
% 2.68/0.74 ((^[X0 : (mworld > $o), X1 : (mworld > $o), X2 : mworld] : ((X0 @ X2) => (X1 @ X2))) = mimplies)),
% 2.68/0.74 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies_def)).
% 2.68/0.74 thf(f7,axiom,(
% 2.68/0.74 ((^[X0 : (mworld > $o), X1 : mworld] : (! [X2 : mworld] : ((mrel @ X1 @ X2) => (X0 @ X2)))) = mbox)),
% 2.68/0.74 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_def)).
% 2.68/0.74 thf(f9,axiom,(
% 2.68/0.74 ! [X0 : mworld] : (mrel @ X0 @ X0)),
% 2.68/0.74 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_reflexive)).
% 2.68/0.74 thf(f10,axiom,(
% 2.68/0.74 ! [X1 : mworld,X0 : mworld,X2 : mworld] : (((mrel @ X0 @ X1) & (mrel @ X0 @ X2)) => (mrel @ X2 @ X1))),
% 2.68/0.74 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_euclidean)).
% 2.68/0.74 thf(f11,axiom,(
% 2.68/0.74 ! [X0 : mworld] : ? [X1 : $i] : (eiw_di @ X1 @ X0)),
% 2.68/0.74 file('/export/starexec/sandbox/benchmark/theBenchmark.p',eiw_di_nonempty)).
% 2.68/0.74 thf(f12,axiom,(
% 2.68/0.74 ! [X1 : mworld,X0 : mworld,X2 : $i] : (((mrel @ X1 @ X0) & (eiw_di @ X2 @ X0)) => (eiw_di @ X2 @ X1))),
% 2.68/0.74 file('/export/starexec/sandbox/benchmark/theBenchmark.p',eiw_di_decr)).
% 2.68/0.74 thf(f13,axiom,(
% 2.68/0.74 (mforall_di = (^[X0 : ($i > mworld > $o), X1 : mworld] : (! [X2 : $i] : ((eiw_di @ X2 @ X1) => (X0 @ X2 @ X1)))))),
% 2.68/0.74 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mforall_di_def)).
% 2.68/0.74 thf(f14,axiom,(
% 2.68/0.74 ((^[X0 : ($i > mworld > $o), X1 : mworld] : (? [X2 : $i] : ((X0 @ X2 @ X1) & (eiw_di @ X2 @ X1)))) = mexists_di)),
% 2.68/0.74 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mexists_di_def)).
% 2.68/0.74 thf(f15,axiom,(
% 2.68/0.74 (mlocal @ (mbox @ (mexists_di @ (^[X0 : $i] : ((mbox @ (mand @ (userid @ u @ X0) @ (string @ X0))))))))),
% 2.68/0.74 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1)).
% 2.68/0.74 thf(f16,axiom,(
% 2.68/0.74 (mlocal @ (mexists_di @ (^[X0 : $i] : ((mbox @ (mand @ (entry_box @ X0) @ (number @ X0 @ one)))))))),
% 2.68/0.74 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2)).
% 2.68/0.74 thf(f17,axiom,(
% 2.68/0.74 (mlocal @ (mbox @ (mforall_di @ (^[X0 : $i] : ((mforall_di @ (^[X1 : $i] : ((mforall_di @ (^[X2 : $i] : ((mimplies @ (mand @ (string @ X1) @ (entry_box @ X2)) @ (mexists_di @ (^[X3 : $i] : ((mbox @ (mforall_di @ (^[X4 : $i] : ((mimplies @ (do @ X0 @ X3 @ X4) @ (in @ X1 @ X2 @ X4)))))))))))))))))))))),
% 2.68/0.74 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3)).
% 2.68/0.74 thf(f18,conjecture,(
% 2.68/0.74 (mlocal @ (mbox @ (mexists_di @ (^[X0 : $i] : ((mexists_di @ (^[X1 : $i] : ((mexists_di @ (^[X2 : $i] : ((mexists_di @ (^[X3 : $i] : ((mand @ (mbox @ (mand @ (userid @ u @ X0) @ (mand @ (entry_box @ X1) @ (number @ X1 @ one)))) @ (mbox @ (mforall_di @ (^[X4 : $i] : ((mimplies @ (do @ X3 @ X2 @ X4) @ (in @ X0 @ X1 @ X4)))))))))))))))))))))),
% 2.68/0.74 file('/export/starexec/sandbox/benchmark/theBenchmark.p',con)).
% 2.68/0.74 thf(f19,negated_conjecture,(
% 2.68/0.74 ~(mlocal @ (mbox @ (mexists_di @ (^[X0 : $i] : ((mexists_di @ (^[X1 : $i] : ((mexists_di @ (^[X2 : $i] : ((mexists_di @ (^[X3 : $i] : ((mand @ (mbox @ (mand @ (userid @ u @ X0) @ (mand @ (entry_box @ X1) @ (number @ X1 @ one)))) @ (mbox @ (mforall_di @ (^[X4 : $i] : ((mimplies @ (do @ X3 @ X2 @ X4) @ (in @ X0 @ X1 @ X4)))))))))))))))))))))),
% 2.68/0.74 inference(negated_conjecture,[status(cth)],[f18])).
% 2.68/0.74 thf(f20,plain,(
% 2.68/0.74 (mlocal @ (mbox @ (mexists_di @ (^[X0 : $i] : ((mbox @ (mand @ (userid @ u @ X0) @ (string @ X0))))))))),
% 2.68/0.74 inference(rectify,[],[f15])).
% 2.68/0.74 thf(f21,plain,(
% 2.68/0.74 ($true = ((mlocal @ (mbox @ (mexists_di @ (^[Y0 : $i]: (mbox @ (mand @ (userid @ u @ Y0) @ (string @ Y0)))))))))),
% 2.68/0.74 inference(fool_elimination,[],[f20])).
% 2.68/0.74 thf(f22,plain,(
% 2.68/0.74 ((^[X0 : (mworld > $o), X1 : (mworld > $o), X2 : mworld] : ((X0 @ X2) => (X1 @ X2))) = mimplies)),
% 2.68/0.74 inference(rectify,[],[f5])).
% 2.68/0.74 thf(f23,plain,(
% 2.68/0.74 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 2.68/0.74 inference(fool_elimination,[],[f22])).
% 2.68/0.74 thf(f24,plain,(
% 2.68/0.74 (mlocal @ (mbox @ (mforall_di @ (^[X0 : $i] : ((mforall_di @ (^[X1 : $i] : ((mforall_di @ (^[X2 : $i] : ((mimplies @ (mand @ (string @ X1) @ (entry_box @ X2)) @ (mexists_di @ (^[X3 : $i] : ((mbox @ (mforall_di @ (^[X4 : $i] : ((mimplies @ (do @ X0 @ X3 @ X4) @ (in @ X1 @ X2 @ X4)))))))))))))))))))))),
% 2.68/0.74 inference(rectify,[],[f17])).
% 2.68/0.74 thf(f25,plain,(
% 2.68/0.74 ($true = ((mlocal @ (mbox @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mforall_di @ (^[Y2 : $i]: (mimplies @ (mand @ (string @ Y1) @ (entry_box @ Y2)) @ (mexists_di @ (^[Y3 : $i]: (mbox @ (mforall_di @ (^[Y4 : $i]: (mimplies @ (do @ Y0 @ Y3 @ Y4) @ (in @ Y1 @ Y2 @ Y4))))))))))))))))))),
% 2.68/0.74 inference(fool_elimination,[],[f24])).
% 2.68/0.74 thf(f26,plain,(
% 2.68/0.74 ((^[X0 : (mworld > $o), X1 : (mworld > $o), X2 : mworld] : ((X0 @ X2) & (X1 @ X2))) = mand)),
% 2.68/0.74 inference(rectify,[],[f3])).
% 2.68/0.74 thf(f27,plain,(
% 2.68/0.74 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) & (Y0 @ Y2))))))))),
% 2.68/0.74 inference(fool_elimination,[],[f26])).
% 2.68/0.74 thf(f28,plain,(
% 2.68/0.74 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 2.68/0.74 inference(fool_elimination,[],[f1])).
% 2.68/0.74 thf(f29,plain,(
% 2.68/0.74 ! [X0 : mworld,X1 : mworld,X2 : mworld] : (((mrel @ X1 @ X0) & (mrel @ X1 @ X2)) => (mrel @ X2 @ X0))),
% 2.68/0.74 inference(rectify,[],[f10])).
% 2.68/0.74 thf(f30,plain,(
% 2.68/0.74 ! [X1 : mworld,X0 : mworld,X2 : mworld] : (((((mrel @ X1 @ X0)) = $true) & (((mrel @ X1 @ X2)) = $true)) => (((mrel @ X2 @ X0)) = $true))),
% 2.68/0.74 inference(fool_elimination,[],[f29])).
% 2.68/0.74 thf(f33,plain,(
% 2.68/0.74 ((^[X0 : (mworld > $o), X1 : mworld] : (! [X2 : mworld] : ((mrel @ X1 @ X2) => (X0 @ X2)))) = mbox)),
% 2.68/0.74 inference(rectify,[],[f7])).
% 2.68/0.74 thf(f34,plain,(
% 2.68/0.74 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 2.68/0.74 inference(fool_elimination,[],[f33])).
% 2.68/0.74 thf(f37,plain,(
% 2.68/0.74 (mforall_di = (^[X0 : ($i > mworld > $o), X1 : mworld] : (! [X2 : $i] : ((eiw_di @ X2 @ X1) => (X0 @ X2 @ X1)))))),
% 2.68/0.74 inference(rectify,[],[f13])).
% 2.68/0.74 thf(f38,plain,(
% 2.68/0.74 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))))),
% 2.68/0.74 inference(fool_elimination,[],[f37])).
% 2.68/0.74 thf(f39,plain,(
% 2.68/0.74 ! [X0 : mworld] : (mrel @ X0 @ X0)),
% 2.68/0.74 inference(rectify,[],[f9])).
% 2.68/0.74 thf(f40,plain,(
% 2.68/0.74 ! [X0 : mworld] : (((mrel @ X0 @ X0)) = $true)),
% 2.68/0.74 inference(fool_elimination,[],[f39])).
% 2.68/0.74 thf(f41,plain,(
% 2.68/0.74 ~(mlocal @ (mbox @ (mexists_di @ (^[X0 : $i] : ((mexists_di @ (^[X1 : $i] : ((mexists_di @ (^[X2 : $i] : ((mexists_di @ (^[X3 : $i] : ((mand @ (mbox @ (mand @ (userid @ u @ X0) @ (mand @ (entry_box @ X1) @ (number @ X1 @ one)))) @ (mbox @ (mforall_di @ (^[X4 : $i] : ((mimplies @ (do @ X3 @ X2 @ X4) @ (in @ X0 @ X1 @ X4)))))))))))))))))))))),
% 2.68/0.74 inference(rectify,[],[f19])).
% 2.68/0.74 thf(f42,plain,(
% 2.68/0.74 ~ ($true = ((mlocal @ (mbox @ (mexists_di @ (^[Y0 : $i]: (mexists_di @ (^[Y1 : $i]: (mexists_di @ (^[Y2 : $i]: (mexists_di @ (^[Y3 : $i]: (mand @ (mbox @ (mand @ (userid @ u @ Y0) @ (mand @ (entry_box @ Y1) @ (number @ Y1 @ one)))) @ (mbox @ (mforall_di @ (^[Y4 : $i]: (mimplies @ (do @ Y3 @ Y2 @ Y4) @ (in @ Y0 @ Y1 @ Y4))))))))))))))))))),
% 2.68/0.74 inference(fool_elimination,[],[f41])).
% 2.68/0.74 thf(f43,plain,(
% 2.68/0.74 ! [X0 : mworld,X1 : mworld,X2 : $i] : (((mrel @ X0 @ X1) & (eiw_di @ X2 @ X1)) => (eiw_di @ X2 @ X0))),
% 2.68/0.74 inference(rectify,[],[f12])).
% 2.68/0.74 thf(f44,plain,(
% 2.68/0.74 ! [X0 : mworld,X1 : mworld,X2 : $i] : (((((eiw_di @ X2 @ X1)) = $true) & (((mrel @ X0 @ X1)) = $true)) => (((eiw_di @ X2 @ X0)) = $true))),
% 2.68/0.74 inference(fool_elimination,[],[f43])).
% 2.68/0.74 thf(f45,plain,(
% 2.68/0.74 ! [X0 : mworld] : ? [X1 : $i] : (eiw_di @ X1 @ X0)),
% 2.68/0.74 inference(rectify,[],[f11])).
% 2.68/0.74 thf(f46,plain,(
% 2.68/0.74 ! [X0 : mworld] : ? [X1 : $i] : (((eiw_di @ X1 @ X0)) = $true)),
% 2.68/0.74 inference(fool_elimination,[],[f45])).
% 2.68/0.74 thf(f49,plain,(
% 2.68/0.74 ((^[X0 : ($i > mworld > $o), X1 : mworld] : (? [X2 : $i] : ((X0 @ X2 @ X1) & (eiw_di @ X2 @ X1)))) = mexists_di)),
% 2.68/0.74 inference(rectify,[],[f14])).
% 2.68/0.74 thf(f50,plain,(
% 2.68/0.74 (mexists_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) & (Y0 @ Y2 @ Y1))))))))),
% 2.68/0.74 inference(fool_elimination,[],[f49])).
% 2.68/0.74 thf(f53,plain,(
% 2.68/0.74 (mlocal @ (mexists_di @ (^[X0 : $i] : ((mbox @ (mand @ (entry_box @ X0) @ (number @ X0 @ one)))))))),
% 2.68/0.74 inference(rectify,[],[f16])).
% 2.68/0.74 thf(f54,plain,(
% 2.68/0.74 ($true = ((mlocal @ (mexists_di @ (^[Y0 : $i]: (mbox @ (mand @ (entry_box @ Y0) @ (number @ Y0 @ one))))))))),
% 2.68/0.74 inference(fool_elimination,[],[f53])).
% 2.68/0.74 thf(f55,plain,(
% 2.68/0.74 ($true != ((mlocal @ (mbox @ (mexists_di @ (^[Y0 : $i]: (mexists_di @ (^[Y1 : $i]: (mexists_di @ (^[Y2 : $i]: (mexists_di @ (^[Y3 : $i]: (mand @ (mbox @ (mand @ (userid @ u @ Y0) @ (mand @ (entry_box @ Y1) @ (number @ Y1 @ one)))) @ (mbox @ (mforall_di @ (^[Y4 : $i]: (mimplies @ (do @ Y3 @ Y2 @ Y4) @ (in @ Y0 @ Y1 @ Y4))))))))))))))))))),
% 2.68/0.74 inference(flattening,[],[f42])).
% 2.68/0.74 thf(f56,plain,(
% 2.68/0.74 ! [X1 : mworld,X0 : mworld,X2 : mworld] : ((((mrel @ X2 @ X0)) = $true) | ((((mrel @ X1 @ X0)) != $true) | (((mrel @ X1 @ X2)) != $true)))),
% 2.68/0.74 inference(ennf_transformation,[],[f30])).
% 2.68/0.74 thf(f57,plain,(
% 2.68/0.74 ! [X1 : mworld,X0 : mworld,X2 : mworld] : ((((mrel @ X1 @ X2)) != $true) | (((mrel @ X1 @ X0)) != $true) | (((mrel @ X2 @ X0)) = $true))),
% 2.68/0.74 inference(flattening,[],[f56])).
% 2.68/0.74 thf(f58,plain,(
% 2.68/0.74 ! [X0 : mworld,X1 : mworld,X2 : $i] : ((((eiw_di @ X2 @ X0)) = $true) | ((((eiw_di @ X2 @ X1)) != $true) | (((mrel @ X0 @ X1)) != $true)))),
% 2.68/0.74 inference(ennf_transformation,[],[f44])).
% 2.68/0.74 thf(f59,plain,(
% 2.68/0.74 ! [X0 : mworld,X1 : mworld,X2 : $i] : ((((mrel @ X0 @ X1)) != $true) | (((eiw_di @ X2 @ X0)) = $true) | (((eiw_di @ X2 @ X1)) != $true))),
% 2.68/0.74 inference(flattening,[],[f58])).
% 2.68/0.74 thf(f60,plain,(
% 2.68/0.74 ! [X0 : mworld] : (((eiw_di @ (sK0 @ X0) @ X0)) = $true)),
% 2.68/0.74 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X1,sK0 @ X0)],[f46])).
% 2.68/0.74 thf(f61,plain,(
% 2.68/0.74 ! [X0 : mworld,X1 : mworld,X2 : mworld] : ((((mrel @ X0 @ X2)) != $true) | (((mrel @ X0 @ X1)) != $true) | (((mrel @ X2 @ X1)) = $true))),
% 2.68/0.74 inference(rectify,[],[f57])).
% 2.68/0.74 thf(f62,plain,(
% 2.68/0.74 (mexists_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) & (Y0 @ Y2 @ Y1))))))))),
% 2.68/0.74 inference(cnf_transformation,[],[f50])).
% 2.68/0.74 thf(f63,plain,(
% 2.68/0.74 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 2.68/0.74 inference(cnf_transformation,[],[f23])).
% 2.68/0.74 thf(f64,plain,(
% 2.68/0.74 ( ! [X0 : mworld] : ((((eiw_di @ (sK0 @ X0) @ X0)) = $true)) )),
% 2.68/0.74 inference(cnf_transformation,[],[f60])).
% 2.68/0.74 thf(f65,plain,(
% 2.68/0.74 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 2.68/0.74 inference(cnf_transformation,[],[f34])).
% 2.68/0.74 thf(f66,plain,(
% 2.68/0.74 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))))),
% 2.68/0.74 inference(cnf_transformation,[],[f38])).
% 2.68/0.75 thf(f67,plain,(
% 2.68/0.75 ($true != ((mlocal @ (mbox @ (mexists_di @ (^[Y0 : $i]: (mexists_di @ (^[Y1 : $i]: (mexists_di @ (^[Y2 : $i]: (mexists_di @ (^[Y3 : $i]: (mand @ (mbox @ (mand @ (userid @ u @ Y0) @ (mand @ (entry_box @ Y1) @ (number @ Y1 @ one)))) @ (mbox @ (mforall_di @ (^[Y4 : $i]: (mimplies @ (do @ Y3 @ Y2 @ Y4) @ (in @ Y0 @ Y1 @ Y4))))))))))))))))))),
% 2.68/0.75 inference(cnf_transformation,[],[f55])).
% 2.68/0.75 thf(f68,plain,(
% 2.68/0.75 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 2.68/0.75 inference(cnf_transformation,[],[f28])).
% 2.68/0.75 thf(f69,plain,(
% 2.68/0.75 ( ! [X2 : $i,X0 : mworld,X1 : mworld] : ((((eiw_di @ X2 @ X0)) = $true) | (((mrel @ X0 @ X1)) != $true) | (((eiw_di @ X2 @ X1)) != $true)) )),
% 2.68/0.75 inference(cnf_transformation,[],[f59])).
% 2.68/0.75 thf(f70,plain,(
% 2.68/0.75 ($true = ((mlocal @ (mbox @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mforall_di @ (^[Y2 : $i]: (mimplies @ (mand @ (string @ Y1) @ (entry_box @ Y2)) @ (mexists_di @ (^[Y3 : $i]: (mbox @ (mforall_di @ (^[Y4 : $i]: (mimplies @ (do @ Y0 @ Y3 @ Y4) @ (in @ Y1 @ Y2 @ Y4))))))))))))))))))),
% 2.68/0.75 inference(cnf_transformation,[],[f25])).
% 2.68/0.75 thf(f71,plain,(
% 2.68/0.75 ( ! [X0 : mworld] : ((((mrel @ X0 @ X0)) = $true)) )),
% 2.68/0.75 inference(cnf_transformation,[],[f40])).
% 2.68/0.75 thf(f72,plain,(
% 2.68/0.75 ($true = ((mlocal @ (mbox @ (mexists_di @ (^[Y0 : $i]: (mbox @ (mand @ (userid @ u @ Y0) @ (string @ Y0)))))))))),
% 2.68/0.75 inference(cnf_transformation,[],[f21])).
% 2.68/0.75 thf(f73,plain,(
% 2.68/0.75 ( ! [X2 : mworld,X0 : mworld,X1 : mworld] : ((((mrel @ X2 @ X1)) = $true) | (((mrel @ X0 @ X1)) != $true) | (((mrel @ X0 @ X2)) != $true)) )),
% 2.68/0.75 inference(cnf_transformation,[],[f61])).
% 2.68/0.75 thf(f74,plain,(
% 2.68/0.75 ($true = ((mlocal @ (mexists_di @ (^[Y0 : $i]: (mbox @ (mand @ (entry_box @ Y0) @ (number @ Y0 @ one))))))))),
% 2.68/0.75 inference(cnf_transformation,[],[f54])).
% 2.68/0.75 thf(f75,plain,(
% 2.68/0.75 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) & (Y0 @ Y2))))))))),
% 2.68/0.75 inference(cnf_transformation,[],[f27])).
% 2.68/0.75 thf(f76,definition,(
% 2.68/0.75 ($true != $false)),
% 2.68/0.75 introduced(theory,[fool_distinctness_axiom])).
% 2.68/0.75 thf(f77,definition,(
% 2.68/0.75 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 2.68/0.75 introduced(theory,[fool_exhaustiveness_axiom])).
% 2.68/0.75 thf(f78,plain,(
% 2.68/0.75 ($true != (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) & (Y0 @ Y2 @ Y1))))))) @ (^[Y0 : $i]: ((^[Y1 : $i > mworld > $o]: ((^[Y2 : mworld]: (?? @ $i @ (^[Y3 : $i]: ((eiw_di @ Y3 @ Y2) & (Y1 @ Y3 @ Y2))))))) @ (^[Y1 : $i]: ((^[Y2 : $i > mworld > $o]: ((^[Y3 : mworld]: (?? @ $i @ (^[Y4 : $i]: ((eiw_di @ Y4 @ Y3) & (Y2 @ Y4 @ Y3))))))) @ (^[Y2 : $i]: ((^[Y3 : $i > mworld > $o]: ((^[Y4 : mworld]: (?? @ $i @ (^[Y5 : $i]: ((eiw_di @ Y5 @ Y4) & (Y3 @ Y5 @ Y4))))))) @ (^[Y3 : $i]: ((^[Y4 : mworld > $o]: ((^[Y5 : mworld > $o]: ((^[Y6 : mworld]: ((Y5 @ Y6) & (Y4 @ Y6))))))) @ ((^[Y4 : mworld > $o]: ((^[Y5 : mworld]: (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ ((^[Y4 : mworld > $o]: ((^[Y5 : mworld > $o]: ((^[Y6 : mworld]: ((Y5 @ Y6) & (Y4 @ Y6))))))) @ (userid @ u @ Y0) @ ((^[Y4 : mworld > $o]: ((^[Y5 : mworld > $o]: ((^[Y6 : mworld]: ((Y5 @ Y6) & (Y4 @ Y6))))))) @ (entry_box @ Y1) @ (number @ Y1 @ one)))) @ ((^[Y4 : mworld > $o]: ((^[Y5 : mworld]: (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ ((^[Y4 : $i > mworld > $o]: ((^[Y5 : mworld]: (!! @ $i @ (^[Y6 : $i]: ((eiw_di @ Y6 @ Y5) => (Y4 @ Y6 @ Y5))))))) @ (^[Y4 : $i]: ((^[Y5 : mworld > $o]: ((^[Y6 : mworld > $o]: ((^[Y7 : mworld]: ((Y5 @ Y7) => (Y6 @ Y7))))))) @ (do @ Y3 @ Y2 @ Y4) @ (in @ Y0 @ Y1 @ Y4))))))))))))))))))),
% 2.68/0.75 inference(definition_unfolding,[],[f67,f68,f65,f62,f62,f62,f62,f75,f65,f75,f75,f65,f66,f63])).
% 2.68/0.75 thf(f79,plain,(
% 2.68/0.75 ($true = (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) @ (^[Y0 : $i]: ((^[Y1 : $i > mworld > $o]: ((^[Y2 : mworld]: (!! @ $i @ (^[Y3 : $i]: ((eiw_di @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) @ (^[Y1 : $i]: ((^[Y2 : $i > mworld > $o]: ((^[Y3 : mworld]: (!! @ $i @ (^[Y4 : $i]: ((eiw_di @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) @ (^[Y2 : $i]: ((^[Y3 : mworld > $o]: ((^[Y4 : mworld > $o]: ((^[Y5 : mworld]: ((Y3 @ Y5) => (Y4 @ Y5))))))) @ ((^[Y3 : mworld > $o]: ((^[Y4 : mworld > $o]: ((^[Y5 : mworld]: ((Y4 @ Y5) & (Y3 @ Y5))))))) @ (string @ Y1) @ (entry_box @ Y2)) @ ((^[Y3 : $i > mworld > $o]: ((^[Y4 : mworld]: (?? @ $i @ (^[Y5 : $i]: ((eiw_di @ Y5 @ Y4) & (Y3 @ Y5 @ Y4))))))) @ (^[Y3 : $i]: ((^[Y4 : mworld > $o]: ((^[Y5 : mworld]: (!! @ mworld @ (^[Y6 : mworld]: ((mrel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ ((^[Y4 : $i > mworld > $o]: ((^[Y5 : mworld]: (!! @ $i @ (^[Y6 : $i]: ((eiw_di @ Y6 @ Y5) => (Y4 @ Y6 @ Y5))))))) @ (^[Y4 : $i]: ((^[Y5 : mworld > $o]: ((^[Y6 : mworld > $o]: ((^[Y7 : mworld]: ((Y5 @ Y7) => (Y6 @ Y7))))))) @ (do @ Y0 @ Y3 @ Y4) @ (in @ Y1 @ Y2 @ Y4))))))))))))))))))),
% 2.68/0.75 inference(definition_unfolding,[],[f70,f68,f65,f66,f66,f66,f63,f75,f62,f65,f66,f63])).
% 2.68/0.75 thf(f80,plain,(
% 2.68/0.75 ($true = (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) & (Y0 @ Y2 @ Y1))))))) @ (^[Y0 : $i]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (Y1 @ Y3))))))) @ ((^[Y1 : mworld > $o]: ((^[Y2 : mworld > $o]: ((^[Y3 : mworld]: ((Y2 @ Y3) & (Y1 @ Y3))))))) @ (userid @ u @ Y0) @ (string @ Y0)))))))))),
% 2.68/0.75 inference(definition_unfolding,[],[f72,f68,f65,f62,f65,f75])).
% 2.68/0.75 thf(f81,plain,(
% 2.68/0.75 ($true = (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) & (Y0 @ Y2 @ Y1))))))) @ (^[Y0 : $i]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (Y1 @ Y3))))))) @ ((^[Y1 : mworld > $o]: ((^[Y2 : mworld > $o]: ((^[Y3 : mworld]: ((Y2 @ Y3) & (Y1 @ Y3))))))) @ (entry_box @ Y0) @ (number @ Y0 @ one))))))))),
% 2.68/0.75 inference(definition_unfolding,[],[f74,f68,f62,f65,f75])).
% 2.68/0.75 thf(f82,plain,(
% 2.68/0.75 ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((eiw_di @ Y3 @ Y0) => (((entry_box @ Y3 @ Y0) & (string @ Y2 @ Y0)) => (?? @ $i @ (^[Y4 : $i]: ((eiw_di @ Y4 @ Y0) & (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y0 @ Y5) => (!! @ $i @ (^[Y6 : $i]: ((eiw_di @ Y6 @ Y5) => ((do @ Y1 @ Y4 @ Y6 @ Y5) => (in @ Y2 @ Y3 @ Y6 @ Y5))))))))))))))))))))))))))),
% 2.68/0.75 inference(beta-eta_normalization,[],[f79])).
% 2.68/0.75 thf(f83,plain,(
% 2.68/0.75 ( ! [X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((eiw_di @ Y3 @ Y0) => (((entry_box @ Y3 @ Y0) & (string @ Y2 @ Y0)) => (?? @ $i @ (^[Y4 : $i]: ((eiw_di @ Y4 @ Y0) & (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y0 @ Y5) => (!! @ $i @ (^[Y6 : $i]: ((eiw_di @ Y6 @ Y5) => ((do @ Y1 @ Y4 @ Y6 @ Y5) => (in @ Y2 @ Y3 @ Y6 @ Y5))))))))))))))))))))))) @ X1)))) )),
% 2.68/0.75 inference(pi_proxy_clausification,[],[f82])).
% 2.68/0.75 thf(f84,plain,(
% 2.68/0.75 ( ! [X1 : mworld] : (($true = (((mrel @ mactual @ X1) => (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ X1) => (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ X1) => (((entry_box @ Y2 @ X1) & (string @ Y1 @ X1)) => (?? @ $i @ (^[Y3 : $i]: ((eiw_di @ Y3 @ X1) & (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ X1 @ Y4) => (!! @ $i @ (^[Y5 : $i]: ((eiw_di @ Y5 @ Y4) => ((do @ Y0 @ Y3 @ Y5 @ Y4) => (in @ Y1 @ Y2 @ Y5 @ Y4))))))))))))))))))))))))) )),
% 2.68/0.75 inference(beta-eta_normalization,[],[f83])).
% 2.68/0.75 thf(f85,plain,(
% 2.68/0.75 ( ! [X1 : mworld] : ((((mrel @ mactual @ X1)) = $false) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ X1) => (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ X1) => (((entry_box @ Y2 @ X1) & (string @ Y1 @ X1)) => (?? @ $i @ (^[Y3 : $i]: ((eiw_di @ Y3 @ X1) & (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ X1 @ Y4) => (!! @ $i @ (^[Y5 : $i]: ((eiw_di @ Y5 @ Y4) => ((do @ Y0 @ Y3 @ Y5 @ Y4) => (in @ Y1 @ Y2 @ Y5 @ Y4)))))))))))))))))))))))) )),
% 2.68/0.75 inference(imp_proxy_clausification,[],[f84])).
% 2.68/0.75 thf(f86,plain,(
% 2.68/0.75 ( ! [X2 : $i,X1 : mworld] : ((((mrel @ mactual @ X1)) = $false) | ($true = (((^[Y0 : $i]: ((eiw_di @ Y0 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ X1) => (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ X1) => (((entry_box @ Y2 @ X1) & (string @ Y1 @ X1)) => (?? @ $i @ (^[Y3 : $i]: ((eiw_di @ Y3 @ X1) & (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ X1 @ Y4) => (!! @ $i @ (^[Y5 : $i]: ((eiw_di @ Y5 @ Y4) => ((do @ Y0 @ Y3 @ Y5 @ Y4) => (in @ Y1 @ Y2 @ Y5 @ Y4)))))))))))))))))))) @ X2)))) )),
% 2.68/0.75 inference(pi_proxy_clausification,[],[f85])).
% 2.68/0.75 thf(f87,plain,(
% 2.68/0.75 ( ! [X2 : $i,X1 : mworld] : (($true = (((eiw_di @ X2 @ X1) => (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ X1) => (((entry_box @ Y1 @ X1) & (string @ Y0 @ X1)) => (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ X1) & (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ X1 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((eiw_di @ Y4 @ Y3) => ((do @ X2 @ Y2 @ Y4 @ Y3) => (in @ Y0 @ Y1 @ Y4 @ Y3))))))))))))))))))))) | (((mrel @ mactual @ X1)) = $false)) )),
% 2.68/0.75 inference(beta-eta_normalization,[],[f86])).
% 2.68/0.75 thf(f88,plain,(
% 2.68/0.75 ( ! [X2 : $i,X1 : mworld] : ((((mrel @ mactual @ X1)) = $false) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ X1) => (((entry_box @ Y1 @ X1) & (string @ Y0 @ X1)) => (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ X1) & (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ X1 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((eiw_di @ Y4 @ Y3) => ((do @ X2 @ Y2 @ Y4 @ Y3) => (in @ Y0 @ Y1 @ Y4 @ Y3)))))))))))))))))))) | (((eiw_di @ X2 @ X1)) = $false)) )),
% 2.68/0.75 inference(imp_proxy_clausification,[],[f87])).
% 2.68/0.75 thf(f89,plain,(
% 2.68/0.75 ( ! [X2 : $i,X3 : $i,X1 : mworld] : (($true = (((^[Y0 : $i]: ((eiw_di @ Y0 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ X1) => (((entry_box @ Y1 @ X1) & (string @ Y0 @ X1)) => (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ X1) & (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ X1 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((eiw_di @ Y4 @ Y3) => ((do @ X2 @ Y2 @ Y4 @ Y3) => (in @ Y0 @ Y1 @ Y4 @ Y3))))))))))))))))) @ X3))) | (((mrel @ mactual @ X1)) = $false) | (((eiw_di @ X2 @ X1)) = $false)) )),
% 2.68/0.75 inference(pi_proxy_clausification,[],[f88])).
% 2.68/0.75 thf(f90,plain,(
% 2.68/0.75 ( ! [X2 : $i,X3 : $i,X1 : mworld] : ((((eiw_di @ X2 @ X1)) = $false) | ((((eiw_di @ X3 @ X1) => (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ X1) => (((entry_box @ Y0 @ X1) & (string @ X3 @ X1)) => (?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ X1) & (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ X1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((eiw_di @ Y3 @ Y2) => ((do @ X2 @ Y1 @ Y3 @ Y2) => (in @ X3 @ Y0 @ Y3 @ Y2))))))))))))))))) = $true) | (((mrel @ mactual @ X1)) = $false)) )),
% 2.68/0.75 inference(beta-eta_normalization,[],[f89])).
% 2.68/0.75 thf(f91,plain,(
% 2.68/0.75 ( ! [X2 : $i,X3 : $i,X1 : mworld] : ((((eiw_di @ X2 @ X1)) = $false) | (((eiw_di @ X3 @ X1)) = $false) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ X1) => (((entry_box @ Y0 @ X1) & (string @ X3 @ X1)) => (?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ X1) & (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ X1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((eiw_di @ Y3 @ Y2) => ((do @ X2 @ Y1 @ Y3 @ Y2) => (in @ X3 @ Y0 @ Y3 @ Y2))))))))))))))))) | (((mrel @ mactual @ X1)) = $false)) )),
% 2.68/0.75 inference(imp_proxy_clausification,[],[f90])).
% 2.68/0.75 thf(f92,plain,(
% 2.68/0.75 ( ! [X2 : $i,X3 : $i,X1 : mworld,X4 : $i] : ((((eiw_di @ X2 @ X1)) = $false) | ($true = (((^[Y0 : $i]: ((eiw_di @ Y0 @ X1) => (((entry_box @ Y0 @ X1) & (string @ X3 @ X1)) => (?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ X1) & (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ X1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((eiw_di @ Y3 @ Y2) => ((do @ X2 @ Y1 @ Y3 @ Y2) => (in @ X3 @ Y0 @ Y3 @ Y2)))))))))))))) @ X4))) | (((eiw_di @ X3 @ X1)) = $false) | (((mrel @ mactual @ X1)) = $false)) )),
% 2.68/0.75 inference(pi_proxy_clausification,[],[f91])).
% 2.68/0.75 thf(f93,plain,(
% 2.68/0.75 ( ! [X2 : $i,X3 : $i,X1 : mworld,X4 : $i] : ((((mrel @ mactual @ X1)) = $false) | ($true = (((eiw_di @ X4 @ X1) => (((entry_box @ X4 @ X1) & (string @ X3 @ X1)) => (?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ X1) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ X1 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => ((do @ X2 @ Y0 @ Y2 @ Y1) => (in @ X3 @ X4 @ Y2 @ Y1))))))))))))))) | (((eiw_di @ X3 @ X1)) = $false) | (((eiw_di @ X2 @ X1)) = $false)) )),
% 2.68/0.75 inference(beta-eta_normalization,[],[f92])).
% 2.68/0.75 thf(f94,plain,(
% 2.68/0.75 ( ! [X2 : $i,X3 : $i,X1 : mworld,X4 : $i] : ((((eiw_di @ X2 @ X1)) = $false) | (((eiw_di @ X4 @ X1)) = $false) | (((eiw_di @ X3 @ X1)) = $false) | ($true = ((((entry_box @ X4 @ X1) & (string @ X3 @ X1)) => (?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ X1) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ X1 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => ((do @ X2 @ Y0 @ Y2 @ Y1) => (in @ X3 @ X4 @ Y2 @ Y1)))))))))))))) | (((mrel @ mactual @ X1)) = $false)) )),
% 2.68/0.75 inference(imp_proxy_clausification,[],[f93])).
% 2.68/0.75 thf(f95,plain,(
% 2.68/0.75 ( ! [X2 : $i,X3 : $i,X1 : mworld,X4 : $i] : ((((eiw_di @ X3 @ X1)) = $false) | (((eiw_di @ X4 @ X1)) = $false) | (((mrel @ mactual @ X1)) = $false) | ($false = (((entry_box @ X4 @ X1) & (string @ X3 @ X1)))) | (((?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ X1) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ X1 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => ((do @ X2 @ Y0 @ Y2 @ Y1) => (in @ X3 @ X4 @ Y2 @ Y1)))))))))))) = $true) | (((eiw_di @ X2 @ X1)) = $false)) )),
% 2.68/0.75 inference(imp_proxy_clausification,[],[f94])).
% 2.68/0.75 thf(f96,plain,(
% 2.68/0.75 ( ! [X2 : $i,X3 : $i,X1 : mworld,X4 : $i] : ((((?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ X1) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ X1 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => ((do @ X2 @ Y0 @ Y2 @ Y1) => (in @ X3 @ X4 @ Y2 @ Y1)))))))))))) = $true) | (((string @ X3 @ X1)) = $false) | (((eiw_di @ X4 @ X1)) = $false) | (((eiw_di @ X2 @ X1)) = $false) | (((eiw_di @ X3 @ X1)) = $false) | (((mrel @ mactual @ X1)) = $false) | (((entry_box @ X4 @ X1)) = $false)) )),
% 2.68/0.75 inference(and_proxy_clausification,[],[f95])).
% 2.68/0.75 thf(f97,plain,(
% 2.68/0.75 ( ! [X2 : $i,X3 : $i,X1 : mworld,X4 : $i] : (($true = (((^[Y0 : $i]: ((eiw_di @ Y0 @ X1) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ X1 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => ((do @ X2 @ Y0 @ Y2 @ Y1) => (in @ X3 @ X4 @ Y2 @ Y1)))))))))) @ (sK1 @ X3 @ X1 @ X4 @ X2)))) | (((mrel @ mactual @ X1)) = $false) | (((eiw_di @ X3 @ X1)) = $false) | (((eiw_di @ X2 @ X1)) = $false) | (((entry_box @ X4 @ X1)) = $false) | (((string @ X3 @ X1)) = $false) | (((eiw_di @ X4 @ X1)) = $false)) )),
% 2.68/0.75 inference(sigma_proxy_clausification,[],[f96])).
% 2.68/0.75 thf(f98,plain,(
% 2.68/0.75 ( ! [X2 : $i,X3 : $i,X1 : mworld,X4 : $i] : ((((entry_box @ X4 @ X1)) = $false) | ($true = (((eiw_di @ (sK1 @ X3 @ X1 @ X4 @ X2) @ X1) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => ((do @ X2 @ (sK1 @ X3 @ X1 @ X4 @ X2) @ Y1 @ Y0) => (in @ X3 @ X4 @ Y1 @ Y0))))))))))) | (((mrel @ mactual @ X1)) = $false) | (((eiw_di @ X2 @ X1)) = $false) | (((eiw_di @ X4 @ X1)) = $false) | (((string @ X3 @ X1)) = $false) | (((eiw_di @ X3 @ X1)) = $false)) )),
% 2.68/0.75 inference(beta-eta_normalization,[],[f97])).
% 2.68/0.75 thf(f99,plain,(
% 2.68/0.75 ( ! [X2 : $i,X3 : $i,X1 : mworld,X4 : $i] : ((((string @ X3 @ X1)) = $false) | (((eiw_di @ X4 @ X1)) = $false) | (((eiw_di @ X3 @ X1)) = $false) | (((mrel @ mactual @ X1)) = $false) | (((entry_box @ X4 @ X1)) = $false) | (((eiw_di @ X2 @ X1)) = $false) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => ((do @ X2 @ (sK1 @ X3 @ X1 @ X4 @ X2) @ Y1 @ Y0) => (in @ X3 @ X4 @ Y1 @ Y0))))))))))) )),
% 2.68/0.75 inference(and_proxy_clausification,[],[f98])).
% 2.68/0.75 thf(f100,plain,(
% 2.68/0.75 ( ! [X2 : $i,X3 : $i,X1 : mworld,X4 : $i] : (($true = ((eiw_di @ (sK1 @ X3 @ X1 @ X4 @ X2) @ X1))) | (((eiw_di @ X3 @ X1)) = $false) | (((entry_box @ X4 @ X1)) = $false) | (((eiw_di @ X4 @ X1)) = $false) | (((mrel @ mactual @ X1)) = $false) | (((string @ X3 @ X1)) = $false) | (((eiw_di @ X2 @ X1)) = $false)) )),
% 2.68/0.75 inference(and_proxy_clausification,[],[f98])).
% 2.68/0.75 thf(f101,plain,(
% 2.68/0.75 ( ! [X2 : $i,X3 : $i,X1 : mworld,X4 : $i,X5 : mworld] : ((((eiw_di @ X3 @ X1)) = $false) | (((entry_box @ X4 @ X1)) = $false) | (((mrel @ mactual @ X1)) = $false) | (((string @ X3 @ X1)) = $false) | (((eiw_di @ X2 @ X1)) = $false) | (((eiw_di @ X4 @ X1)) = $false) | ($true = (((^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => ((do @ X2 @ (sK1 @ X3 @ X1 @ X4 @ X2) @ Y1 @ Y0) => (in @ X3 @ X4 @ Y1 @ Y0))))))) @ X5)))) )),
% 2.68/0.75 inference(pi_proxy_clausification,[],[f99])).
% 2.68/0.75 thf(f102,plain,(
% 2.68/0.75 ( ! [X2 : $i,X3 : $i,X1 : mworld,X4 : $i,X5 : mworld] : ((((entry_box @ X4 @ X1)) = $false) | (((eiw_di @ X2 @ X1)) = $false) | (((string @ X3 @ X1)) = $false) | (((mrel @ mactual @ X1)) = $false) | ($true = (((mrel @ X1 @ X5) => (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ X5) => ((do @ X2 @ (sK1 @ X3 @ X1 @ X4 @ X2) @ Y0 @ X5) => (in @ X3 @ X4 @ Y0 @ X5)))))))) | (((eiw_di @ X3 @ X1)) = $false) | (((eiw_di @ X4 @ X1)) = $false)) )),
% 2.68/0.75 inference(beta-eta_normalization,[],[f101])).
% 2.68/0.75 thf(f103,plain,(
% 2.68/0.75 ( ! [X2 : $i,X3 : $i,X1 : mworld,X4 : $i,X5 : mworld] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ X5) => ((do @ X2 @ (sK1 @ X3 @ X1 @ X4 @ X2) @ Y0 @ X5) => (in @ X3 @ X4 @ Y0 @ X5))))))) | (((eiw_di @ X3 @ X1)) = $false) | (((mrel @ mactual @ X1)) = $false) | (((string @ X3 @ X1)) = $false) | ($false = ((mrel @ X1 @ X5))) | (((eiw_di @ X2 @ X1)) = $false) | (((entry_box @ X4 @ X1)) = $false) | (((eiw_di @ X4 @ X1)) = $false)) )),
% 2.68/0.75 inference(imp_proxy_clausification,[],[f102])).
% 2.68/0.75 thf(f104,plain,(
% 2.68/0.75 ( ! [X2 : $i,X3 : $i,X1 : mworld,X6 : $i,X4 : $i,X5 : mworld] : ((((entry_box @ X4 @ X1)) = $false) | (((eiw_di @ X3 @ X1)) = $false) | ($true = (((^[Y0 : $i]: ((eiw_di @ Y0 @ X5) => ((do @ X2 @ (sK1 @ X3 @ X1 @ X4 @ X2) @ Y0 @ X5) => (in @ X3 @ X4 @ Y0 @ X5)))) @ X6))) | ($false = ((mrel @ X1 @ X5))) | (((eiw_di @ X4 @ X1)) = $false) | (((mrel @ mactual @ X1)) = $false) | (((eiw_di @ X2 @ X1)) = $false) | (((string @ X3 @ X1)) = $false)) )),
% 2.68/0.75 inference(pi_proxy_clausification,[],[f103])).
% 2.68/0.75 thf(f105,plain,(
% 2.68/0.75 ( ! [X2 : $i,X3 : $i,X1 : mworld,X6 : $i,X4 : $i,X5 : mworld] : (($false = ((mrel @ X1 @ X5))) | ((((eiw_di @ X6 @ X5) => ((do @ X2 @ (sK1 @ X3 @ X1 @ X4 @ X2) @ X6 @ X5) => (in @ X3 @ X4 @ X6 @ X5)))) = $true) | (((entry_box @ X4 @ X1)) = $false) | (((eiw_di @ X2 @ X1)) = $false) | (((eiw_di @ X3 @ X1)) = $false) | (((mrel @ mactual @ X1)) = $false) | (((eiw_di @ X4 @ X1)) = $false) | (((string @ X3 @ X1)) = $false)) )),
% 2.68/0.75 inference(beta-eta_normalization,[],[f104])).
% 2.68/0.75 thf(f106,plain,(
% 2.68/0.75 ( ! [X2 : $i,X3 : $i,X1 : mworld,X6 : $i,X4 : $i,X5 : mworld] : ((((eiw_di @ X2 @ X1)) = $false) | (((mrel @ mactual @ X1)) = $false) | (((string @ X3 @ X1)) = $false) | (((eiw_di @ X3 @ X1)) = $false) | (((eiw_di @ X4 @ X1)) = $false) | ($false = ((mrel @ X1 @ X5))) | ($true = (((do @ X2 @ (sK1 @ X3 @ X1 @ X4 @ X2) @ X6 @ X5) => (in @ X3 @ X4 @ X6 @ X5)))) | (((entry_box @ X4 @ X1)) = $false) | (((eiw_di @ X6 @ X5)) = $false)) )),
% 2.68/0.75 inference(imp_proxy_clausification,[],[f105])).
% 2.68/0.75 thf(f107,plain,(
% 2.68/0.75 ( ! [X2 : $i,X3 : $i,X1 : mworld,X6 : $i,X4 : $i,X5 : mworld] : ((((do @ X2 @ (sK1 @ X3 @ X1 @ X4 @ X2) @ X6 @ X5)) = $false) | (((string @ X3 @ X1)) = $false) | (((eiw_di @ X3 @ X1)) = $false) | (((eiw_di @ X2 @ X1)) = $false) | ($false = ((mrel @ X1 @ X5))) | ($true = ((in @ X3 @ X4 @ X6 @ X5))) | (((mrel @ mactual @ X1)) = $false) | (((eiw_di @ X4 @ X1)) = $false) | (((entry_box @ X4 @ X1)) = $false) | (((eiw_di @ X6 @ X5)) = $false)) )),
% 2.68/0.75 inference(imp_proxy_clausification,[],[f106])).
% 2.68/0.75 thf(f108,plain,(
% 2.68/0.75 ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) & (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) => ((string @ Y1 @ Y2) & (userid @ u @ Y1 @ Y2)))))))))))))),
% 2.68/0.75 inference(beta-eta_normalization,[],[f80])).
% 2.68/0.75 thf(f109,plain,(
% 2.68/0.75 ( ! [X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) & (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) => ((string @ Y1 @ Y2) & (userid @ u @ Y1 @ Y2)))))))))) @ X1)))) )),
% 2.68/0.75 inference(pi_proxy_clausification,[],[f108])).
% 2.68/0.75 thf(f110,plain,(
% 2.68/0.75 ( ! [X1 : mworld] : (($true = (((mrel @ mactual @ X1) => (?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ X1) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ X1 @ Y1) => ((string @ Y0 @ Y1) & (userid @ u @ Y0 @ Y1)))))))))))) )),
% 2.68/0.75 inference(beta-eta_normalization,[],[f109])).
% 2.68/0.75 thf(f111,plain,(
% 2.68/0.75 ( ! [X1 : mworld] : (($true = ((?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ X1) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ X1 @ Y1) => ((string @ Y0 @ Y1) & (userid @ u @ Y0 @ Y1)))))))))) | (((mrel @ mactual @ X1)) = $false)) )),
% 2.68/0.75 inference(imp_proxy_clausification,[],[f110])).
% 2.68/0.75 thf(f112,plain,(
% 2.68/0.75 ( ! [X1 : mworld] : (($true = (((^[Y0 : $i]: ((eiw_di @ Y0 @ X1) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ X1 @ Y1) => ((string @ Y0 @ Y1) & (userid @ u @ Y0 @ Y1))))))) @ (sK2 @ X1)))) | (((mrel @ mactual @ X1)) = $false)) )),
% 2.68/0.75 inference(sigma_proxy_clausification,[],[f111])).
% 2.68/0.75 thf(f113,plain,(
% 2.68/0.75 ( ! [X1 : mworld] : ((((mrel @ mactual @ X1)) = $false) | ($true = (((eiw_di @ (sK2 @ X1) @ X1) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => ((string @ (sK2 @ X1) @ Y0) & (userid @ u @ (sK2 @ X1) @ Y0))))))))) )),
% 2.68/0.75 inference(beta-eta_normalization,[],[f112])).
% 2.68/0.75 thf(f114,plain,(
% 2.68/0.75 ( ! [X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => ((string @ (sK2 @ X1) @ Y0) & (userid @ u @ (sK2 @ X1) @ Y0))))))) | (((mrel @ mactual @ X1)) = $false)) )),
% 2.68/0.75 inference(and_proxy_clausification,[],[f113])).
% 2.68/0.75 thf(f115,plain,(
% 2.68/0.75 ( ! [X1 : mworld] : (($true = ((eiw_di @ (sK2 @ X1) @ X1))) | (((mrel @ mactual @ X1)) = $false)) )),
% 2.68/0.75 inference(and_proxy_clausification,[],[f113])).
% 2.68/0.75 thf(f116,plain,(
% 2.68/0.75 ( ! [X2 : mworld,X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ X1 @ Y0) => ((string @ (sK2 @ X1) @ Y0) & (userid @ u @ (sK2 @ X1) @ Y0)))) @ X2))) | (((mrel @ mactual @ X1)) = $false)) )),
% 2.68/0.75 inference(pi_proxy_clausification,[],[f114])).
% 2.68/0.75 thf(f117,plain,(
% 2.68/0.75 ( ! [X2 : mworld,X1 : mworld] : (($true = (((mrel @ X1 @ X2) => ((string @ (sK2 @ X1) @ X2) & (userid @ u @ (sK2 @ X1) @ X2))))) | (((mrel @ mactual @ X1)) = $false)) )),
% 2.68/0.75 inference(beta-eta_normalization,[],[f116])).
% 2.68/0.75 thf(f118,plain,(
% 2.68/0.75 ( ! [X2 : mworld,X1 : mworld] : (($true = (((string @ (sK2 @ X1) @ X2) & (userid @ u @ (sK2 @ X1) @ X2)))) | (((mrel @ mactual @ X1)) = $false) | (((mrel @ X1 @ X2)) = $false)) )),
% 2.68/0.75 inference(imp_proxy_clausification,[],[f117])).
% 2.68/0.75 thf(f119,plain,(
% 2.68/0.75 ( ! [X2 : mworld,X1 : mworld] : (($true = ((userid @ u @ (sK2 @ X1) @ X2))) | (((mrel @ mactual @ X1)) = $false) | (((mrel @ X1 @ X2)) = $false)) )),
% 2.68/0.75 inference(and_proxy_clausification,[],[f118])).
% 2.68/0.75 thf(f120,plain,(
% 2.68/0.75 ( ! [X2 : mworld,X1 : mworld] : (($true = ((string @ (sK2 @ X1) @ X2))) | (((mrel @ mactual @ X1)) = $false) | (((mrel @ X1 @ X2)) = $false)) )),
% 2.68/0.75 inference(and_proxy_clausification,[],[f118])).
% 2.68/0.75 thf(f121,plain,(
% 2.68/0.75 (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) & (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y0) & (?? @ $i @ (^[Y3 : $i]: ((eiw_di @ Y3 @ Y0) & (?? @ $i @ (^[Y4 : $i]: ((eiw_di @ Y4 @ Y0) & ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y0 @ Y5) => (!! @ $i @ (^[Y6 : $i]: ((eiw_di @ Y6 @ Y5) => ((do @ Y4 @ Y3 @ Y6 @ Y5) => (in @ Y1 @ Y2 @ Y6 @ Y5)))))))) & (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y0 @ Y5) => (((number @ Y2 @ one @ Y5) & (entry_box @ Y2 @ Y5)) & (userid @ u @ Y1 @ Y5)))))))))))))))))))))) != $true)),
% 2.68/0.75 inference(beta-eta_normalization,[],[f78])).
% 2.68/0.75 thf(f122,plain,(
% 2.68/0.75 ((((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) & (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y0) & (?? @ $i @ (^[Y3 : $i]: ((eiw_di @ Y3 @ Y0) & (?? @ $i @ (^[Y4 : $i]: ((eiw_di @ Y4 @ Y0) & ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y0 @ Y5) => (!! @ $i @ (^[Y6 : $i]: ((eiw_di @ Y6 @ Y5) => ((do @ Y4 @ Y3 @ Y6 @ Y5) => (in @ Y1 @ Y2 @ Y6 @ Y5)))))))) & (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y0 @ Y5) => (((number @ Y2 @ one @ Y5) & (entry_box @ Y2 @ Y5)) & (userid @ u @ Y1 @ Y5)))))))))))))))))))) @ sK3)) = $false)),
% 2.68/0.75 inference(sigma_proxy_clausification,[],[f121])).
% 2.68/0.75 thf(f123,plain,(
% 2.68/0.75 ((((mrel @ mactual @ sK3) => (?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ sK3) & (?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ sK3) & (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ sK3) & (?? @ $i @ (^[Y3 : $i]: ((eiw_di @ Y3 @ sK3) & ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ sK3 @ Y4) => (!! @ $i @ (^[Y5 : $i]: ((eiw_di @ Y5 @ Y4) => ((do @ Y3 @ Y2 @ Y5 @ Y4) => (in @ Y0 @ Y1 @ Y5 @ Y4)))))))) & (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ sK3 @ Y4) => (((number @ Y1 @ one @ Y4) & (entry_box @ Y1 @ Y4)) & (userid @ u @ Y0 @ Y4)))))))))))))))))))) = $false)),
% 2.68/0.75 inference(beta-eta_normalization,[],[f122])).
% 2.68/0.75 thf(f124,plain,(
% 2.68/0.75 (((?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ sK3) & (?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ sK3) & (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ sK3) & (?? @ $i @ (^[Y3 : $i]: ((eiw_di @ Y3 @ sK3) & ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ sK3 @ Y4) => (!! @ $i @ (^[Y5 : $i]: ((eiw_di @ Y5 @ Y4) => ((do @ Y3 @ Y2 @ Y5 @ Y4) => (in @ Y0 @ Y1 @ Y5 @ Y4)))))))) & (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ sK3 @ Y4) => (((number @ Y1 @ one @ Y4) & (entry_box @ Y1 @ Y4)) & (userid @ u @ Y0 @ Y4))))))))))))))))))) = $false)),
% 2.68/0.75 inference(imp_proxy_clausification,[],[f123])).
% 2.68/0.75 thf(f125,plain,(
% 2.68/0.75 ($true = ((mrel @ mactual @ sK3)))),
% 2.68/0.75 inference(imp_proxy_clausification,[],[f123])).
% 2.68/0.75 thf(f126,plain,(
% 2.68/0.75 ( ! [X1 : $i] : (($false = (((^[Y0 : $i]: ((eiw_di @ Y0 @ sK3) & (?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ sK3) & (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ sK3) & (?? @ $i @ (^[Y3 : $i]: ((eiw_di @ Y3 @ sK3) & ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ sK3 @ Y4) => (!! @ $i @ (^[Y5 : $i]: ((eiw_di @ Y5 @ Y4) => ((do @ Y3 @ Y2 @ Y5 @ Y4) => (in @ Y0 @ Y1 @ Y5 @ Y4)))))))) & (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ sK3 @ Y4) => (((number @ Y1 @ one @ Y4) & (entry_box @ Y1 @ Y4)) & (userid @ u @ Y0 @ Y4))))))))))))))))) @ X1)))) )),
% 2.68/0.75 inference(pi_proxy_clausification,[],[f124])).
% 2.68/0.75 thf(f127,plain,(
% 2.68/0.75 ( ! [X1 : $i] : (($false = (((eiw_di @ X1 @ sK3) & (?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ sK3) & (?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ sK3) & (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ sK3) & ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ sK3 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((eiw_di @ Y4 @ Y3) => ((do @ Y2 @ Y1 @ Y4 @ Y3) => (in @ X1 @ Y0 @ Y4 @ Y3)))))))) & (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ sK3 @ Y3) => (((number @ Y0 @ one @ Y3) & (entry_box @ Y0 @ Y3)) & (userid @ u @ X1 @ Y3))))))))))))))))))) )),
% 2.68/0.75 inference(beta-eta_normalization,[],[f126])).
% 2.68/0.75 thf(f128,plain,(
% 2.68/0.75 ( ! [X1 : $i] : ((((?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ sK3) & (?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ sK3) & (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ sK3) & ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ sK3 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((eiw_di @ Y4 @ Y3) => ((do @ Y2 @ Y1 @ Y4 @ Y3) => (in @ X1 @ Y0 @ Y4 @ Y3)))))))) & (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ sK3 @ Y3) => (((number @ Y0 @ one @ Y3) & (entry_box @ Y0 @ Y3)) & (userid @ u @ X1 @ Y3)))))))))))))))) = $false) | (((eiw_di @ X1 @ sK3)) = $false)) )),
% 2.68/0.75 inference(and_proxy_clausification,[],[f127])).
% 2.68/0.75 thf(f129,plain,(
% 2.68/0.75 ( ! [X2 : $i,X1 : $i] : ((((eiw_di @ X1 @ sK3)) = $false) | ((((^[Y0 : $i]: ((eiw_di @ Y0 @ sK3) & (?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ sK3) & (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ sK3) & ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ sK3 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((eiw_di @ Y4 @ Y3) => ((do @ Y2 @ Y1 @ Y4 @ Y3) => (in @ X1 @ Y0 @ Y4 @ Y3)))))))) & (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ sK3 @ Y3) => (((number @ Y0 @ one @ Y3) & (entry_box @ Y0 @ Y3)) & (userid @ u @ X1 @ Y3)))))))))))))) @ X2)) = $false)) )),
% 2.68/0.75 inference(pi_proxy_clausification,[],[f128])).
% 2.68/0.75 thf(f130,plain,(
% 2.68/0.75 ( ! [X2 : $i,X1 : $i] : ((((eiw_di @ X1 @ sK3)) = $false) | ((((eiw_di @ X2 @ sK3) & (?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ sK3) & (?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ sK3) & ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ sK3 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((eiw_di @ Y3 @ Y2) => ((do @ Y1 @ Y0 @ Y3 @ Y2) => (in @ X1 @ X2 @ Y3 @ Y2)))))))) & (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ sK3 @ Y2) => (((number @ X2 @ one @ Y2) & (entry_box @ X2 @ Y2)) & (userid @ u @ X1 @ Y2)))))))))))))) = $false)) )),
% 2.68/0.75 inference(beta-eta_normalization,[],[f129])).
% 2.68/0.75 thf(f131,plain,(
% 2.68/0.75 ( ! [X2 : $i,X1 : $i] : ((((eiw_di @ X1 @ sK3)) = $false) | ($false = ((?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ sK3) & (?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ sK3) & ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ sK3 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((eiw_di @ Y3 @ Y2) => ((do @ Y1 @ Y0 @ Y3 @ Y2) => (in @ X1 @ X2 @ Y3 @ Y2)))))))) & (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ sK3 @ Y2) => (((number @ X2 @ one @ Y2) & (entry_box @ X2 @ Y2)) & (userid @ u @ X1 @ Y2)))))))))))))) | (((eiw_di @ X2 @ sK3)) = $false)) )),
% 2.68/0.75 inference(and_proxy_clausification,[],[f130])).
% 2.68/0.75 thf(f132,plain,(
% 2.68/0.75 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((eiw_di @ X2 @ sK3)) = $false) | (((eiw_di @ X1 @ sK3)) = $false) | ((((^[Y0 : $i]: ((eiw_di @ Y0 @ sK3) & (?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ sK3) & ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ sK3 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((eiw_di @ Y3 @ Y2) => ((do @ Y1 @ Y0 @ Y3 @ Y2) => (in @ X1 @ X2 @ Y3 @ Y2)))))))) & (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ sK3 @ Y2) => (((number @ X2 @ one @ Y2) & (entry_box @ X2 @ Y2)) & (userid @ u @ X1 @ Y2))))))))))) @ X3)) = $false)) )),
% 2.68/0.75 inference(pi_proxy_clausification,[],[f131])).
% 2.68/0.75 thf(f133,plain,(
% 2.68/0.75 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((eiw_di @ X2 @ sK3)) = $false) | (((eiw_di @ X1 @ sK3)) = $false) | ((((eiw_di @ X3 @ sK3) & (?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ sK3) & ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ sK3 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => ((do @ Y0 @ X3 @ Y2 @ Y1) => (in @ X1 @ X2 @ Y2 @ Y1)))))))) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ sK3 @ Y1) => (((number @ X2 @ one @ Y1) & (entry_box @ X2 @ Y1)) & (userid @ u @ X1 @ Y1))))))))))) = $false)) )),
% 2.68/0.75 inference(beta-eta_normalization,[],[f132])).
% 2.68/0.75 thf(f134,plain,(
% 2.68/0.75 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((eiw_di @ X2 @ sK3)) = $false) | (((eiw_di @ X3 @ sK3)) = $false) | ($false = ((?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ sK3) & ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ sK3 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => ((do @ Y0 @ X3 @ Y2 @ Y1) => (in @ X1 @ X2 @ Y2 @ Y1)))))))) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ sK3 @ Y1) => (((number @ X2 @ one @ Y1) & (entry_box @ X2 @ Y1)) & (userid @ u @ X1 @ Y1))))))))))) | (((eiw_di @ X1 @ sK3)) = $false)) )),
% 2.68/0.75 inference(and_proxy_clausification,[],[f133])).
% 2.68/0.75 thf(f135,plain,(
% 2.68/0.75 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((eiw_di @ X2 @ sK3)) = $false) | ((((^[Y0 : $i]: ((eiw_di @ Y0 @ sK3) & ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ sK3 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => ((do @ Y0 @ X3 @ Y2 @ Y1) => (in @ X1 @ X2 @ Y2 @ Y1)))))))) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ sK3 @ Y1) => (((number @ X2 @ one @ Y1) & (entry_box @ X2 @ Y1)) & (userid @ u @ X1 @ Y1)))))))) @ X4)) = $false) | (((eiw_di @ X3 @ sK3)) = $false) | (((eiw_di @ X1 @ sK3)) = $false)) )),
% 2.68/0.75 inference(pi_proxy_clausification,[],[f134])).
% 2.68/0.75 thf(f136,plain,(
% 2.68/0.75 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((eiw_di @ X2 @ sK3)) = $false) | (((eiw_di @ X1 @ sK3)) = $false) | ((((eiw_di @ X4 @ sK3) & ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK3 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => ((do @ X4 @ X3 @ Y1 @ Y0) => (in @ X1 @ X2 @ Y1 @ Y0)))))))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK3 @ Y0) => (((number @ X2 @ one @ Y0) & (entry_box @ X2 @ Y0)) & (userid @ u @ X1 @ Y0)))))))) = $false) | (((eiw_di @ X3 @ sK3)) = $false)) )),
% 2.68/0.75 inference(beta-eta_normalization,[],[f135])).
% 2.68/0.75 thf(f137,plain,(
% 2.68/0.75 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((eiw_di @ X4 @ sK3)) = $false) | (((eiw_di @ X1 @ sK3)) = $false) | (((eiw_di @ X2 @ sK3)) = $false) | ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK3 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => ((do @ X4 @ X3 @ Y1 @ Y0) => (in @ X1 @ X2 @ Y1 @ Y0)))))))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK3 @ Y0) => (((number @ X2 @ one @ Y0) & (entry_box @ X2 @ Y0)) & (userid @ u @ X1 @ Y0))))))) = $false) | (((eiw_di @ X3 @ sK3)) = $false)) )),
% 2.68/0.75 inference(and_proxy_clausification,[],[f136])).
% 2.68/0.75 thf(f138,plain,(
% 2.68/0.75 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK3 @ Y0) => (((number @ X2 @ one @ Y0) & (entry_box @ X2 @ Y0)) & (userid @ u @ X1 @ Y0)))))) = $false) | (((eiw_di @ X2 @ sK3)) = $false) | (((eiw_di @ X4 @ sK3)) = $false) | (((eiw_di @ X3 @ sK3)) = $false) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK3 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => ((do @ X4 @ X3 @ Y1 @ Y0) => (in @ X1 @ X2 @ Y1 @ Y0))))))))) = $false) | (((eiw_di @ X1 @ sK3)) = $false)) )),
% 2.68/0.75 inference(and_proxy_clausification,[],[f137])).
% 2.68/0.75 thf(f139,plain,(
% 2.68/0.75 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((eiw_di @ X4 @ sK3)) = $false) | (((eiw_di @ X3 @ sK3)) = $false) | ((((^[Y0 : mworld]: ((mrel @ sK3 @ Y0) => (((number @ X2 @ one @ Y0) & (entry_box @ X2 @ Y0)) & (userid @ u @ X1 @ Y0)))) @ (sK4 @ X1 @ X2))) = $false) | (((eiw_di @ X1 @ sK3)) = $false) | (((eiw_di @ X2 @ sK3)) = $false) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK3 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => ((do @ X4 @ X3 @ Y1 @ Y0) => (in @ X1 @ X2 @ Y1 @ Y0))))))))) = $false)) )),
% 2.68/0.75 inference(sigma_proxy_clausification,[],[f138])).
% 2.68/0.75 thf(f140,plain,(
% 2.68/0.75 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((eiw_di @ X4 @ sK3)) = $false) | (((eiw_di @ X3 @ sK3)) = $false) | (((eiw_di @ X2 @ sK3)) = $false) | (((eiw_di @ X1 @ sK3)) = $false) | ((((^[Y0 : mworld]: ((mrel @ sK3 @ Y0) => (((number @ X2 @ one @ Y0) & (entry_box @ X2 @ Y0)) & (userid @ u @ X1 @ Y0)))) @ (sK4 @ X1 @ X2))) = $false) | ((((^[Y0 : mworld]: ((mrel @ sK3 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => ((do @ X4 @ X3 @ Y1 @ Y0) => (in @ X1 @ X2 @ Y1 @ Y0))))))) @ (sK5 @ X3 @ X1 @ X4 @ X2))) = $false)) )),
% 2.68/0.75 inference(sigma_proxy_clausification,[],[f139])).
% 2.68/0.75 thf(f141,plain,(
% 2.68/0.75 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((((mrel @ sK3 @ (sK4 @ X1 @ X2)) => (((number @ X2 @ one @ (sK4 @ X1 @ X2)) & (entry_box @ X2 @ (sK4 @ X1 @ X2))) & (userid @ u @ X1 @ (sK4 @ X1 @ X2))))) = $false) | (((eiw_di @ X1 @ sK3)) = $false) | ((((mrel @ sK3 @ (sK5 @ X3 @ X1 @ X4 @ X2)) => (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ (sK5 @ X3 @ X1 @ X4 @ X2)) => ((do @ X4 @ X3 @ Y0 @ (sK5 @ X3 @ X1 @ X4 @ X2)) => (in @ X1 @ X2 @ Y0 @ (sK5 @ X3 @ X1 @ X4 @ X2)))))))) = $false) | (((eiw_di @ X2 @ sK3)) = $false) | (((eiw_di @ X4 @ sK3)) = $false) | (((eiw_di @ X3 @ sK3)) = $false)) )),
% 2.68/0.75 inference(beta-eta_normalization,[],[f140])).
% 2.68/0.75 thf(f142,plain,(
% 2.68/0.75 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((eiw_di @ X4 @ sK3)) = $false) | ((((mrel @ sK3 @ (sK5 @ X3 @ X1 @ X4 @ X2)) => (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ (sK5 @ X3 @ X1 @ X4 @ X2)) => ((do @ X4 @ X3 @ Y0 @ (sK5 @ X3 @ X1 @ X4 @ X2)) => (in @ X1 @ X2 @ Y0 @ (sK5 @ X3 @ X1 @ X4 @ X2)))))))) = $false) | (((((number @ X2 @ one @ (sK4 @ X1 @ X2)) & (entry_box @ X2 @ (sK4 @ X1 @ X2))) & (userid @ u @ X1 @ (sK4 @ X1 @ X2)))) = $false) | (((eiw_di @ X1 @ sK3)) = $false) | (((eiw_di @ X3 @ sK3)) = $false) | (((eiw_di @ X2 @ sK3)) = $false)) )),
% 2.68/0.75 inference(imp_proxy_clausification,[],[f141])).
% 2.68/0.75 thf(f143,plain,(
% 2.68/0.75 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((eiw_di @ X3 @ sK3)) = $false) | (((eiw_di @ X4 @ sK3)) = $false) | ((((mrel @ sK3 @ (sK5 @ X3 @ X1 @ X4 @ X2)) => (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ (sK5 @ X3 @ X1 @ X4 @ X2)) => ((do @ X4 @ X3 @ Y0 @ (sK5 @ X3 @ X1 @ X4 @ X2)) => (in @ X1 @ X2 @ Y0 @ (sK5 @ X3 @ X1 @ X4 @ X2)))))))) = $false) | (((eiw_di @ X1 @ sK3)) = $false) | (((eiw_di @ X2 @ sK3)) = $false) | ($true = ((mrel @ sK3 @ (sK4 @ X1 @ X2))))) )),
% 2.68/0.75 inference(imp_proxy_clausification,[],[f141])).
% 2.68/0.75 thf(f144,plain,(
% 2.68/0.75 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ (sK5 @ X3 @ X1 @ X4 @ X2)) => ((do @ X4 @ X3 @ Y0 @ (sK5 @ X3 @ X1 @ X4 @ X2)) => (in @ X1 @ X2 @ Y0 @ (sK5 @ X3 @ X1 @ X4 @ X2)))))))) | ($true = ((mrel @ sK3 @ (sK4 @ X1 @ X2)))) | (((eiw_di @ X1 @ sK3)) = $false) | (((eiw_di @ X2 @ sK3)) = $false) | (((eiw_di @ X4 @ sK3)) = $false) | (((eiw_di @ X3 @ sK3)) = $false)) )),
% 2.68/0.75 inference(imp_proxy_clausification,[],[f143])).
% 2.68/0.75 thf(f145,plain,(
% 2.68/0.75 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((mrel @ sK3 @ (sK5 @ X3 @ X1 @ X4 @ X2)))) | ($true = ((mrel @ sK3 @ (sK4 @ X1 @ X2)))) | (((eiw_di @ X4 @ sK3)) = $false) | (((eiw_di @ X1 @ sK3)) = $false) | (((eiw_di @ X3 @ sK3)) = $false) | (((eiw_di @ X2 @ sK3)) = $false)) )),
% 2.68/0.75 inference(imp_proxy_clausification,[],[f143])).
% 2.68/0.75 thf(f146,plain,(
% 2.68/0.75 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((mrel @ sK3 @ (sK4 @ X1 @ X2)))) | (((eiw_di @ X1 @ sK3)) = $false) | (((eiw_di @ X4 @ sK3)) = $false) | (((eiw_di @ X3 @ sK3)) = $false) | ($false = (((^[Y0 : $i]: ((eiw_di @ Y0 @ (sK5 @ X3 @ X1 @ X4 @ X2)) => ((do @ X4 @ X3 @ Y0 @ (sK5 @ X3 @ X1 @ X4 @ X2)) => (in @ X1 @ X2 @ Y0 @ (sK5 @ X3 @ X1 @ X4 @ X2))))) @ (sK6 @ X1 @ X2 @ X3 @ X4)))) | (((eiw_di @ X2 @ sK3)) = $false)) )),
% 2.68/0.75 inference(sigma_proxy_clausification,[],[f144])).
% 2.68/0.75 thf(f147,plain,(
% 2.68/0.75 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((mrel @ sK3 @ (sK4 @ X1 @ X2)))) | (((eiw_di @ X3 @ sK3)) = $false) | (((eiw_di @ X4 @ sK3)) = $false) | ((((eiw_di @ (sK6 @ X1 @ X2 @ X3 @ X4) @ (sK5 @ X3 @ X1 @ X4 @ X2)) => ((do @ X4 @ X3 @ (sK6 @ X1 @ X2 @ X3 @ X4) @ (sK5 @ X3 @ X1 @ X4 @ X2)) => (in @ X1 @ X2 @ (sK6 @ X1 @ X2 @ X3 @ X4) @ (sK5 @ X3 @ X1 @ X4 @ X2))))) = $false) | (((eiw_di @ X1 @ sK3)) = $false) | (((eiw_di @ X2 @ sK3)) = $false)) )),
% 2.68/0.75 inference(beta-eta_normalization,[],[f146])).
% 2.68/0.75 thf(f148,plain,(
% 2.68/0.75 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((eiw_di @ X2 @ sK3)) = $false) | ($false = (((do @ X4 @ X3 @ (sK6 @ X1 @ X2 @ X3 @ X4) @ (sK5 @ X3 @ X1 @ X4 @ X2)) => (in @ X1 @ X2 @ (sK6 @ X1 @ X2 @ X3 @ X4) @ (sK5 @ X3 @ X1 @ X4 @ X2))))) | ($true = ((mrel @ sK3 @ (sK4 @ X1 @ X2)))) | (((eiw_di @ X4 @ sK3)) = $false) | (((eiw_di @ X3 @ sK3)) = $false) | (((eiw_di @ X1 @ sK3)) = $false)) )),
% 2.68/0.75 inference(imp_proxy_clausification,[],[f147])).
% 2.68/0.75 thf(f149,plain,(
% 2.68/0.75 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((eiw_di @ (sK6 @ X1 @ X2 @ X3 @ X4) @ (sK5 @ X3 @ X1 @ X4 @ X2))) = $true) | (((eiw_di @ X3 @ sK3)) = $false) | (((eiw_di @ X4 @ sK3)) = $false) | (((eiw_di @ X2 @ sK3)) = $false) | (((eiw_di @ X1 @ sK3)) = $false) | ($true = ((mrel @ sK3 @ (sK4 @ X1 @ X2))))) )),
% 2.68/0.75 inference(imp_proxy_clausification,[],[f147])).
% 2.68/0.75 thf(f150,plain,(
% 2.68/0.75 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((in @ X1 @ X2 @ (sK6 @ X1 @ X2 @ X3 @ X4) @ (sK5 @ X3 @ X1 @ X4 @ X2)))) | (((eiw_di @ X2 @ sK3)) = $false) | ($true = ((mrel @ sK3 @ (sK4 @ X1 @ X2)))) | (((eiw_di @ X3 @ sK3)) = $false) | (((eiw_di @ X1 @ sK3)) = $false) | (((eiw_di @ X4 @ sK3)) = $false)) )),
% 2.68/0.75 inference(imp_proxy_clausification,[],[f148])).
% 2.68/0.75 thf(f151,plain,(
% 2.68/0.75 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((do @ X4 @ X3 @ (sK6 @ X1 @ X2 @ X3 @ X4) @ (sK5 @ X3 @ X1 @ X4 @ X2)))) | (((eiw_di @ X1 @ sK3)) = $false) | (((eiw_di @ X4 @ sK3)) = $false) | (((eiw_di @ X2 @ sK3)) = $false) | (((eiw_di @ X3 @ sK3)) = $false) | ($true = ((mrel @ sK3 @ (sK4 @ X1 @ X2))))) )),
% 2.68/0.75 inference(imp_proxy_clausification,[],[f148])).
% 2.68/0.75 thf(f152,plain,(
% 2.68/0.75 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((eiw_di @ X3 @ sK3)) = $false) | (((((number @ X2 @ one @ (sK4 @ X1 @ X2)) & (entry_box @ X2 @ (sK4 @ X1 @ X2))) & (userid @ u @ X1 @ (sK4 @ X1 @ X2)))) = $false) | (((eiw_di @ X4 @ sK3)) = $false) | (((eiw_di @ X2 @ sK3)) = $false) | (((eiw_di @ X1 @ sK3)) = $false) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ (sK5 @ X3 @ X1 @ X4 @ X2)) => ((do @ X4 @ X3 @ Y0 @ (sK5 @ X3 @ X1 @ X4 @ X2)) => (in @ X1 @ X2 @ Y0 @ (sK5 @ X3 @ X1 @ X4 @ X2))))))))) )),
% 2.68/0.75 inference(imp_proxy_clausification,[],[f142])).
% 2.68/0.75 thf(f153,plain,(
% 2.68/0.75 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((eiw_di @ X4 @ sK3)) = $false) | (((eiw_di @ X3 @ sK3)) = $false) | (((eiw_di @ X1 @ sK3)) = $false) | (((eiw_di @ X2 @ sK3)) = $false) | (((((number @ X2 @ one @ (sK4 @ X1 @ X2)) & (entry_box @ X2 @ (sK4 @ X1 @ X2))) & (userid @ u @ X1 @ (sK4 @ X1 @ X2)))) = $false) | ($true = ((mrel @ sK3 @ (sK5 @ X3 @ X1 @ X4 @ X2))))) )),
% 2.68/0.75 inference(imp_proxy_clausification,[],[f142])).
% 2.68/0.75 thf(f154,plain,(
% 2.68/0.75 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((eiw_di @ X4 @ sK3)) = $false) | (((eiw_di @ X3 @ sK3)) = $false) | ((((number @ X2 @ one @ (sK4 @ X1 @ X2)) & (entry_box @ X2 @ (sK4 @ X1 @ X2)))) = $false) | (((eiw_di @ X2 @ sK3)) = $false) | (((eiw_di @ X1 @ sK3)) = $false) | ($false = ((userid @ u @ X1 @ (sK4 @ X1 @ X2)))) | ($true = ((mrel @ sK3 @ (sK5 @ X3 @ X1 @ X4 @ X2))))) )),
% 2.68/0.75 inference(and_proxy_clausification,[],[f153])).
% 2.68/0.75 thf(f155,plain,(
% 2.68/0.75 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((mrel @ sK3 @ (sK5 @ X3 @ X1 @ X4 @ X2)))) | (((eiw_di @ X2 @ sK3)) = $false) | (((eiw_di @ X3 @ sK3)) = $false) | ($false = ((userid @ u @ X1 @ (sK4 @ X1 @ X2)))) | (((eiw_di @ X1 @ sK3)) = $false) | (((eiw_di @ X4 @ sK3)) = $false) | ($false = ((number @ X2 @ one @ (sK4 @ X1 @ X2)))) | (((entry_box @ X2 @ (sK4 @ X1 @ X2))) = $false)) )),
% 2.68/0.75 inference(and_proxy_clausification,[],[f154])).
% 2.68/0.75 thf(f156,plain,(
% 2.68/0.75 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ (sK5 @ X3 @ X1 @ X4 @ X2)) => ((do @ X4 @ X3 @ Y0 @ (sK5 @ X3 @ X1 @ X4 @ X2)) => (in @ X1 @ X2 @ Y0 @ (sK5 @ X3 @ X1 @ X4 @ X2)))))))) | ((((number @ X2 @ one @ (sK4 @ X1 @ X2)) & (entry_box @ X2 @ (sK4 @ X1 @ X2)))) = $false) | (((eiw_di @ X4 @ sK3)) = $false) | ($false = ((userid @ u @ X1 @ (sK4 @ X1 @ X2)))) | (((eiw_di @ X3 @ sK3)) = $false) | (((eiw_di @ X1 @ sK3)) = $false) | (((eiw_di @ X2 @ sK3)) = $false)) )),
% 2.68/0.75 inference(and_proxy_clausification,[],[f152])).
% 2.68/0.75 thf(f157,plain,(
% 2.68/0.75 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((eiw_di @ X4 @ sK3)) = $false) | (((eiw_di @ X2 @ sK3)) = $false) | ((((number @ X2 @ one @ (sK4 @ X1 @ X2)) & (entry_box @ X2 @ (sK4 @ X1 @ X2)))) = $false) | ($false = (((^[Y0 : $i]: ((eiw_di @ Y0 @ (sK5 @ X3 @ X1 @ X4 @ X2)) => ((do @ X4 @ X3 @ Y0 @ (sK5 @ X3 @ X1 @ X4 @ X2)) => (in @ X1 @ X2 @ Y0 @ (sK5 @ X3 @ X1 @ X4 @ X2))))) @ (sK7 @ X1 @ X3 @ X4 @ X2)))) | (((eiw_di @ X1 @ sK3)) = $false) | (((eiw_di @ X3 @ sK3)) = $false) | ($false = ((userid @ u @ X1 @ (sK4 @ X1 @ X2))))) )),
% 2.68/0.75 inference(sigma_proxy_clausification,[],[f156])).
% 2.68/0.75 thf(f158,plain,(
% 2.68/0.75 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (((^[Y0 : $i]: ((eiw_di @ Y0 @ (sK5 @ X3 @ X1 @ X4 @ X2)) => ((do @ X4 @ X3 @ Y0 @ (sK5 @ X3 @ X1 @ X4 @ X2)) => (in @ X1 @ X2 @ Y0 @ (sK5 @ X3 @ X1 @ X4 @ X2))))) @ (sK7 @ X1 @ X3 @ X4 @ X2)))) | (((eiw_di @ X4 @ sK3)) = $false) | (((entry_box @ X2 @ (sK4 @ X1 @ X2))) = $false) | (((eiw_di @ X1 @ sK3)) = $false) | ($false = ((userid @ u @ X1 @ (sK4 @ X1 @ X2)))) | (((eiw_di @ X2 @ sK3)) = $false) | (((eiw_di @ X3 @ sK3)) = $false) | ($false = ((number @ X2 @ one @ (sK4 @ X1 @ X2))))) )),
% 2.68/0.75 inference(and_proxy_clausification,[],[f157])).
% 2.68/0.75 thf(f159,plain,(
% 2.68/0.75 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((userid @ u @ X1 @ (sK4 @ X1 @ X2)))) | (((entry_box @ X2 @ (sK4 @ X1 @ X2))) = $false) | (((eiw_di @ X3 @ sK3)) = $false) | (((eiw_di @ X1 @ sK3)) = $false) | (((eiw_di @ X4 @ sK3)) = $false) | ($false = ((number @ X2 @ one @ (sK4 @ X1 @ X2)))) | ((((eiw_di @ (sK7 @ X1 @ X3 @ X4 @ X2) @ (sK5 @ X3 @ X1 @ X4 @ X2)) => ((do @ X4 @ X3 @ (sK7 @ X1 @ X3 @ X4 @ X2) @ (sK5 @ X3 @ X1 @ X4 @ X2)) => (in @ X1 @ X2 @ (sK7 @ X1 @ X3 @ X4 @ X2) @ (sK5 @ X3 @ X1 @ X4 @ X2))))) = $false) | (((eiw_di @ X2 @ sK3)) = $false)) )),
% 2.68/0.75 inference(beta-eta_normalization,[],[f158])).
% 2.68/0.75 thf(f160,plain,(
% 2.68/0.75 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((eiw_di @ X1 @ sK3)) = $false) | (((entry_box @ X2 @ (sK4 @ X1 @ X2))) = $false) | (((eiw_di @ X2 @ sK3)) = $false) | ($false = ((userid @ u @ X1 @ (sK4 @ X1 @ X2)))) | (((eiw_di @ X3 @ sK3)) = $false) | (((eiw_di @ X4 @ sK3)) = $false) | ((((do @ X4 @ X3 @ (sK7 @ X1 @ X3 @ X4 @ X2) @ (sK5 @ X3 @ X1 @ X4 @ X2)) => (in @ X1 @ X2 @ (sK7 @ X1 @ X3 @ X4 @ X2) @ (sK5 @ X3 @ X1 @ X4 @ X2)))) = $false) | ($false = ((number @ X2 @ one @ (sK4 @ X1 @ X2))))) )),
% 2.68/0.75 inference(imp_proxy_clausification,[],[f159])).
% 2.68/0.75 thf(f161,plain,(
% 2.68/0.75 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((eiw_di @ (sK7 @ X1 @ X3 @ X4 @ X2) @ (sK5 @ X3 @ X1 @ X4 @ X2)))) | (((eiw_di @ X1 @ sK3)) = $false) | (((eiw_di @ X4 @ sK3)) = $false) | (((eiw_di @ X3 @ sK3)) = $false) | (((eiw_di @ X2 @ sK3)) = $false) | ($false = ((userid @ u @ X1 @ (sK4 @ X1 @ X2)))) | ($false = ((number @ X2 @ one @ (sK4 @ X1 @ X2)))) | (((entry_box @ X2 @ (sK4 @ X1 @ X2))) = $false)) )),
% 2.68/0.75 inference(imp_proxy_clausification,[],[f159])).
% 2.68/0.75 thf(f162,plain,(
% 2.68/0.75 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((in @ X1 @ X2 @ (sK7 @ X1 @ X3 @ X4 @ X2) @ (sK5 @ X3 @ X1 @ X4 @ X2))) = $false) | (((eiw_di @ X2 @ sK3)) = $false) | (((eiw_di @ X1 @ sK3)) = $false) | (((entry_box @ X2 @ (sK4 @ X1 @ X2))) = $false) | ($false = ((userid @ u @ X1 @ (sK4 @ X1 @ X2)))) | ($false = ((number @ X2 @ one @ (sK4 @ X1 @ X2)))) | (((eiw_di @ X3 @ sK3)) = $false) | (((eiw_di @ X4 @ sK3)) = $false)) )),
% 2.68/0.75 inference(imp_proxy_clausification,[],[f160])).
% 2.68/0.75 thf(f163,plain,(
% 2.68/0.75 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((do @ X4 @ X3 @ (sK7 @ X1 @ X3 @ X4 @ X2) @ (sK5 @ X3 @ X1 @ X4 @ X2)))) | (((eiw_di @ X4 @ sK3)) = $false) | (((entry_box @ X2 @ (sK4 @ X1 @ X2))) = $false) | ($false = ((number @ X2 @ one @ (sK4 @ X1 @ X2)))) | (((eiw_di @ X3 @ sK3)) = $false) | (((eiw_di @ X2 @ sK3)) = $false) | ($false = ((userid @ u @ X1 @ (sK4 @ X1 @ X2)))) | (((eiw_di @ X1 @ sK3)) = $false)) )),
% 2.68/0.75 inference(imp_proxy_clausification,[],[f160])).
% 2.68/0.75 thf(f164,plain,(
% 2.68/0.75 (((?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ mactual @ Y1) => ((number @ Y0 @ one @ Y1) & (entry_box @ Y0 @ Y1))))))))) = $true)),
% 2.68/0.75 inference(beta-eta_normalization,[],[f81])).
% 2.68/0.75 thf(f165,plain,(
% 2.68/0.75 ((((^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ mactual @ Y1) => ((number @ Y0 @ one @ Y1) & (entry_box @ Y0 @ Y1))))))) @ sK8)) = $true)),
% 2.68/0.75 inference(sigma_proxy_clausification,[],[f164])).
% 2.68/0.75 thf(f166,plain,(
% 2.68/0.75 ($true = (((eiw_di @ sK8 @ mactual) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((number @ sK8 @ one @ Y0) & (entry_box @ sK8 @ Y0))))))))),
% 2.68/0.75 inference(beta-eta_normalization,[],[f165])).
% 2.68/0.75 thf(f167,plain,(
% 2.68/0.75 ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((number @ sK8 @ one @ Y0) & (entry_box @ sK8 @ Y0)))))))),
% 2.68/0.75 inference(and_proxy_clausification,[],[f166])).
% 2.68/0.75 thf(f168,plain,(
% 2.68/0.75 (((eiw_di @ sK8 @ mactual)) = $true)),
% 2.68/0.75 inference(and_proxy_clausification,[],[f166])).
% 2.68/0.75 thf(f169,plain,(
% 2.68/0.75 ( ! [X1 : mworld] : (((((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((number @ sK8 @ one @ Y0) & (entry_box @ sK8 @ Y0)))) @ X1)) = $true)) )),
% 2.68/0.75 inference(pi_proxy_clausification,[],[f167])).
% 2.68/0.75 thf(f170,plain,(
% 2.68/0.75 ( ! [X1 : mworld] : (($true = (((mrel @ mactual @ X1) => ((number @ sK8 @ one @ X1) & (entry_box @ sK8 @ X1)))))) )),
% 2.68/0.75 inference(beta-eta_normalization,[],[f169])).
% 2.68/0.75 thf(f171,plain,(
% 2.68/0.75 ( ! [X1 : mworld] : ((((mrel @ mactual @ X1)) = $false) | ($true = (((number @ sK8 @ one @ X1) & (entry_box @ sK8 @ X1))))) )),
% 2.68/0.75 inference(imp_proxy_clausification,[],[f170])).
% 2.68/0.75 thf(f172,plain,(
% 2.68/0.75 ( ! [X1 : mworld] : (($true = ((entry_box @ sK8 @ X1))) | (((mrel @ mactual @ X1)) = $false)) )),
% 2.68/0.75 inference(and_proxy_clausification,[],[f171])).
% 2.68/0.75 thf(f173,plain,(
% 2.68/0.75 ( ! [X1 : mworld] : (($true = ((number @ sK8 @ one @ X1))) | (((mrel @ mactual @ X1)) = $false)) )),
% 2.68/0.75 inference(and_proxy_clausification,[],[f171])).
% 2.68/0.75 thf(f175,definition,(
% 2.68/0.75 spl9_1 <=> ($true = ((mrel @ mactual @ sK3)))),
% 2.68/0.75 introduced(definition,[new_symbols(definition,[spl9_1])],[avatar_definition])).
% 2.68/0.75 thf(f177,plain,(
% 2.68/0.75 ($true = ((mrel @ mactual @ sK3))) | ~spl9_1),
% 2.68/0.75 inference(avatar_component_clause,[],[f175])).
% 2.68/0.75 thf(f178,plain,(
% 2.68/0.75 spl9_1),
% 2.68/0.75 inference(avatar_split_clause,[],[f125,f175])).
% 2.68/0.75 thf(f180,definition,(
% 2.68/0.75 spl9_2 <=> (((eiw_di @ sK8 @ mactual)) = $true)),
% 2.68/0.75 introduced(definition,[new_symbols(definition,[spl9_2])],[avatar_definition])).
% 2.68/0.75 thf(f182,plain,(
% 2.68/0.75 (((eiw_di @ sK8 @ mactual)) = $true) | ~spl9_2),
% 2.68/0.75 inference(avatar_component_clause,[],[f180])).
% 2.68/0.75 thf(f183,plain,(
% 2.68/0.75 spl9_2),
% 2.68/0.75 inference(avatar_split_clause,[],[f168,f180])).
% 2.68/0.75 thf(f185,definition,(
% 2.68/0.75 spl9_3 <=> ($true = $false)),
% 2.68/0.75 introduced(definition,[new_symbols(definition,[spl9_3])],[avatar_definition])).
% 2.68/0.75 thf(f188,plain,(
% 2.68/0.75 ~spl9_3),
% 2.68/0.75 inference(avatar_split_clause,[],[f76,f185])).
% 2.68/0.75 thf(f201,plain,(
% 2.68/0.75 ( ! [X2 : mworld,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : ((((eiw_di @ X0 @ sK3)) = $false) | (((mrel @ X2 @ (sK5 @ (sK1 @ X1 @ X2 @ X3 @ X0) @ X4 @ X0 @ X5))) = $false) | (((entry_box @ X3 @ X2)) = $false) | ($false = ((eiw_di @ (sK6 @ X4 @ X5 @ (sK1 @ X1 @ X2 @ X3 @ X0) @ X0) @ (sK5 @ (sK1 @ X1 @ X2 @ X3 @ X0) @ X4 @ X0 @ X5)))) | ($true = $false) | (((eiw_di @ (sK1 @ X1 @ X2 @ X3 @ X0) @ sK3)) = $false) | (((mrel @ sK3 @ (sK4 @ X4 @ X5))) = $true) | ($false = ((string @ X1 @ X2))) | ($false = ((eiw_di @ X5 @ sK3))) | (((eiw_di @ X0 @ X2)) = $false) | (((eiw_di @ X3 @ X2)) = $false) | (((mrel @ mactual @ X2)) = $false) | (((eiw_di @ X4 @ sK3)) = $false) | (((eiw_di @ X1 @ X2)) = $false) | ($true = ((in @ X1 @ X3 @ (sK6 @ X4 @ X5 @ (sK1 @ X1 @ X2 @ X3 @ X0) @ X0) @ (sK5 @ (sK1 @ X1 @ X2 @ X3 @ X0) @ X4 @ X0 @ X5))))) )),
% 2.68/0.75 inference(superposition,[],[f107,f151])).
% 2.68/0.75 thf(f202,plain,(
% 2.68/0.75 ( ! [X2 : mworld,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true = ((in @ X1 @ X3 @ (sK6 @ X4 @ X5 @ (sK1 @ X1 @ X2 @ X3 @ X0) @ X0) @ (sK5 @ (sK1 @ X1 @ X2 @ X3 @ X0) @ X4 @ X0 @ X5)))) | (((mrel @ X2 @ (sK5 @ (sK1 @ X1 @ X2 @ X3 @ X0) @ X4 @ X0 @ X5))) = $false) | (((eiw_di @ X0 @ sK3)) = $false) | ($false = ((string @ X1 @ X2))) | (((eiw_di @ X3 @ X2)) = $false) | ($false = ((eiw_di @ X5 @ sK3))) | (((entry_box @ X3 @ X2)) = $false) | (((eiw_di @ X1 @ X2)) = $false) | (((eiw_di @ X0 @ X2)) = $false) | ($false = ((eiw_di @ (sK6 @ X4 @ X5 @ (sK1 @ X1 @ X2 @ X3 @ X0) @ X0) @ (sK5 @ (sK1 @ X1 @ X2 @ X3 @ X0) @ X4 @ X0 @ X5)))) | (((eiw_di @ (sK1 @ X1 @ X2 @ X3 @ X0) @ sK3)) = $false) | (((mrel @ sK3 @ (sK4 @ X4 @ X5))) = $true) | (((mrel @ mactual @ X2)) = $false) | (((eiw_di @ X4 @ sK3)) = $false)) )),
% 2.68/0.75 inference(trivial_inequality_removal,[],[f201])).
% 2.68/0.75 thf(f206,plain,(
% 2.68/0.75 ( ! [X2 : mworld,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : ((((eiw_di @ (sK7 @ X4 @ (sK1 @ X1 @ X2 @ X3 @ X0) @ X0 @ X5) @ (sK5 @ (sK1 @ X1 @ X2 @ X3 @ X0) @ X4 @ X0 @ X5))) = $false) | ($false = ((number @ X5 @ one @ (sK4 @ X4 @ X5)))) | ($true = $false) | (((userid @ u @ X4 @ (sK4 @ X4 @ X5))) = $false) | (((eiw_di @ X1 @ X2)) = $false) | ($false = ((string @ X1 @ X2))) | (((eiw_di @ X4 @ sK3)) = $false) | (((eiw_di @ X3 @ X2)) = $false) | (((eiw_di @ X0 @ sK3)) = $false) | ($false = ((entry_box @ X5 @ (sK4 @ X4 @ X5)))) | (((mrel @ X2 @ (sK5 @ (sK1 @ X1 @ X2 @ X3 @ X0) @ X4 @ X0 @ X5))) = $false) | (((eiw_di @ (sK1 @ X1 @ X2 @ X3 @ X0) @ sK3)) = $false) | (((in @ X1 @ X3 @ (sK7 @ X4 @ (sK1 @ X1 @ X2 @ X3 @ X0) @ X0 @ X5) @ (sK5 @ (sK1 @ X1 @ X2 @ X3 @ X0) @ X4 @ X0 @ X5))) = $true) | (((mrel @ mactual @ X2)) = $false) | ($false = ((eiw_di @ X5 @ sK3))) | (((entry_box @ X3 @ X2)) = $false) | (((eiw_di @ X0 @ X2)) = $false)) )),
% 2.68/0.75 inference(superposition,[],[f163,f107])).
% 2.68/0.75 thf(f208,plain,(
% 2.68/0.75 ( ! [X2 : mworld,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : ((((in @ X1 @ X3 @ (sK7 @ X4 @ (sK1 @ X1 @ X2 @ X3 @ X0) @ X0 @ X5) @ (sK5 @ (sK1 @ X1 @ X2 @ X3 @ X0) @ X4 @ X0 @ X5))) = $true) | (((eiw_di @ X1 @ X2)) = $false) | ($false = ((eiw_di @ X5 @ sK3))) | (((mrel @ mactual @ X2)) = $false) | (((mrel @ X2 @ (sK5 @ (sK1 @ X1 @ X2 @ X3 @ X0) @ X4 @ X0 @ X5))) = $false) | ($false = ((string @ X1 @ X2))) | ($false = ((number @ X5 @ one @ (sK4 @ X4 @ X5)))) | (((eiw_di @ X3 @ X2)) = $false) | (((eiw_di @ X4 @ sK3)) = $false) | ($false = ((entry_box @ X5 @ (sK4 @ X4 @ X5)))) | (((entry_box @ X3 @ X2)) = $false) | (((eiw_di @ (sK7 @ X4 @ (sK1 @ X1 @ X2 @ X3 @ X0) @ X0 @ X5) @ (sK5 @ (sK1 @ X1 @ X2 @ X3 @ X0) @ X4 @ X0 @ X5))) = $false) | (((eiw_di @ X0 @ sK3)) = $false) | (((eiw_di @ X0 @ X2)) = $false) | (((eiw_di @ (sK1 @ X1 @ X2 @ X3 @ X0) @ sK3)) = $false) | (((userid @ u @ X4 @ (sK4 @ X4 @ X5))) = $false)) )),
% 2.68/0.75 inference(trivial_inequality_removal,[],[f206])).
% 2.68/0.75 thf(f210,plain,(
% 2.68/0.75 ( ! [X2 : mworld,X3 : $i,X0 : $i,X1 : $i] : ((((eiw_di @ X1 @ X2)) = $false) | (((eiw_di @ X3 @ X2)) = $false) | (((eiw_di @ X3 @ sK3)) = $false) | (((mrel @ X2 @ (sK5 @ (sK1 @ X0 @ X2 @ X1 @ X3) @ X0 @ X3 @ X1))) = $false) | ($false = ((eiw_di @ (sK1 @ X0 @ X2 @ X1 @ X3) @ sK3))) | (((eiw_di @ X0 @ sK3)) = $false) | (((mrel @ mactual @ X2)) = $false) | (((eiw_di @ X0 @ sK3)) = $false) | ($false = ((eiw_di @ (sK6 @ X0 @ X1 @ (sK1 @ X0 @ X2 @ X1 @ X3) @ X3) @ (sK5 @ (sK1 @ X0 @ X2 @ X1 @ X3) @ X0 @ X3 @ X1)))) | (((mrel @ sK3 @ (sK4 @ X0 @ X1))) = $true) | (((eiw_di @ X0 @ X2)) = $false) | (((mrel @ sK3 @ (sK4 @ X0 @ X1))) = $true) | ($true = $false) | (((eiw_di @ X3 @ sK3)) = $false) | (((eiw_di @ X1 @ sK3)) = $false) | (((string @ X0 @ X2)) = $false) | (((eiw_di @ X1 @ sK3)) = $false) | ($false = ((eiw_di @ (sK1 @ X0 @ X2 @ X1 @ X3) @ sK3))) | (((entry_box @ X1 @ X2)) = $false)) )),
% 2.68/0.75 inference(superposition,[],[f202,f150])).
% 2.68/0.75 thf(f212,plain,(
% 2.68/0.75 ( ! [X2 : mworld,X3 : $i,X0 : $i,X1 : $i] : ((((eiw_di @ X1 @ X2)) = $false) | (((string @ X0 @ X2)) = $false) | (((entry_box @ X1 @ X2)) = $false) | (((eiw_di @ X0 @ sK3)) = $false) | (((eiw_di @ X1 @ sK3)) = $false) | (((eiw_di @ X3 @ sK3)) = $false) | (((mrel @ X2 @ (sK5 @ (sK1 @ X0 @ X2 @ X1 @ X3) @ X0 @ X3 @ X1))) = $false) | (((mrel @ sK3 @ (sK4 @ X0 @ X1))) = $true) | ($true = $false) | (((mrel @ mactual @ X2)) = $false) | (((eiw_di @ X3 @ X2)) = $false) | ($false = ((eiw_di @ (sK1 @ X0 @ X2 @ X1 @ X3) @ sK3))) | (((eiw_di @ X0 @ X2)) = $false) | ($false = ((eiw_di @ (sK6 @ X0 @ X1 @ (sK1 @ X0 @ X2 @ X1 @ X3) @ X3) @ (sK5 @ (sK1 @ X0 @ X2 @ X1 @ X3) @ X0 @ X3 @ X1))))) )),
% 2.68/0.75 inference(duplicate_literal_removal,[],[f210])).
% 2.68/0.75 thf(f213,plain,(
% 2.68/0.75 ( ! [X2 : mworld,X3 : $i,X0 : $i,X1 : $i] : (($false = ((eiw_di @ (sK6 @ X0 @ X1 @ (sK1 @ X0 @ X2 @ X1 @ X3) @ X3) @ (sK5 @ (sK1 @ X0 @ X2 @ X1 @ X3) @ X0 @ X3 @ X1)))) | (((entry_box @ X1 @ X2)) = $false) | ($false = ((eiw_di @ (sK1 @ X0 @ X2 @ X1 @ X3) @ sK3))) | (((mrel @ sK3 @ (sK4 @ X0 @ X1))) = $true) | (((string @ X0 @ X2)) = $false) | (((eiw_di @ X3 @ X2)) = $false) | (((mrel @ mactual @ X2)) = $false) | (((eiw_di @ X0 @ sK3)) = $false) | (((mrel @ X2 @ (sK5 @ (sK1 @ X0 @ X2 @ X1 @ X3) @ X0 @ X3 @ X1))) = $false) | (((eiw_di @ X3 @ sK3)) = $false) | (((eiw_di @ X0 @ X2)) = $false) | (((eiw_di @ X1 @ sK3)) = $false) | (((eiw_di @ X1 @ X2)) = $false)) )),
% 2.68/0.75 inference(trivial_inequality_removal,[],[f212])).
% 2.68/0.75 thf(f218,plain,(
% 2.68/0.75 ( ! [X2 : mworld,X3 : $i,X0 : $i,X1 : $i] : ((((string @ X0 @ X2)) = $false) | (((eiw_di @ X3 @ X2)) = $false) | (((mrel @ sK3 @ (sK4 @ X0 @ X1))) = $true) | (((eiw_di @ X0 @ X2)) = $false) | (((mrel @ sK3 @ (sK4 @ X0 @ X1))) = $true) | (((eiw_di @ X1 @ sK3)) = $false) | ($false = ((eiw_di @ (sK1 @ X0 @ X2 @ X1 @ X3) @ sK3))) | (((eiw_di @ X1 @ sK3)) = $false) | (((eiw_di @ X3 @ sK3)) = $false) | (((mrel @ X2 @ (sK5 @ (sK1 @ X0 @ X2 @ X1 @ X3) @ X0 @ X3 @ X1))) = $false) | ($true = $false) | (((mrel @ mactual @ X2)) = $false) | (((eiw_di @ X0 @ sK3)) = $false) | (((eiw_di @ X3 @ sK3)) = $false) | (((eiw_di @ X0 @ sK3)) = $false) | (((entry_box @ X1 @ X2)) = $false) | (((eiw_di @ X1 @ X2)) = $false) | ($false = ((eiw_di @ (sK1 @ X0 @ X2 @ X1 @ X3) @ sK3)))) )),
% 2.68/0.75 inference(superposition,[],[f149,f213])).
% 2.68/0.75 thf(f220,plain,(
% 2.68/0.75 ( ! [X2 : mworld,X3 : $i,X0 : $i,X1 : $i] : ((((eiw_di @ X0 @ sK3)) = $false) | ($false = ((eiw_di @ (sK1 @ X0 @ X2 @ X1 @ X3) @ sK3))) | ($true = $false) | (((mrel @ mactual @ X2)) = $false) | (((string @ X0 @ X2)) = $false) | (((eiw_di @ X3 @ X2)) = $false) | (((eiw_di @ X1 @ sK3)) = $false) | (((mrel @ X2 @ (sK5 @ (sK1 @ X0 @ X2 @ X1 @ X3) @ X0 @ X3 @ X1))) = $false) | (((eiw_di @ X3 @ sK3)) = $false) | (((mrel @ sK3 @ (sK4 @ X0 @ X1))) = $true) | (((entry_box @ X1 @ X2)) = $false) | (((eiw_di @ X0 @ X2)) = $false) | (((eiw_di @ X1 @ X2)) = $false)) )),
% 2.68/0.75 inference(duplicate_literal_removal,[],[f218])).
% 2.68/0.75 thf(f221,plain,(
% 2.68/0.75 ( ! [X2 : mworld,X3 : $i,X0 : $i,X1 : $i] : ((((mrel @ X2 @ (sK5 @ (sK1 @ X0 @ X2 @ X1 @ X3) @ X0 @ X3 @ X1))) = $false) | (((eiw_di @ X1 @ sK3)) = $false) | (((entry_box @ X1 @ X2)) = $false) | (((mrel @ mactual @ X2)) = $false) | (((eiw_di @ X0 @ X2)) = $false) | (((mrel @ sK3 @ (sK4 @ X0 @ X1))) = $true) | (((eiw_di @ X1 @ X2)) = $false) | (((eiw_di @ X3 @ X2)) = $false) | (((eiw_di @ X0 @ sK3)) = $false) | ($false = ((eiw_di @ (sK1 @ X0 @ X2 @ X1 @ X3) @ sK3))) | (((string @ X0 @ X2)) = $false) | (((eiw_di @ X3 @ sK3)) = $false)) )),
% 2.68/0.75 inference(trivial_inequality_removal,[],[f220])).
% 2.68/0.75 thf(f225,plain,(
% 2.68/0.75 ( ! [X2 : mworld,X3 : $i,X0 : $i,X1 : $i] : ((((eiw_di @ X3 @ X2)) = $false) | (((eiw_di @ X3 @ sK3)) = $false) | ($false = ((eiw_di @ (sK7 @ X0 @ (sK1 @ X0 @ X2 @ X1 @ X3) @ X3 @ X1) @ (sK5 @ (sK1 @ X0 @ X2 @ X1 @ X3) @ X0 @ X3 @ X1)))) | (((eiw_di @ X1 @ X2)) = $false) | (((string @ X0 @ X2)) = $false) | (((eiw_di @ X1 @ sK3)) = $false) | (((eiw_di @ X1 @ sK3)) = $false) | (((userid @ u @ X0 @ (sK4 @ X0 @ X1))) = $false) | (((entry_box @ X1 @ (sK4 @ X0 @ X1))) = $false) | ($false = ((eiw_di @ (sK1 @ X0 @ X2 @ X1 @ X3) @ sK3))) | ($true = $false) | (((eiw_di @ X3 @ sK3)) = $false) | (((eiw_di @ X0 @ sK3)) = $false) | (((eiw_di @ X0 @ sK3)) = $false) | (((mrel @ mactual @ X2)) = $false) | (((number @ X1 @ one @ (sK4 @ X0 @ X1))) = $false) | (((eiw_di @ X0 @ X2)) = $false) | ($false = ((eiw_di @ (sK1 @ X0 @ X2 @ X1 @ X3) @ sK3))) | (((userid @ u @ X0 @ (sK4 @ X0 @ X1))) = $false) | (((entry_box @ X1 @ (sK4 @ X0 @ X1))) = $false) | (((entry_box @ X1 @ X2)) = $false) | (((mrel @ X2 @ (sK5 @ (sK1 @ X0 @ X2 @ X1 @ X3) @ X0 @ X3 @ X1))) = $false) | (((number @ X1 @ one @ (sK4 @ X0 @ X1))) = $false)) )),
% 2.68/0.75 inference(superposition,[],[f162,f208])).
% 2.68/0.75 thf(f226,plain,(
% 2.68/0.75 ( ! [X2 : mworld,X3 : $i,X0 : $i,X1 : $i] : ((((entry_box @ X1 @ X2)) = $false) | (((eiw_di @ X3 @ sK3)) = $false) | ($true = $false) | (((mrel @ mactual @ X2)) = $false) | (((eiw_di @ X3 @ X2)) = $false) | ($false = ((eiw_di @ (sK1 @ X0 @ X2 @ X1 @ X3) @ sK3))) | (((number @ X1 @ one @ (sK4 @ X0 @ X1))) = $false) | (((userid @ u @ X0 @ (sK4 @ X0 @ X1))) = $false) | (((eiw_di @ X0 @ sK3)) = $false) | (((eiw_di @ X1 @ X2)) = $false) | (((entry_box @ X1 @ (sK4 @ X0 @ X1))) = $false) | (((string @ X0 @ X2)) = $false) | (((mrel @ X2 @ (sK5 @ (sK1 @ X0 @ X2 @ X1 @ X3) @ X0 @ X3 @ X1))) = $false) | (((eiw_di @ X0 @ X2)) = $false) | (((eiw_di @ X1 @ sK3)) = $false) | ($false = ((eiw_di @ (sK7 @ X0 @ (sK1 @ X0 @ X2 @ X1 @ X3) @ X3 @ X1) @ (sK5 @ (sK1 @ X0 @ X2 @ X1 @ X3) @ X0 @ X3 @ X1))))) )),
% 2.68/0.75 inference(duplicate_literal_removal,[],[f225])).
% 2.68/0.75 thf(f227,plain,(
% 2.68/0.75 ( ! [X2 : mworld,X3 : $i,X0 : $i,X1 : $i] : (($false = ((eiw_di @ (sK7 @ X0 @ (sK1 @ X0 @ X2 @ X1 @ X3) @ X3 @ X1) @ (sK5 @ (sK1 @ X0 @ X2 @ X1 @ X3) @ X0 @ X3 @ X1)))) | (((eiw_di @ X3 @ sK3)) = $false) | (((eiw_di @ X1 @ sK3)) = $false) | (((eiw_di @ X3 @ X2)) = $false) | (((number @ X1 @ one @ (sK4 @ X0 @ X1))) = $false) | (((mrel @ mactual @ X2)) = $false) | (((eiw_di @ X1 @ X2)) = $false) | ($false = ((eiw_di @ (sK1 @ X0 @ X2 @ X1 @ X3) @ sK3))) | (((entry_box @ X1 @ X2)) = $false) | (((mrel @ X2 @ (sK5 @ (sK1 @ X0 @ X2 @ X1 @ X3) @ X0 @ X3 @ X1))) = $false) | (((eiw_di @ X0 @ X2)) = $false) | (((userid @ u @ X0 @ (sK4 @ X0 @ X1))) = $false) | (((eiw_di @ X0 @ sK3)) = $false) | (((string @ X0 @ X2)) = $false) | (((entry_box @ X1 @ (sK4 @ X0 @ X1))) = $false)) )),
% 2.68/0.75 inference(trivial_inequality_removal,[],[f226])).
% 2.68/0.75 thf(f234,plain,(
% 2.68/0.75 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((eiw_di @ X1 @ sK3)) = $false) | (((eiw_di @ X1 @ sK3)) = $false) | (((eiw_di @ X2 @ sK3)) = $false) | (((eiw_di @ X2 @ sK3)) = $false) | ($true = $false) | (((entry_box @ X1 @ sK3)) = $false) | (((eiw_di @ X1 @ sK3)) = $false) | (((mrel @ mactual @ sK3)) = $false) | ($false = ((string @ X0 @ sK3))) | (((mrel @ sK3 @ (sK4 @ X0 @ X1))) = $true) | (((eiw_di @ X2 @ sK3)) = $false) | (((eiw_di @ (sK1 @ X0 @ sK3 @ X1 @ X2) @ sK3)) = $false) | (((eiw_di @ X0 @ sK3)) = $false) | (((eiw_di @ X0 @ sK3)) = $false) | (((mrel @ sK3 @ (sK4 @ X0 @ X1))) = $true) | (((eiw_di @ (sK1 @ X0 @ sK3 @ X1 @ X2) @ sK3)) = $false) | (((eiw_di @ X0 @ sK3)) = $false)) )),
% 2.68/0.75 inference(superposition,[],[f145,f221])).
% 2.68/0.75 thf(f235,plain,(
% 2.68/0.75 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((mrel @ mactual @ sK3)) = $false) | (((eiw_di @ X1 @ sK3)) = $false) | (((entry_box @ X1 @ sK3)) = $false) | (((eiw_di @ X0 @ sK3)) = $false) | (((mrel @ sK3 @ (sK4 @ X0 @ X1))) = $true) | ($false = ((string @ X0 @ sK3))) | (((eiw_di @ X2 @ sK3)) = $false) | (((eiw_di @ (sK1 @ X0 @ sK3 @ X1 @ X2) @ sK3)) = $false) | ($true = $false)) )),
% 2.68/0.75 inference(duplicate_literal_removal,[],[f234])).
% 2.68/0.75 thf(f236,plain,(
% 2.68/0.75 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((eiw_di @ (sK1 @ X0 @ sK3 @ X1 @ X2) @ sK3)) = $false) | (((eiw_di @ X1 @ sK3)) = $false) | (((eiw_di @ X2 @ sK3)) = $false) | (((entry_box @ X1 @ sK3)) = $false) | ($false = ((string @ X0 @ sK3))) | (((mrel @ mactual @ sK3)) = $false) | (((mrel @ sK3 @ (sK4 @ X0 @ X1))) = $true) | (((eiw_di @ X0 @ sK3)) = $false)) )),
% 2.68/0.75 inference(trivial_inequality_removal,[],[f235])).
% 2.68/0.75 thf(f244,plain,(
% 2.68/0.75 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((eiw_di @ X0 @ sK3)) = $false) | (((eiw_di @ (sK1 @ X0 @ sK3 @ X1 @ X2) @ sK3)) = $false) | (((entry_box @ X1 @ sK3)) = $false) | ($true = $false) | (((eiw_di @ X2 @ sK3)) = $false) | (((mrel @ sK3 @ (sK4 @ X0 @ X1))) = $true) | ($false = ((string @ X0 @ sK3))) | (((eiw_di @ X1 @ sK3)) = $false)) ) | ~spl9_1),
% 2.68/0.75 inference(forward_demodulation,[],[f236,f177])).
% 2.68/0.75 thf(f245,plain,(
% 2.68/0.75 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((eiw_di @ (sK1 @ X0 @ sK3 @ X1 @ X2) @ sK3)) = $false) | (((eiw_di @ X2 @ sK3)) = $false) | (((eiw_di @ X1 @ sK3)) = $false) | (((eiw_di @ X0 @ sK3)) = $false) | (((entry_box @ X1 @ sK3)) = $false) | ($false = ((string @ X0 @ sK3))) | (((mrel @ sK3 @ (sK4 @ X0 @ X1))) = $true)) ) | ~spl9_1),
% 2.68/0.75 inference(trivial_inequality_removal,[],[f244])).
% 2.68/0.75 thf(f252,plain,(
% 2.68/0.75 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : mworld] : ((((eiw_di @ X2 @ sK3)) = $false) | ($false = ((string @ X0 @ X1))) | ($true = $false) | (((eiw_di @ X0 @ sK3)) = $false) | (((eiw_di @ X3 @ sK3)) = $false) | (((number @ X2 @ one @ (sK4 @ X0 @ X2))) = $false) | (((eiw_di @ (sK1 @ X0 @ X1 @ X2 @ X3) @ sK3)) = $false) | (((mrel @ mactual @ X1)) = $false) | (((eiw_di @ (sK1 @ X0 @ X1 @ X2 @ X3) @ sK3)) = $false) | (((entry_box @ X2 @ (sK4 @ X0 @ X2))) = $false) | ($false = ((entry_box @ X2 @ X1))) | (((userid @ u @ X0 @ (sK4 @ X0 @ X2))) = $false) | (((number @ X2 @ one @ (sK4 @ X0 @ X2))) = $false) | (((eiw_di @ X0 @ sK3)) = $false) | (((userid @ u @ X0 @ (sK4 @ X0 @ X2))) = $false) | (((eiw_di @ X3 @ sK3)) = $false) | (((eiw_di @ X2 @ X1)) = $false) | (((eiw_di @ X3 @ X1)) = $false) | (((entry_box @ X2 @ (sK4 @ X0 @ X2))) = $false) | (((eiw_di @ X0 @ X1)) = $false) | (((mrel @ X1 @ (sK5 @ (sK1 @ X0 @ X1 @ X2 @ X3) @ X0 @ X3 @ X2))) = $false) | (((eiw_di @ X2 @ sK3)) = $false)) )),
% 2.68/0.75 inference(superposition,[],[f227,f161])).
% 2.68/0.75 thf(f255,plain,(
% 2.68/0.75 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : mworld] : ((((eiw_di @ X0 @ X1)) = $false) | (((userid @ u @ X0 @ (sK4 @ X0 @ X2))) = $false) | (((entry_box @ X2 @ (sK4 @ X0 @ X2))) = $false) | (((mrel @ X1 @ (sK5 @ (sK1 @ X0 @ X1 @ X2 @ X3) @ X0 @ X3 @ X2))) = $false) | (((eiw_di @ X3 @ X1)) = $false) | (((number @ X2 @ one @ (sK4 @ X0 @ X2))) = $false) | (((eiw_di @ X2 @ X1)) = $false) | ($true = $false) | ($false = ((string @ X0 @ X1))) | (((eiw_di @ X0 @ sK3)) = $false) | (((mrel @ mactual @ X1)) = $false) | (((eiw_di @ (sK1 @ X0 @ X1 @ X2 @ X3) @ sK3)) = $false) | (((eiw_di @ X2 @ sK3)) = $false) | ($false = ((entry_box @ X2 @ X1))) | (((eiw_di @ X3 @ sK3)) = $false)) )),
% 2.68/0.75 inference(duplicate_literal_removal,[],[f252])).
% 2.68/0.75 thf(f256,plain,(
% 2.68/0.75 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : mworld] : ((((mrel @ X1 @ (sK5 @ (sK1 @ X0 @ X1 @ X2 @ X3) @ X0 @ X3 @ X2))) = $false) | (((eiw_di @ X0 @ sK3)) = $false) | (((eiw_di @ X3 @ sK3)) = $false) | (((eiw_di @ X0 @ X1)) = $false) | (((eiw_di @ X2 @ sK3)) = $false) | ($false = ((string @ X0 @ X1))) | (((eiw_di @ X3 @ X1)) = $false) | (((eiw_di @ (sK1 @ X0 @ X1 @ X2 @ X3) @ sK3)) = $false) | ($false = ((entry_box @ X2 @ X1))) | (((userid @ u @ X0 @ (sK4 @ X0 @ X2))) = $false) | (((entry_box @ X2 @ (sK4 @ X0 @ X2))) = $false) | (((number @ X2 @ one @ (sK4 @ X0 @ X2))) = $false) | (((mrel @ mactual @ X1)) = $false) | (((eiw_di @ X2 @ X1)) = $false)) )),
% 2.68/0.75 inference(trivial_inequality_removal,[],[f255])).
% 2.68/0.75 thf(f262,plain,(
% 2.68/0.75 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = ((string @ X0 @ sK3))) | (((eiw_di @ X0 @ sK3)) = $false) | (((entry_box @ X1 @ sK3)) = $false) | (((mrel @ sK3 @ (sK4 @ X0 @ X1))) = $true) | (((eiw_di @ X1 @ sK3)) = $false) | (((eiw_di @ X2 @ sK3)) = $false) | ($false = ((string @ X0 @ sK3))) | (((eiw_di @ X2 @ sK3)) = $false) | (((entry_box @ X1 @ sK3)) = $false) | (((eiw_di @ X0 @ sK3)) = $false) | (((eiw_di @ X1 @ sK3)) = $false) | (((mrel @ mactual @ sK3)) = $false) | ($true = $false)) ) | ~spl9_1),
% 2.68/0.75 inference(superposition,[],[f100,f245])).
% 2.68/0.75 thf(f266,plain,(
% 2.68/0.75 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((mrel @ sK3 @ (sK4 @ X0 @ X1))) = $true) | (((eiw_di @ X0 @ sK3)) = $false) | (((entry_box @ X1 @ sK3)) = $false) | (((mrel @ mactual @ sK3)) = $false) | (((eiw_di @ X1 @ sK3)) = $false) | (((eiw_di @ X2 @ sK3)) = $false) | ($true = $false) | ($false = ((string @ X0 @ sK3)))) ) | ~spl9_1),
% 2.68/0.75 inference(duplicate_literal_removal,[],[f262])).
% 2.68/0.75 thf(f267,plain,(
% 2.68/0.75 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((mrel @ mactual @ sK3)) = $false) | (((eiw_di @ X2 @ sK3)) = $false) | (((eiw_di @ X0 @ sK3)) = $false) | ($false = ((string @ X0 @ sK3))) | (((entry_box @ X1 @ sK3)) = $false) | (((mrel @ sK3 @ (sK4 @ X0 @ X1))) = $true) | (((eiw_di @ X1 @ sK3)) = $false)) ) | ~spl9_1),
% 2.68/0.75 inference(trivial_inequality_removal,[],[f266])).
% 2.68/0.75 thf(f270,plain,(
% 2.68/0.75 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = ((string @ X0 @ sK3))) | (((eiw_di @ X2 @ sK3)) = $false) | (((eiw_di @ X0 @ sK3)) = $false) | (((entry_box @ X1 @ sK3)) = $false) | ($true = $false) | (((eiw_di @ X1 @ sK3)) = $false) | (((mrel @ sK3 @ (sK4 @ X0 @ X1))) = $true)) ) | ~spl9_1),
% 2.68/0.75 inference(forward_demodulation,[],[f267,f177])).
% 2.68/0.75 thf(f271,plain,(
% 2.68/0.75 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = ((string @ X0 @ sK3))) | (((eiw_di @ X0 @ sK3)) = $false) | (((entry_box @ X1 @ sK3)) = $false) | (((eiw_di @ X2 @ sK3)) = $false) | (((mrel @ sK3 @ (sK4 @ X0 @ X1))) = $true) | (((eiw_di @ X1 @ sK3)) = $false)) ) | ~spl9_1),
% 2.68/0.75 inference(trivial_inequality_removal,[],[f270])).
% 2.68/0.75 thf(f273,definition,(
% 2.68/0.75 spl9_4 <=> ! [X2 : $i] : (((eiw_di @ X2 @ sK3)) = $false)),
% 2.68/0.75 introduced(definition,[new_symbols(definition,[spl9_4])],[avatar_definition])).
% 2.68/0.75 thf(f274,plain,(
% 2.68/0.75 ( ! [X2 : $i] : ((((eiw_di @ X2 @ sK3)) = $false)) ) | ~spl9_4),
% 2.68/0.75 inference(avatar_component_clause,[],[f273])).
% 2.68/0.75 thf(f276,definition,(
% 2.68/0.75 spl9_5 <=> ! [X0 : $i,X1 : $i] : ((((mrel @ sK3 @ (sK4 @ X0 @ X1))) = $true) | ($false = ((string @ X0 @ sK3))) | (((entry_box @ X1 @ sK3)) = $false) | (((eiw_di @ X0 @ sK3)) = $false) | (((eiw_di @ X1 @ sK3)) = $false))),
% 2.68/0.75 introduced(definition,[new_symbols(definition,[spl9_5])],[avatar_definition])).
% 2.68/0.75 thf(f277,plain,(
% 2.68/0.75 ( ! [X0 : $i,X1 : $i] : ((((mrel @ sK3 @ (sK4 @ X0 @ X1))) = $true) | (((eiw_di @ X1 @ sK3)) = $false) | ($false = ((string @ X0 @ sK3))) | (((eiw_di @ X0 @ sK3)) = $false) | (((entry_box @ X1 @ sK3)) = $false)) ) | ~spl9_5),
% 2.68/0.75 inference(avatar_component_clause,[],[f276])).
% 2.68/0.75 thf(f279,plain,(
% 2.68/0.75 spl9_5 | spl9_4 | ~spl9_1),
% 2.68/0.75 inference(avatar_split_clause,[],[f271,f175,f273,f276])).
% 2.68/0.75 thf(f280,plain,(
% 2.68/0.75 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((eiw_di @ X2 @ sK3)) = $false) | (((userid @ u @ X0 @ (sK4 @ X0 @ X1))) = $false) | (((mrel @ mactual @ sK3)) = $false) | (((number @ X1 @ one @ (sK4 @ X0 @ X1))) = $false) | (((userid @ u @ X0 @ (sK4 @ X0 @ X1))) = $false) | (((eiw_di @ X2 @ sK3)) = $false) | (((eiw_di @ X1 @ sK3)) = $false) | (((entry_box @ X1 @ (sK4 @ X0 @ X1))) = $false) | (((eiw_di @ (sK1 @ X0 @ sK3 @ X1 @ X2) @ sK3)) = $false) | (((eiw_di @ X0 @ sK3)) = $false) | (((entry_box @ X1 @ sK3)) = $false) | (((entry_box @ X1 @ (sK4 @ X0 @ X1))) = $false) | (((eiw_di @ X1 @ sK3)) = $false) | (((number @ X1 @ one @ (sK4 @ X0 @ X1))) = $false) | (((eiw_di @ X2 @ sK3)) = $false) | (((eiw_di @ X1 @ sK3)) = $false) | ($true = $false) | ($false = ((string @ X0 @ sK3))) | (((eiw_di @ X0 @ sK3)) = $false) | (((eiw_di @ (sK1 @ X0 @ sK3 @ X1 @ X2) @ sK3)) = $false) | (((eiw_di @ X0 @ sK3)) = $false)) )),
% 2.68/0.75 inference(superposition,[],[f256,f155])).
% 2.68/0.75 thf(f290,plain,(
% 2.68/0.75 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((userid @ u @ X0 @ (sK4 @ X0 @ X1))) = $false) | ($false = ((string @ X0 @ sK3))) | (((eiw_di @ (sK1 @ X0 @ sK3 @ X1 @ X2) @ sK3)) = $false) | (((entry_box @ X1 @ (sK4 @ X0 @ X1))) = $false) | ($true = $false) | (((entry_box @ X1 @ sK3)) = $false) | (((number @ X1 @ one @ (sK4 @ X0 @ X1))) = $false) | (((eiw_di @ X2 @ sK3)) = $false) | (((mrel @ mactual @ sK3)) = $false) | (((eiw_di @ X0 @ sK3)) = $false) | (((eiw_di @ X1 @ sK3)) = $false)) )),
% 2.68/0.75 inference(duplicate_literal_removal,[],[f280])).
% 2.68/0.75 thf(f291,plain,(
% 2.68/0.75 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((userid @ u @ X0 @ (sK4 @ X0 @ X1))) = $false) | (((eiw_di @ X2 @ sK3)) = $false) | (((number @ X1 @ one @ (sK4 @ X0 @ X1))) = $false) | (((eiw_di @ (sK1 @ X0 @ sK3 @ X1 @ X2) @ sK3)) = $false) | (((entry_box @ X1 @ sK3)) = $false) | (((mrel @ mactual @ sK3)) = $false) | ($false = ((string @ X0 @ sK3))) | (((eiw_di @ X0 @ sK3)) = $false) | (((entry_box @ X1 @ (sK4 @ X0 @ X1))) = $false) | (((eiw_di @ X1 @ sK3)) = $false)) )),
% 2.68/0.75 inference(trivial_inequality_removal,[],[f290])).
% 2.68/0.75 thf(f294,plain,(
% 2.68/0.75 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((userid @ u @ X0 @ (sK4 @ X0 @ X1))) = $false) | (((eiw_di @ X1 @ sK3)) = $false) | (((number @ X1 @ one @ (sK4 @ X0 @ X1))) = $false) | (((eiw_di @ X0 @ sK3)) = $false) | (((eiw_di @ (sK1 @ X0 @ sK3 @ X1 @ X2) @ sK3)) = $false) | ($false = ((string @ X0 @ sK3))) | (((entry_box @ X1 @ sK3)) = $false) | (((entry_box @ X1 @ (sK4 @ X0 @ X1))) = $false) | ($true = $false) | (((eiw_di @ X2 @ sK3)) = $false)) ) | ~spl9_1),
% 2.68/0.75 inference(forward_demodulation,[],[f291,f177])).
% 2.68/0.75 thf(f295,plain,(
% 2.68/0.75 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((eiw_di @ (sK1 @ X0 @ sK3 @ X1 @ X2) @ sK3)) = $false) | (((entry_box @ X1 @ (sK4 @ X0 @ X1))) = $false) | (((entry_box @ X1 @ sK3)) = $false) | (((eiw_di @ X1 @ sK3)) = $false) | (((number @ X1 @ one @ (sK4 @ X0 @ X1))) = $false) | (((eiw_di @ X0 @ sK3)) = $false) | ($false = ((string @ X0 @ sK3))) | (((userid @ u @ X0 @ (sK4 @ X0 @ X1))) = $false) | (((eiw_di @ X2 @ sK3)) = $false)) ) | ~spl9_1),
% 2.68/0.75 inference(trivial_inequality_removal,[],[f294])).
% 2.68/0.75 thf(f298,plain,(
% 2.68/0.75 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((eiw_di @ X2 @ sK3)) = $false) | (((mrel @ mactual @ sK3)) = $false) | (((entry_box @ X1 @ (sK4 @ X0 @ X1))) = $false) | (((userid @ u @ X0 @ (sK4 @ X0 @ X1))) = $false) | ($false = ((string @ X0 @ sK3))) | (((entry_box @ X1 @ sK3)) = $false) | (((eiw_di @ X2 @ sK3)) = $false) | (((entry_box @ X1 @ sK3)) = $false) | (((eiw_di @ X0 @ sK3)) = $false) | ($false = ((string @ X0 @ sK3))) | ($true = $false) | (((eiw_di @ X1 @ sK3)) = $false) | (((number @ X1 @ one @ (sK4 @ X0 @ X1))) = $false) | (((eiw_di @ X1 @ sK3)) = $false) | (((eiw_di @ X0 @ sK3)) = $false)) ) | ~spl9_1),
% 2.68/0.75 inference(superposition,[],[f295,f100])).
% 2.68/0.75 thf(f304,plain,(
% 2.68/0.75 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((eiw_di @ X1 @ sK3)) = $false) | (((userid @ u @ X0 @ (sK4 @ X0 @ X1))) = $false) | (((entry_box @ X1 @ sK3)) = $false) | (((entry_box @ X1 @ (sK4 @ X0 @ X1))) = $false) | ($true = $false) | (((eiw_di @ X0 @ sK3)) = $false) | (((mrel @ mactual @ sK3)) = $false) | ($false = ((string @ X0 @ sK3))) | (((number @ X1 @ one @ (sK4 @ X0 @ X1))) = $false) | (((eiw_di @ X2 @ sK3)) = $false)) ) | ~spl9_1),
% 2.68/0.75 inference(duplicate_literal_removal,[],[f298])).
% 2.68/0.75 thf(f305,plain,(
% 2.68/0.75 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((number @ X1 @ one @ (sK4 @ X0 @ X1))) = $false) | (((eiw_di @ X2 @ sK3)) = $false) | (((mrel @ mactual @ sK3)) = $false) | (((userid @ u @ X0 @ (sK4 @ X0 @ X1))) = $false) | (((eiw_di @ X0 @ sK3)) = $false) | (((entry_box @ X1 @ sK3)) = $false) | (((eiw_di @ X1 @ sK3)) = $false) | (((entry_box @ X1 @ (sK4 @ X0 @ X1))) = $false) | ($false = ((string @ X0 @ sK3)))) ) | ~spl9_1),
% 2.68/0.75 inference(trivial_inequality_removal,[],[f304])).
% 2.68/0.75 thf(f308,plain,(
% 2.68/0.75 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((entry_box @ X1 @ sK3)) = $false) | (((eiw_di @ X2 @ sK3)) = $false) | ($false = ((string @ X0 @ sK3))) | (((eiw_di @ X0 @ sK3)) = $false) | (((userid @ u @ X0 @ (sK4 @ X0 @ X1))) = $false) | ($true = $false) | (((eiw_di @ X1 @ sK3)) = $false) | (((number @ X1 @ one @ (sK4 @ X0 @ X1))) = $false) | (((entry_box @ X1 @ (sK4 @ X0 @ X1))) = $false)) ) | ~spl9_1),
% 2.68/0.75 inference(forward_demodulation,[],[f305,f177])).
% 2.68/0.75 thf(f309,plain,(
% 2.68/0.75 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = ((string @ X0 @ sK3))) | (((eiw_di @ X0 @ sK3)) = $false) | (((eiw_di @ X2 @ sK3)) = $false) | (((number @ X1 @ one @ (sK4 @ X0 @ X1))) = $false) | (((entry_box @ X1 @ sK3)) = $false) | (((userid @ u @ X0 @ (sK4 @ X0 @ X1))) = $false) | (((eiw_di @ X1 @ sK3)) = $false) | (((entry_box @ X1 @ (sK4 @ X0 @ X1))) = $false)) ) | ~spl9_1),
% 2.68/0.75 inference(trivial_inequality_removal,[],[f308])).
% 2.68/0.75 thf(f311,definition,(
% 2.68/0.75 spl9_6 <=> ! [X0 : $i,X1 : $i] : (($false = ((string @ X0 @ sK3))) | (((eiw_di @ X1 @ sK3)) = $false) | (((userid @ u @ X0 @ (sK4 @ X0 @ X1))) = $false) | (((eiw_di @ X0 @ sK3)) = $false) | (((number @ X1 @ one @ (sK4 @ X0 @ X1))) = $false) | (((entry_box @ X1 @ (sK4 @ X0 @ X1))) = $false) | (((entry_box @ X1 @ sK3)) = $false))),
% 2.68/0.75 introduced(definition,[new_symbols(definition,[spl9_6])],[avatar_definition])).
% 2.68/0.75 thf(f312,plain,(
% 2.68/0.75 ( ! [X0 : $i,X1 : $i] : ((((userid @ u @ X0 @ (sK4 @ X0 @ X1))) = $false) | (((entry_box @ X1 @ (sK4 @ X0 @ X1))) = $false) | (((entry_box @ X1 @ sK3)) = $false) | (((number @ X1 @ one @ (sK4 @ X0 @ X1))) = $false) | (((eiw_di @ X0 @ sK3)) = $false) | ($false = ((string @ X0 @ sK3))) | (((eiw_di @ X1 @ sK3)) = $false)) ) | ~spl9_6),
% 2.68/0.75 inference(avatar_component_clause,[],[f311])).
% 2.68/0.75 thf(f314,plain,(
% 2.68/0.75 spl9_6 | spl9_4 | ~spl9_1),
% 2.68/0.75 inference(avatar_split_clause,[],[f309,f175,f273,f311])).
% 2.68/0.75 thf(f316,plain,(
% 2.68/0.75 ($true = $false) | ~spl9_4),
% 2.68/0.75 inference(superposition,[],[f274,f64])).
% 2.68/0.75 thf(f329,plain,(
% 2.68/0.75 $false | ~spl9_4),
% 2.68/0.75 inference(trivial_inequality_removal,[],[f316])).
% 2.68/0.75 thf(f330,plain,(
% 2.68/0.75 ~spl9_4),
% 2.68/0.75 inference(avatar_contradiction_clause,[],[f329])).
% 2.68/0.75 thf(f332,definition,(
% 2.68/0.75 spl9_7 <=> (((mrel @ mactual @ sK3)) = $false)),
% 2.68/0.75 introduced(definition,[new_symbols(definition,[spl9_7])],[avatar_definition])).
% 2.68/0.75 thf(f338,plain,(
% 2.68/0.75 ( ! [X0 : mworld,X1 : $i] : ((((mrel @ mactual @ X0)) = $false) | ($true = $false) | (((eiw_di @ (sK2 @ X0) @ sK3)) = $false) | (((mrel @ X0 @ (sK4 @ (sK2 @ X0) @ X1))) = $false) | (((entry_box @ X1 @ sK3)) = $false) | (((eiw_di @ X1 @ sK3)) = $false) | (((entry_box @ X1 @ (sK4 @ (sK2 @ X0) @ X1))) = $false) | (((string @ (sK2 @ X0) @ sK3)) = $false) | (((number @ X1 @ one @ (sK4 @ (sK2 @ X0) @ X1))) = $false)) ) | ~spl9_6),
% 2.68/0.75 inference(superposition,[],[f119,f312])).
% 2.68/0.75 thf(f340,plain,(
% 2.68/0.75 ( ! [X0 : mworld,X1 : $i] : ((((number @ X1 @ one @ (sK4 @ (sK2 @ X0) @ X1))) = $false) | (((string @ (sK2 @ X0) @ sK3)) = $false) | (((eiw_di @ (sK2 @ X0) @ sK3)) = $false) | (((mrel @ mactual @ X0)) = $false) | (((entry_box @ X1 @ (sK4 @ (sK2 @ X0) @ X1))) = $false) | (((mrel @ X0 @ (sK4 @ (sK2 @ X0) @ X1))) = $false) | (((entry_box @ X1 @ sK3)) = $false) | (((eiw_di @ X1 @ sK3)) = $false)) ) | ~spl9_6),
% 2.68/0.75 inference(trivial_inequality_removal,[],[f338])).
% 2.68/0.75 thf(f344,plain,(
% 2.68/0.75 ( ! [X0 : mworld] : ((((entry_box @ sK8 @ sK3)) = $false) | (((mrel @ mactual @ (sK4 @ (sK2 @ X0) @ sK8))) = $false) | (((eiw_di @ sK8 @ sK3)) = $false) | ($true = $false) | (((entry_box @ sK8 @ (sK4 @ (sK2 @ X0) @ sK8))) = $false) | (((string @ (sK2 @ X0) @ sK3)) = $false) | (((mrel @ mactual @ X0)) = $false) | (((eiw_di @ (sK2 @ X0) @ sK3)) = $false) | ($false = ((mrel @ X0 @ (sK4 @ (sK2 @ X0) @ sK8))))) ) | ~spl9_6),
% 2.68/0.75 inference(superposition,[],[f173,f340])).
% 2.68/0.75 thf(f347,plain,(
% 2.68/0.75 ( ! [X0 : mworld] : ((((entry_box @ sK8 @ (sK4 @ (sK2 @ X0) @ sK8))) = $false) | ($false = ((mrel @ X0 @ (sK4 @ (sK2 @ X0) @ sK8)))) | (((string @ (sK2 @ X0) @ sK3)) = $false) | (((mrel @ mactual @ X0)) = $false) | (((eiw_di @ (sK2 @ X0) @ sK3)) = $false) | (((entry_box @ sK8 @ sK3)) = $false) | (((eiw_di @ sK8 @ sK3)) = $false) | (((mrel @ mactual @ (sK4 @ (sK2 @ X0) @ sK8))) = $false)) ) | ~spl9_6),
% 2.68/0.75 inference(trivial_inequality_removal,[],[f344])).
% 2.68/0.75 thf(f349,definition,(
% 2.68/0.75 spl9_8 <=> (((entry_box @ sK8 @ sK3)) = $false)),
% 2.68/0.75 introduced(definition,[new_symbols(definition,[spl9_8])],[avatar_definition])).
% 2.68/0.75 thf(f350,plain,(
% 2.68/0.75 (((entry_box @ sK8 @ sK3)) != $false) | spl9_8),
% 2.68/0.75 inference(avatar_component_clause,[],[f349])).
% 2.68/0.75 thf(f351,plain,(
% 2.68/0.75 (((entry_box @ sK8 @ sK3)) = $false) | ~spl9_8),
% 2.68/0.75 inference(avatar_component_clause,[],[f349])).
% 2.68/0.75 thf(f353,definition,(
% 2.68/0.75 spl9_9 <=> (((eiw_di @ sK8 @ sK3)) = $false)),
% 2.68/0.75 introduced(definition,[new_symbols(definition,[spl9_9])],[avatar_definition])).
% 2.68/0.75 thf(f355,plain,(
% 2.68/0.75 (((eiw_di @ sK8 @ sK3)) = $false) | ~spl9_9),
% 2.68/0.75 inference(avatar_component_clause,[],[f353])).
% 2.68/0.75 thf(f357,definition,(
% 2.68/0.75 spl9_10 <=> ! [X0 : mworld] : ((((mrel @ mactual @ (sK4 @ (sK2 @ X0) @ sK8))) = $false) | (((eiw_di @ (sK2 @ X0) @ sK3)) = $false) | (((entry_box @ sK8 @ (sK4 @ (sK2 @ X0) @ sK8))) = $false) | (((string @ (sK2 @ X0) @ sK3)) = $false) | ($false = ((mrel @ X0 @ (sK4 @ (sK2 @ X0) @ sK8)))) | (((mrel @ mactual @ X0)) = $false))),
% 2.68/0.75 introduced(definition,[new_symbols(definition,[spl9_10])],[avatar_definition])).
% 2.68/0.75 thf(f358,plain,(
% 2.68/0.75 ( ! [X0 : mworld] : (($false = ((mrel @ X0 @ (sK4 @ (sK2 @ X0) @ sK8)))) | (((entry_box @ sK8 @ (sK4 @ (sK2 @ X0) @ sK8))) = $false) | (((mrel @ mactual @ X0)) = $false) | (((string @ (sK2 @ X0) @ sK3)) = $false) | (((mrel @ mactual @ (sK4 @ (sK2 @ X0) @ sK8))) = $false) | (((eiw_di @ (sK2 @ X0) @ sK3)) = $false)) ) | ~spl9_10),
% 2.68/0.75 inference(avatar_component_clause,[],[f357])).
% 2.68/0.75 thf(f360,plain,(
% 2.68/0.75 spl9_9 | spl9_10 | spl9_8 | ~spl9_6),
% 2.68/0.75 inference(avatar_split_clause,[],[f347,f311,f349,f357,f353])).
% 2.68/0.75 thf(f363,plain,(
% 2.68/0.75 ($true = $false) | (((mrel @ mactual @ sK3)) = $false) | ~spl9_8),
% 2.68/0.75 inference(superposition,[],[f172,f351])).
% 2.68/0.75 thf(f364,plain,(
% 2.68/0.75 (((mrel @ mactual @ sK3)) = $false) | ~spl9_8),
% 2.68/0.75 inference(trivial_inequality_removal,[],[f363])).
% 2.68/0.75 thf(f367,plain,(
% 2.68/0.75 spl9_7 | ~spl9_8),
% 2.68/0.75 inference(avatar_split_clause,[],[f364,f349,f332])).
% 2.68/0.75 thf(f368,definition,(
% 2.68/0.75 ($true != ((mrel @ mactual @ sK3))) | (((mrel @ mactual @ sK3)) != $false) | ($true = $false)),
% 2.68/0.75 introduced(theory,[theory_tautology_sat_conflict])).
% 2.68/0.75 thf(f372,plain,(
% 2.68/0.75 (((mrel @ mactual @ sK3)) = $false) | (((entry_box @ sK8 @ (sK4 @ (sK2 @ sK3) @ sK8))) = $false) | (((string @ (sK2 @ sK3) @ sK3)) = $false) | ($true = $false) | (((eiw_di @ (sK2 @ sK3) @ sK3)) = $false) | (((eiw_di @ (sK2 @ sK3) @ sK3)) = $false) | (((mrel @ mactual @ (sK4 @ (sK2 @ sK3) @ sK8))) = $false) | (((eiw_di @ sK8 @ sK3)) = $false) | (((entry_box @ sK8 @ sK3)) = $false) | (((string @ (sK2 @ sK3) @ sK3)) = $false) | (~spl9_5 | ~spl9_10)),
% 2.68/0.75 inference(superposition,[],[f358,f277])).
% 2.68/0.75 thf(f377,plain,(
% 2.68/0.75 (((entry_box @ sK8 @ (sK4 @ (sK2 @ sK3) @ sK8))) = $false) | (((eiw_di @ (sK2 @ sK3) @ sK3)) = $false) | (((mrel @ mactual @ sK3)) = $false) | ($true = $false) | (((eiw_di @ sK8 @ sK3)) = $false) | (((mrel @ mactual @ (sK4 @ (sK2 @ sK3) @ sK8))) = $false) | (((entry_box @ sK8 @ sK3)) = $false) | (((string @ (sK2 @ sK3) @ sK3)) = $false) | (~spl9_5 | ~spl9_10)),
% 2.68/0.75 inference(duplicate_literal_removal,[],[f372])).
% 2.68/0.75 thf(f378,plain,(
% 2.68/0.75 (((eiw_di @ sK8 @ sK3)) = $false) | (((entry_box @ sK8 @ sK3)) = $false) | (((entry_box @ sK8 @ (sK4 @ (sK2 @ sK3) @ sK8))) = $false) | (((string @ (sK2 @ sK3) @ sK3)) = $false) | (((mrel @ mactual @ (sK4 @ (sK2 @ sK3) @ sK8))) = $false) | (((mrel @ mactual @ sK3)) = $false) | (((eiw_di @ (sK2 @ sK3) @ sK3)) = $false) | (~spl9_5 | ~spl9_10)),
% 2.68/0.75 inference(trivial_inequality_removal,[],[f377])).
% 2.68/0.75 thf(f382,plain,(
% 2.68/0.75 (((mrel @ mactual @ sK3)) = $false) | (((string @ (sK2 @ sK3) @ sK3)) = $false) | (((mrel @ mactual @ (sK4 @ (sK2 @ sK3) @ sK8))) = $false) | (((eiw_di @ (sK2 @ sK3) @ sK3)) = $false) | (((entry_box @ sK8 @ (sK4 @ (sK2 @ sK3) @ sK8))) = $false) | (((eiw_di @ sK8 @ sK3)) = $false) | (~spl9_5 | spl9_8 | ~spl9_10)),
% 2.68/0.75 inference(forward_subsumption_resolution,[],[f378,f350])).
% 2.68/0.75 thf(f386,plain,(
% 2.68/0.75 (((mrel @ mactual @ (sK4 @ (sK2 @ sK3) @ sK8))) = $false) | ($true = $false) | (((entry_box @ sK8 @ (sK4 @ (sK2 @ sK3) @ sK8))) = $false) | (((eiw_di @ (sK2 @ sK3) @ sK3)) = $false) | (((eiw_di @ sK8 @ sK3)) = $false) | (((string @ (sK2 @ sK3) @ sK3)) = $false) | (~spl9_1 | ~spl9_5 | spl9_8 | ~spl9_10)),
% 2.68/0.75 inference(forward_demodulation,[],[f382,f177])).
% 2.68/0.75 thf(f408,definition,(
% 2.68/0.75 spl9_15 <=> (((entry_box @ sK8 @ (sK4 @ (sK2 @ sK3) @ sK8))) = $false)),
% 2.68/0.75 introduced(definition,[new_symbols(definition,[spl9_15])],[avatar_definition])).
% 2.68/0.75 thf(f410,plain,(
% 2.68/0.75 (((entry_box @ sK8 @ (sK4 @ (sK2 @ sK3) @ sK8))) = $false) | ~spl9_15),
% 2.68/0.75 inference(avatar_component_clause,[],[f408])).
% 2.68/0.75 thf(f412,definition,(
% 2.68/0.75 spl9_16 <=> (((eiw_di @ (sK2 @ sK3) @ sK3)) = $false)),
% 2.68/0.75 introduced(definition,[new_symbols(definition,[spl9_16])],[avatar_definition])).
% 2.68/0.75 thf(f414,plain,(
% 2.68/0.75 (((eiw_di @ (sK2 @ sK3) @ sK3)) = $false) | ~spl9_16),
% 2.68/0.75 inference(avatar_component_clause,[],[f412])).
% 2.68/0.75 thf(f416,definition,(
% 2.68/0.75 spl9_17 <=> (((string @ (sK2 @ sK3) @ sK3)) = $false)),
% 2.68/0.75 introduced(definition,[new_symbols(definition,[spl9_17])],[avatar_definition])).
% 2.68/0.75 thf(f418,plain,(
% 2.68/0.75 (((string @ (sK2 @ sK3) @ sK3)) = $false) | ~spl9_17),
% 2.68/0.75 inference(avatar_component_clause,[],[f416])).
% 2.68/0.75 thf(f420,definition,(
% 2.68/0.75 spl9_18 <=> (((mrel @ mactual @ (sK4 @ (sK2 @ sK3) @ sK8))) = $false)),
% 2.68/0.75 introduced(definition,[new_symbols(definition,[spl9_18])],[avatar_definition])).
% 2.68/0.75 thf(f422,plain,(
% 2.68/0.75 (((mrel @ mactual @ (sK4 @ (sK2 @ sK3) @ sK8))) = $false) | ~spl9_18),
% 2.68/0.75 inference(avatar_component_clause,[],[f420])).
% 2.68/0.75 thf(f445,plain,(
% 2.68/0.75 ( ! [X0 : mworld] : ((((mrel @ sK3 @ X0)) != $true) | ($true = $false) | ($true != ((eiw_di @ sK8 @ X0)))) ) | ~spl9_9),
% 2.68/0.75 inference(superposition,[],[f355,f69])).
% 2.68/0.75 thf(f452,plain,(
% 2.68/0.75 ( ! [X0 : mworld] : (($true != ((eiw_di @ sK8 @ X0))) | (((mrel @ sK3 @ X0)) != $true)) ) | ~spl9_9),
% 2.68/0.75 inference(trivial_inequality_removal,[],[f445])).
% 2.68/0.75 thf(f460,plain,(
% 2.68/0.75 ($true != $true) | ($true != ((mrel @ sK3 @ mactual))) | (~spl9_2 | ~spl9_9)),
% 2.68/0.75 inference(superposition,[],[f452,f182])).
% 2.68/0.75 thf(f464,plain,(
% 2.68/0.75 ($true != ((mrel @ sK3 @ mactual))) | (~spl9_2 | ~spl9_9)),
% 2.68/0.75 inference(trivial_inequality_removal,[],[f460])).
% 2.68/0.75 thf(f468,definition,(
% 2.68/0.75 spl9_19 <=> ($true = ((mrel @ sK3 @ mactual)))),
% 2.68/0.75 introduced(definition,[new_symbols(definition,[spl9_19])],[avatar_definition])).
% 2.68/0.75 thf(f470,plain,(
% 2.68/0.75 ($true != ((mrel @ sK3 @ mactual))) | spl9_19),
% 2.68/0.75 inference(avatar_component_clause,[],[f468])).
% 2.68/0.75 thf(f471,plain,(
% 2.68/0.75 ~spl9_19 | ~spl9_2 | ~spl9_9),
% 2.68/0.75 inference(avatar_split_clause,[],[f464,f353,f180,f468])).
% 2.68/0.75 thf(f481,plain,(
% 2.68/0.75 ($true != $true) | (((mrel @ sK3 @ mactual)) = $false) | spl9_19),
% 2.68/0.75 inference(superposition,[],[f470,f77])).
% 2.68/0.75 thf(f482,plain,(
% 2.68/0.75 (((mrel @ sK3 @ mactual)) = $false) | spl9_19),
% 2.68/0.75 inference(trivial_inequality_removal,[],[f481])).
% 2.68/0.75 thf(f485,definition,(
% 2.68/0.75 spl9_20 <=> (((mrel @ sK3 @ mactual)) = $false)),
% 2.68/0.75 introduced(definition,[new_symbols(definition,[spl9_20])],[avatar_definition])).
% 2.68/0.75 thf(f487,plain,(
% 2.68/0.75 (((mrel @ sK3 @ mactual)) = $false) | ~spl9_20),
% 2.68/0.75 inference(avatar_component_clause,[],[f485])).
% 2.68/0.75 thf(f488,plain,(
% 2.68/0.75 spl9_20 | spl9_19),
% 2.68/0.75 inference(avatar_split_clause,[],[f482,f468,f485])).
% 2.68/0.75 thf(f489,plain,(
% 2.68/0.75 (((mrel @ mactual @ (sK4 @ (sK2 @ sK3) @ sK8))) = $false) | (((eiw_di @ (sK2 @ sK3) @ sK3)) = $false) | (((eiw_di @ sK8 @ sK3)) = $false) | (((entry_box @ sK8 @ (sK4 @ (sK2 @ sK3) @ sK8))) = $false) | (((string @ (sK2 @ sK3) @ sK3)) = $false) | (~spl9_1 | ~spl9_5 | spl9_8 | ~spl9_10)),
% 2.68/0.75 inference(trivial_inequality_removal,[],[f386])).
% 2.68/0.75 thf(f495,plain,(
% 2.68/0.75 spl9_16 | spl9_15 | spl9_9 | spl9_17 | spl9_18 | ~spl9_1 | ~spl9_5 | spl9_8 | ~spl9_10),
% 2.68/0.75 inference(avatar_split_clause,[],[f489,f357,f349,f276,f175,f420,f416,f353,f408,f412])).
% 2.68/0.75 thf(f530,plain,(
% 2.68/0.75 ($true = $false) | (((mrel @ mactual @ (sK4 @ (sK2 @ sK3) @ sK8))) = $false) | ~spl9_15),
% 2.68/0.75 inference(superposition,[],[f410,f172])).
% 2.68/0.75 thf(f533,plain,(
% 2.68/0.75 (((mrel @ mactual @ (sK4 @ (sK2 @ sK3) @ sK8))) = $false) | ~spl9_15),
% 2.68/0.75 inference(trivial_inequality_removal,[],[f530])).
% 2.68/0.75 thf(f536,plain,(
% 2.68/0.75 spl9_18 | ~spl9_15),
% 2.68/0.75 inference(avatar_split_clause,[],[f533,f408,f420])).
% 2.68/0.75 thf(f537,plain,(
% 2.68/0.75 ( ! [X0 : mworld] : (($true != ((mrel @ X0 @ (sK4 @ (sK2 @ sK3) @ sK8)))) | ($true != ((mrel @ X0 @ mactual))) | ($true = $false)) ) | ~spl9_18),
% 2.68/0.75 inference(superposition,[],[f422,f73])).
% 2.68/0.75 thf(f540,plain,(
% 2.68/0.75 ( ! [X0 : mworld] : (($true != ((mrel @ X0 @ (sK4 @ (sK2 @ sK3) @ sK8)))) | ($true != ((mrel @ X0 @ mactual)))) ) | ~spl9_18),
% 2.68/0.75 inference(trivial_inequality_removal,[],[f537])).
% 2.68/0.75 thf(f567,plain,(
% 2.68/0.75 (((eiw_di @ (sK2 @ sK3) @ sK3)) = $false) | (((string @ (sK2 @ sK3) @ sK3)) = $false) | (((entry_box @ sK8 @ sK3)) = $false) | (((eiw_di @ sK8 @ sK3)) = $false) | ($true != $true) | ($true != ((mrel @ sK3 @ mactual))) | (~spl9_5 | ~spl9_18)),
% 2.68/0.75 inference(superposition,[],[f540,f277])).
% 2.68/0.75 thf(f572,plain,(
% 2.68/0.75 ($true != ((mrel @ sK3 @ mactual))) | (((eiw_di @ sK8 @ sK3)) = $false) | (((eiw_di @ (sK2 @ sK3) @ sK3)) = $false) | (((entry_box @ sK8 @ sK3)) = $false) | (((string @ (sK2 @ sK3) @ sK3)) = $false) | (~spl9_5 | ~spl9_18)),
% 2.68/0.75 inference(trivial_inequality_removal,[],[f567])).
% 2.68/0.75 thf(f576,plain,(
% 2.68/0.75 (((string @ (sK2 @ sK3) @ sK3)) = $false) | (((eiw_di @ (sK2 @ sK3) @ sK3)) = $false) | ($true != ((mrel @ sK3 @ mactual))) | (((eiw_di @ sK8 @ sK3)) = $false) | (~spl9_5 | spl9_8 | ~spl9_18)),
% 2.68/0.75 inference(forward_subsumption_resolution,[],[f572,f350])).
% 2.68/0.75 thf(f583,plain,(
% 2.68/0.75 ( ! [X0 : mworld] : (($true = $false) | ($true != ((mrel @ X0 @ mactual))) | ($true != ((mrel @ X0 @ sK3)))) ) | ~spl9_20),
% 2.68/0.75 inference(superposition,[],[f487,f73])).
% 2.68/0.75 thf(f587,plain,(
% 2.68/0.75 ( ! [X0 : mworld] : (($true != ((mrel @ X0 @ sK3))) | ($true != ((mrel @ X0 @ mactual)))) ) | ~spl9_20),
% 2.68/0.75 inference(trivial_inequality_removal,[],[f583])).
% 2.68/0.75 thf(f598,plain,(
% 2.68/0.75 ($true != ((mrel @ mactual @ mactual))) | ($true != $true) | (~spl9_1 | ~spl9_20)),
% 2.68/0.75 inference(superposition,[],[f587,f177])).
% 2.68/0.75 thf(f605,plain,(
% 2.68/0.75 ($true != ((mrel @ mactual @ mactual))) | (~spl9_1 | ~spl9_20)),
% 2.68/0.75 inference(trivial_inequality_removal,[],[f598])).
% 2.68/0.75 thf(f607,plain,(
% 2.68/0.75 $false | (~spl9_1 | ~spl9_20)),
% 2.68/0.75 inference(forward_subsumption_resolution,[],[f605,f71])).
% 2.68/0.75 thf(f608,plain,(
% 2.68/0.75 ~spl9_1 | ~spl9_20),
% 2.68/0.75 inference(avatar_contradiction_clause,[],[f607])).
% 2.68/0.75 thf(f610,plain,(
% 2.68/0.75 spl9_9 | ~spl9_19 | spl9_16 | spl9_17 | ~spl9_5 | spl9_8 | ~spl9_18),
% 2.68/0.75 inference(avatar_split_clause,[],[f576,f420,f349,f276,f416,f412,f468,f353])).
% 2.68/0.75 thf(f625,plain,(
% 2.68/0.75 (((mrel @ mactual @ sK3)) = $false) | ($true = $false) | ~spl9_16),
% 2.68/0.75 inference(superposition,[],[f115,f414])).
% 2.68/0.75 thf(f630,plain,(
% 2.68/0.75 (((mrel @ mactual @ sK3)) = $false) | ~spl9_16),
% 2.68/0.75 inference(trivial_inequality_removal,[],[f625])).
% 2.68/0.75 thf(f632,plain,(
% 2.68/0.75 spl9_7 | ~spl9_16),
% 2.68/0.75 inference(avatar_split_clause,[],[f630,f412,f332])).
% 2.68/0.75 thf(f636,plain,(
% 2.68/0.75 ($true = $false) | ($false = ((mrel @ sK3 @ sK3))) | (((mrel @ mactual @ sK3)) = $false) | ~spl9_17),
% 2.68/0.75 inference(superposition,[],[f418,f120])).
% 2.68/0.75 thf(f640,plain,(
% 2.68/0.75 (((mrel @ mactual @ sK3)) = $false) | ($false = ((mrel @ sK3 @ sK3))) | ~spl9_17),
% 2.68/0.75 inference(trivial_inequality_removal,[],[f636])).
% 2.68/0.75 thf(f644,plain,(
% 2.68/0.75 ($false = ((mrel @ sK3 @ sK3))) | ($true = $false) | (~spl9_1 | ~spl9_17)),
% 2.68/0.75 inference(forward_demodulation,[],[f640,f177])).
% 2.68/0.75 thf(f645,plain,(
% 2.68/0.75 ($false = ((mrel @ sK3 @ sK3))) | (~spl9_1 | ~spl9_17)),
% 2.68/0.75 inference(trivial_inequality_removal,[],[f644])).
% 2.68/0.75 thf(f649,plain,(
% 2.68/0.75 ($true = $false) | (~spl9_1 | ~spl9_17)),
% 2.68/0.75 inference(forward_demodulation,[],[f645,f71])).
% 2.68/0.75 thf(f650,plain,(
% 2.68/0.75 $false | (~spl9_1 | ~spl9_17)),
% 2.68/0.75 inference(trivial_inequality_removal,[],[f649])).
% 2.68/0.75 thf(f651,plain,(
% 2.68/0.75 ~spl9_1 | ~spl9_17),
% 2.68/0.75 inference(avatar_contradiction_clause,[],[f650])).
% 2.68/0.75 cnf(s1, plain, spl9_1, inference(sat_conversion,[],[f178])).
% 2.68/0.75 cnf(s2, plain, spl9_2, inference(sat_conversion,[],[f183])).
% 2.68/0.75 cnf(s3, plain, ~spl9_3, inference(sat_conversion,[],[f188])).
% 2.68/0.75 cnf(s5, plain, ~spl9_1 | spl9_4 | spl9_5, inference(sat_conversion,[],[f279])).
% 2.68/0.75 cnf(s7, plain, ~spl9_1 | spl9_4 | spl9_6, inference(sat_conversion,[],[f314])).
% 2.68/0.75 cnf(s9, plain, ~spl9_4, inference(sat_conversion,[],[f330])).
% 2.68/0.75 cnf(s13, plain, ~spl9_6 | spl9_8 | spl9_9 | spl9_10, inference(sat_conversion,[],[f360])).
% 2.68/0.75 cnf(s14, plain, spl9_7 | ~spl9_8, inference(sat_conversion,[],[f367])).
% 2.68/0.75 cnf(s16, plain, ~spl9_1 | spl9_3 | ~spl9_7, inference(sat_conversion,[],[f368])).
% 2.68/0.75 cnf(s22, plain, ~spl9_2 | ~spl9_9 | ~spl9_19, inference(sat_conversion,[],[f471])).
% 2.68/0.75 cnf(s23, plain, spl9_19 | spl9_20, inference(sat_conversion,[],[f488])).
% 2.68/0.75 cnf(s24, plain, ~spl9_1 | ~spl9_5 | spl9_8 | spl9_9 | ~spl9_10 | spl9_15 | spl9_16 | spl9_17 | spl9_18, inference(sat_conversion,[],[f495])).
% 2.68/0.75 cnf(s27, plain, ~spl9_15 | spl9_18, inference(sat_conversion,[],[f536])).
% 2.68/0.75 cnf(s33, plain, ~spl9_1 | ~spl9_20, inference(sat_conversion,[],[f608])).
% 2.68/0.75 cnf(s36, plain, ~spl9_5 | spl9_8 | spl9_9 | spl9_16 | spl9_17 | ~spl9_18 | ~spl9_19, inference(sat_conversion,[],[f610])).
% 2.68/0.75 cnf(s37, plain, spl9_7 | ~spl9_16, inference(sat_conversion,[],[f632])).
% 2.68/0.75 cnf(s40, plain, ~spl9_1 | ~spl9_17, inference(sat_conversion,[],[f651])).
% 2.68/0.75 cnf(s41, plain, ~spl9_1 | spl9_6, inference(rat,[],[s7,s9])).
% 2.68/0.75 cnf(s43, plain, ~spl9_1 | spl9_5, inference(rat,[],[s5,s9])).
% 2.68/0.75 cnf(s45, plain, ~spl9_17, inference(rat,[],[s40,s1])).
% 2.68/0.75 cnf(s46, plain, ~spl9_20, inference(rat,[],[s33,s1])).
% 2.68/0.75 cnf(s47, plain, ~spl9_7, inference(rat,[],[s16,s3,s1])).
% 2.68/0.75 cnf(s48, plain, spl9_6, inference(rat,[],[s41,s1])).
% 2.68/0.75 cnf(s49, plain, spl9_5, inference(rat,[],[s43,s1])).
% 2.68/0.75 cnf(s50, plain, spl9_19, inference(rat,[],[s23,s46])).
% 2.68/0.75 cnf(s51, plain, ~spl9_16, inference(rat,[],[s37,s47])).
% 2.68/0.75 cnf(s53, plain, ~spl9_8, inference(rat,[],[s14,s47])).
% 2.68/0.75 cnf(s54, plain, ~spl9_9, inference(rat,[],[s22,s2,s50])).
% 2.68/0.75 cnf(s55, plain, spl9_10, inference(rat,[],[s13,s53,s48,s54])).
% 2.68/0.75 cnf(s56, plain, ~spl9_18, inference(rat,[],[s36,s50,s53,s45,s51,s49,s54])).
% 2.68/0.75 cnf(s57, plain, spl9_15, inference(rat,[],[s24,s56,s45,s51,s54,s53,s49,s1,s55])).
% 2.68/0.75 cnf(s58, plain, $false, inference(rat,[],[s27,s56,s57])).
% 2.68/0.75 thf(f652,plain,(
% 2.68/0.75 $false),
% 2.68/0.75 inference(avatar_sat_refutation,[],[s58])).
% 2.68/0.75 % SZS output end Proof for theBenchmark
% 2.68/0.75 % (2752163)------------------------------
% 2.68/0.75 % (2752163)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.68/0.75 % (2752163)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/0.75 % (2752163)CaDiCaL version: 2.1.3
% 2.68/0.75 % (2752163)Termination reason: Refutation
% 2.68/0.75 % (2752163)Time elapsed: 0.106 s
% 2.68/0.75 % (2752163)Peak memory usage: 13 MB
% 2.68/0.75 % (2752163)Instructions burned: 117 (million)
% 2.68/0.75 % (2752094)Success in time 0.452 s
% 2.68/0.75 % Vampire exiting
%------------------------------------------------------------------------------