%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV441^1 : TPTP v9.3.1. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 08:38:38 AM UTC 2026
% Result : Satisfiable 0.86s 0.38s
% Output : Saturation 0.86s
% Verified :
% SZS Type : Derivation
% Derivation depth : 0
% Number of leaves : 1
% Syntax : Number of clauses : 1 ( 1 unt; 0 nHn; 1 RR)
% Number of literals : 1 ( 1 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 0 ( 0 avg)
% Number of predicates : 3 ( 0 usr; 2 prp; 0-2 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(u113,axiom,
$true != $false ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV441^1 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n018.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 15:49:12 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running higher-order theorem proving
% 0.07/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.34 % (252224)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.34 % (252246)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.19/0.34 % (252246)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
% 0.19/0.34 % (252246)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=1001179228:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.19/0.34 % (252242)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2430094037:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.19/0.34 % (252240)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4023658273:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.19/0.34 % (252241)lrs+10_16_si=on:nwc=1.5:random_seed=105656878:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.19/0.34 % (252245)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1705772105:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.19/0.34 % (252243)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=3112284112: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)
% 0.19/0.34 % (252244)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3988149905:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.19/0.34 % (252242)Instruction limit reached!
% 0.19/0.34 % (252242)------------------------------
% 0.19/0.34 % (252242)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.34 % (252242)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.34 % (252242)CaDiCaL version: 2.1.3
% 0.19/0.34 % (252242)Termination reason: Instruction limit
% 0.19/0.34 % (252242)Termination phase: Property scanning
% 0.19/0.34 % (252242)Time elapsed: 0.002 s
% 0.19/0.34 % (252242)Peak memory usage: 10 MB
% 0.19/0.34 % (252242)Instructions burned: 4 (million)
% 0.19/0.34 % (252241)Instruction limit reached!
% 0.19/0.34 % (252241)------------------------------
% 0.19/0.34 % (252241)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.34 % (252241)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.34 % (252241)CaDiCaL version: 2.1.3
% 0.19/0.34 % (252241)Termination reason: Instruction limit
% 0.19/0.34 % (252241)Termination phase: Saturation
% 0.19/0.34 % (252241)Time elapsed: 0.009 s
% 0.19/0.34 % (252241)Peak memory usage: 11 MB
% 0.19/0.34 % (252241)Instructions burned: 20 (million)
% 0.19/0.34 % (252244)Instruction limit reached!
% 0.19/0.34 % (252244)------------------------------
% 0.19/0.34 % (252244)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.34 % (252244)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.34 % (252244)CaDiCaL version: 2.1.3
% 0.19/0.34 % (252244)Termination reason: Instruction limit
% 0.19/0.34 % (252244)Termination phase: Saturation
% 0.19/0.34 % (252244)Time elapsed: 0.014 s
% 0.19/0.34 % (252244)Peak memory usage: 11 MB
% 0.19/0.34 % (252244)Instructions burned: 25 (million)
% 0.19/0.34 % (252266)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1133989095:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.19/0.34 % (252266)Instruction limit reached!
% 0.19/0.34 % (252266)------------------------------
% 0.19/0.34 % (252266)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.34 % (252266)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.34 % (252266)CaDiCaL version: 2.1.3
% 0.19/0.34 % (252266)Termination reason: Instruction limit
% 0.19/0.34 % (252266)Termination phase: Property scanning
% 0.19/0.34 % (252266)Time elapsed: 0.002 s
% 0.19/0.34 % (252266)Peak memory usage: 10 MB
% 0.19/0.34 % (252266)Instructions burned: 4 (million)
% 0.19/0.34 % (252271)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=654381682:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.19/0.34 % (252275)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.19/0.36 % (252245)Instruction limit reached!
% 0.19/0.36 % (252245)------------------------------
% 0.19/0.36 % (252245)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.36 % (252245)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.36 % (252245)CaDiCaL version: 2.1.3
% 0.19/0.36 % (252245)Termination reason: Instruction limit
% 0.19/0.36 % (252245)Termination phase: Saturation
% 0.19/0.36 % (252245)Time elapsed: 0.031 s
% 0.19/0.36 % (252245)Peak memory usage: 12 MB
% 0.19/0.36 % (252245)Instructions burned: 75 (million)
% 0.19/0.36 % (252271)Instruction limit reached!
% 0.19/0.36 % (252271)------------------------------
% 0.19/0.36 % (252271)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.36 % (252271)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.36 % (252271)CaDiCaL version: 2.1.3
% 0.19/0.36 % (252271)Termination reason: Instruction limit
% 0.19/0.36 % (252271)Termination phase: Function definition elimination
% 0.19/0.36 % (252271)Time elapsed: 0.003 s
% 0.19/0.36 % (252271)Peak memory usage: 10 MB
% 0.19/0.36 % (252271)Instructions burned: 6 (million)
% 0.19/0.36 % (252246)Instruction limit reached!
% 0.19/0.36 % (252246)------------------------------
% 0.19/0.36 % (252246)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.36 % (252246)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.36 % (252246)CaDiCaL version: 2.1.3
% 0.19/0.36 % (252246)Termination reason: Instruction limit
% 0.19/0.36 % (252246)Termination phase: Saturation
% 0.19/0.36 % (252246)Time elapsed: 0.040 s
% 0.19/0.36 % (252246)Peak memory usage: 12 MB
% 0.19/0.36 % (252246)Instructions burned: 161 (million)
% 0.19/0.36 % (252275)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1282815416:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.19/0.36 % (252240)Instruction limit reached!
% 0.19/0.36 % (252240)------------------------------
% 0.19/0.36 % (252240)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.36 % (252240)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.36 % (252240)CaDiCaL version: 2.1.3
% 0.19/0.36 % (252240)Termination reason: Instruction limit
% 0.19/0.36 % (252240)Termination phase: Saturation
% 0.19/0.36 % (252240)Time elapsed: 0.036 s
% 0.19/0.36 % (252240)Peak memory usage: 12 MB
% 0.19/0.36 % (252240)Instructions burned: 88 (million)
% 0.19/0.36 % (252275)Instruction limit reached!
% 0.19/0.36 % (252275)------------------------------
% 0.19/0.36 % (252275)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.36 % (252275)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.36 % (252275)CaDiCaL version: 2.1.3
% 0.19/0.36 % (252275)Termination reason: Instruction limit
% 0.19/0.36 % (252275)Termination phase: Function definition elimination
% 0.19/0.36 % (252275)Time elapsed: 0.003 s
% 0.19/0.36 % (252275)Peak memory usage: 10 MB
% 0.19/0.36 % (252275)Instructions burned: 7 (million)
% 0.19/0.36 % (252279)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1045405499:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.19/0.36 % (252285)lrs+10_1_si=on:cs=on:random_seed=3154940295:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.19/0.36 % (252285)Instruction limit reached!
% 0.19/0.36 % (252285)------------------------------
% 0.19/0.36 % (252285)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.36 % (252285)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.36 % (252285)CaDiCaL version: 2.1.3
% 0.19/0.36 % (252285)Termination reason: Instruction limit
% 0.19/0.36 % (252285)Termination phase: Saturation
% 0.19/0.36 % (252285)Time elapsed: 0.002 s
% 0.19/0.36 % (252285)Peak memory usage: 11 MB
% 0.19/0.36 % (252285)Instructions burned: 8 (million)
% 0.19/0.36 % (252283)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
% 0.19/0.36 % (252283)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.19/0.36 % (252279)Instruction limit reached!
% 0.86/0.38 % (252279)------------------------------
% 0.86/0.38 % (252279)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.38 % (252279)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.38 % (252279)CaDiCaL version: 2.1.3
% 0.86/0.38 % (252279)Termination reason: Instruction limit
% 0.86/0.38 % (252279)Termination phase: Saturation
% 0.86/0.38 % (252279)Time elapsed: 0.006 s
% 0.86/0.38 % (252279)Peak memory usage: 12 MB
% 0.86/0.38 % (252279)Instructions burned: 13 (million)
% 0.86/0.38 % (252283)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3410854114:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.86/0.38 % (252284)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=1870828347:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.86/0.38 % (252287)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.86/0.38 % (252287)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=1883920542:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.86/0.38 % (252294)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=4007156243:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.86/0.38 % (252288)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1534610264:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.86/0.38 % (252287)Instruction limit reached!
% 0.86/0.38 % (252287)------------------------------
% 0.86/0.38 % (252287)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.38 % (252287)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.38 % (252287)CaDiCaL version: 2.1.3
% 0.86/0.38 % (252287)Termination reason: Instruction limit
% 0.86/0.38 % (252287)Termination phase: Preprocessing 2
% 0.86/0.38 % (252287)Time elapsed: 0.002 s
% 0.86/0.38 % (252287)Peak memory usage: 10 MB
% 0.86/0.38 % (252287)Instructions burned: 4 (million)
% 0.86/0.38 % (252294)Refutation not found, incomplete strategy
% 0.86/0.38 % (252294)------------------------------
% 0.86/0.38 % (252294)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.38 % (252294)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.38 % (252294)CaDiCaL version: 2.1.3
% 0.86/0.38 % (252294)Termination reason: Refutation not found, incomplete strategy
% 0.86/0.38 % (252294)Time elapsed: 0.001 s
% 0.86/0.38 % (252294)Peak memory usage: 11 MB
% 0.86/0.38 % (252294)Instructions burned: 5 (million)
% 0.86/0.38 % (252294)------------------------------
% 0.86/0.38 % (252294)------------------------------
% 0.86/0.38 % (252288)Refutation not found, incomplete strategy
% 0.86/0.38 % (252288)------------------------------
% 0.86/0.38 % (252288)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.38 % (252288)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.38 % (252288)CaDiCaL version: 2.1.3
% 0.86/0.38 % (252288)Termination reason: Refutation not found, incomplete strategy
% 0.86/0.38 % (252288)Time elapsed: 0.003 s
% 0.86/0.38 % (252288)Peak memory usage: 11 MB
% 0.86/0.38 % (252288)Instructions burned: 5 (million)
% 0.86/0.38 % (252288)------------------------------
% 0.86/0.38 % (252288)------------------------------
% 0.86/0.38 % (252283)Instruction limit reached!
% 0.86/0.38 % (252283)------------------------------
% 0.86/0.38 % (252283)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.38 % (252283)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.38 % (252283)CaDiCaL version: 2.1.3
% 0.86/0.38 % (252283)Termination reason: Instruction limit
% 0.86/0.38 % (252283)Termination phase: Saturation
% 0.86/0.38 % (252283)Time elapsed: 0.013 s
% 0.86/0.38 % (252283)Peak memory usage: 11 MB
% 0.86/0.38 % (252283)Instructions burned: 29 (million)
% 0.86/0.38 % (252296)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=1893085833:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 0.86/0.38 % (252296)Refutation not found, incomplete strategy
% 0.86/0.38 % (252296)------------------------------
% 0.86/0.38 % (252296)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.38 % (252296)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.38 % (252296)CaDiCaL version: 2.1.3
% 0.86/0.38 % (252296)Termination reason: Refutation not found, incomplete strategy
% 0.86/0.38 % (252296)Time elapsed: 0.003 s
% 0.86/0.38 % (252296)Peak memory usage: 11 MB
% 0.86/0.38 % (252296)Instructions burned: 5 (million)
% 0.86/0.38 % (252296)------------------------------
% 0.86/0.38 % (252296)------------------------------
% 0.86/0.38 % (252302)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=848507309:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2999 on theBenchmark for (2999ds/14Mi)
% 0.86/0.38 % (252303)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=4076059711:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/327Mi)
% 0.86/0.38 % (252304)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=3596243121:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/14Mi)
% 0.86/0.38 % (252303)Refutation not found, incomplete strategy
% 0.86/0.38 % (252303)------------------------------
% 0.86/0.38 % (252303)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.38 % (252303)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.38 % (252303)CaDiCaL version: 2.1.3
% 0.86/0.38 % (252303)Termination reason: Refutation not found, incomplete strategy
% 0.86/0.38 % (252303)Time elapsed: 0.003 s
% 0.86/0.38 % (252303)Peak memory usage: 12 MB
% 0.86/0.38 % (252303)Instructions burned: 6 (million)
% 0.86/0.38 % (252303)------------------------------
% 0.86/0.38 % (252303)------------------------------
% 0.86/0.38 % (252284)Instruction limit reached!
% 0.86/0.38 % (252284)------------------------------
% 0.86/0.38 % (252284)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.38 % (252284)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.38 % (252284)CaDiCaL version: 2.1.3
% 0.86/0.38 % (252284)Termination reason: Instruction limit
% 0.86/0.38 % (252284)Termination phase: Saturation
% 0.86/0.38 % (252284)Time elapsed: 0.031 s
% 0.86/0.38 % (252284)Peak memory usage: 11 MB
% 0.86/0.38 % (252284)Instructions burned: 88 (million)
% 0.86/0.38 % (252305)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=506562229:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.86/0.38 % (252302)Instruction limit reached!
% 0.86/0.38 % (252302)------------------------------
% 0.86/0.38 % (252302)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.38 % (252302)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.38 % (252302)CaDiCaL version: 2.1.3
% 0.86/0.38 % (252302)Termination reason: Instruction limit
% 0.86/0.38 % (252302)Termination phase: Saturation
% 0.86/0.38 % (252302)Time elapsed: 0.007 s
% 0.86/0.38 % (252302)Peak memory usage: 12 MB
% 0.86/0.38 % (252302)Instructions burned: 15 (million)
% 0.86/0.38 % (252304)Instruction limit reached!
% 0.86/0.38 % (252304)------------------------------
% 0.86/0.38 % (252304)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.38 % (252304)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.38 % (252304)CaDiCaL version: 2.1.3
% 0.86/0.38 % (252304)Termination reason: Instruction limit
% 0.86/0.38 % (252304)Termination phase: Saturation
% 0.86/0.38 % (252304)Time elapsed: 0.007 s
% 0.86/0.38 % (252304)Peak memory usage: 12 MB
% 0.86/0.38 % (252304)Instructions burned: 15 (million)
% 0.86/0.38 % (252305)Refutation not found, incomplete strategy
% 0.86/0.38 % (252305)------------------------------
% 0.86/0.38 % (252305)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.38 % (252305)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.38 % (252307)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=3297670712:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 0.86/0.38 % (252305)CaDiCaL version: 2.1.3
% 0.86/0.38 % (252305)Termination reason: Refutation not found, incomplete strategy
% 0.86/0.38 % (252305)Time elapsed: 0.007 s
% 0.86/0.38 % (252305)Peak memory usage: 11 MB
% 0.86/0.38 % (252305)Instructions burned: 5 (million)
% 0.86/0.38 % (252305)------------------------------
% 0.86/0.38 % (252305)------------------------------
% 0.86/0.38 % (252314)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
% 0.86/0.38 % (252314)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 0.86/0.38 % (252312)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=3845463707:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 0.86/0.38 % (252315)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 0.86/0.38 % (252307)Instruction limit reached!
% 0.86/0.38 % (252307)------------------------------
% 0.86/0.38 % (252307)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.38 % (252307)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.38 % (252307)CaDiCaL version: 2.1.3
% 0.86/0.38 % (252307)Termination reason: Instruction limit
% 0.86/0.38 % (252307)Termination phase: Saturation
% 0.86/0.38 % (252307)Time elapsed: 0.011 s
% 0.86/0.38 % (252307)Peak memory usage: 11 MB
% 0.86/0.38 % (252307)Instructions burned: 26 (million)
% 0.86/0.38 % (252314)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=131832881:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.86/0.38 % (252317)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=3316734649:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 0.86/0.38 % (252311)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=2049248955:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 0.86/0.38 % (252315)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=2090139918:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 0.86/0.38 % (252317)Refutation not found, incomplete strategy
% 0.86/0.38 % (252317)------------------------------
% 0.86/0.38 % (252317)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.38 % (252317)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.38 % (252317)CaDiCaL version: 2.1.3
% 0.86/0.38 % (252317)Termination reason: Refutation not found, incomplete strategy
% 0.86/0.38 % (252317)Time elapsed: 0.002 s
% 0.86/0.38 % (252317)Peak memory usage: 12 MB
% 0.86/0.38 % (252317)Instructions burned: 6 (million)
% 0.86/0.38 % (252317)------------------------------
% 0.86/0.38 % (252317)------------------------------
% 0.86/0.38 % (252314) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-252224-252314"...
% 0.86/0.38 % (252314)...printing done.
% 0.86/0.38 % (252315)Instruction limit reached!
% 0.86/0.38 % (252315)------------------------------
% 0.86/0.38 % (252315)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.38 % (252315)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.38 % (252315)CaDiCaL version: 2.1.3
% 0.86/0.38 % (252315)Termination reason: Instruction limit
% 0.86/0.38 % (252315)Termination phase: Function definition elimination
% 0.86/0.38 % (252315)Time elapsed: 0.004 s
% 0.86/0.38 % (252315)Peak memory usage: 10 MB
% 0.86/0.38 % (252315)Instructions burned: 9 (million)
% 0.86/0.38 % SZS status Satisfiable for theBenchmark
% 0.86/0.38 % SZS output start Saturation.
% See solution above
% 0.86/0.38 % SZS output start Definitions and Model Updates.
% 0.86/0.38 for all inputs,
% 0.86/0.38 define cr := (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((^[Y3 : $i > $i > $o]: ((^[Y4 : $i > $i > $o]: ((^[Y5 : $i]: ((^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (Y4 @ Y6 @ Y5))))))) @ ((^[Y4 : $i > $i > $o]: ((^[Y5 : $i]: ((^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (Y5 = Y6))))))) @ ((^[Y4 : $i > $i > $o]: ((^[Y5 : $i]: ((^[Y6 : $i]: (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: ((((^[Y8 : $i > $i > $o]: ((^[Y9 : $i > $i > $o]: (!! @ $i @ (^[Y10 : $i]: (!! @ $i @ (^[Y11 : $i]: ((Y8 @ Y10 @ Y11) => (Y9 @ Y10 @ Y11))))))))) @ Y4 @ Y7) & ((^[Y8 : $i > $i > $o]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (!! @ $i @ (^[Y11 : $i]: (((Y8 @ Y10 @ Y11) & (Y8 @ Y9 @ Y10)) => (Y8 @ Y9 @ Y11))))))))) @ Y7)) => (Y7 @ Y5 @ Y6))))))))) @ Y3)))) @ Y0 @ Y2 @ Y1) => ((^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: ((^[Y5 : $i]: (?? @ $i @ (^[Y6 : $i]: (((^[Y7 : $i > $i > $o]: ((^[Y8 : $i > $i > $o]: ((^[Y9 : $i]: ((^[Y10 : $i]: ((Y8 @ Y9 @ Y10) | (Y9 = Y10))))))) @ ((^[Y8 : $i > $i > $o]: ((^[Y9 : $i]: ((^[Y10 : $i]: (!! @ ($i > $i > $o) @ (^[Y11 : $i > $i > $o]: ((((^[Y12 : $i > $i > $o]: ((^[Y13 : $i > $i > $o]: (!! @ $i @ (^[Y14 : $i]: (!! @ $i @ (^[Y15 : $i]: ((Y12 @ Y14 @ Y15) => (Y13 @ Y14 @ Y15))))))))) @ Y8 @ Y11) & ((^[Y12 : $i > $i > $o]: (!! @ $i @ (^[Y13 : $i]: (!! @ $i @ (^[Y14 : $i]: (!! @ $i @ (^[Y15 : $i]: (((Y12 @ Y14 @ Y15) & (Y12 @ Y13 @ Y14)) => (Y12 @ Y13 @ Y15))))))))) @ Y11)) => (Y11 @ Y9 @ Y10))))))))) @ Y7))) @ Y3 @ Y5 @ Y6) & ((^[Y7 : $i > $i > $o]: ((^[Y8 : $i > $i > $o]: ((^[Y9 : $i]: ((^[Y10 : $i]: ((Y8 @ Y9 @ Y10) | (Y9 = Y10))))))) @ ((^[Y8 : $i > $i > $o]: ((^[Y9 : $i]: ((^[Y10 : $i]: (!! @ ($i > $i > $o) @ (^[Y11 : $i > $i > $o]: ((((^[Y12 : $i > $i > $o]: ((^[Y13 : $i > $i > $o]: (!! @ $i @ (^[Y14 : $i]: (!! @ $i @ (^[Y15 : $i]: ((Y12 @ Y14 @ Y15) => (Y13 @ Y14 @ Y15))))))))) @ Y8 @ Y11) & ((^[Y12 : $i > $i > $o]: (!! @ $i @ (^[Y13 : $i]: (!! @ $i @ (^[Y14 : $i]: (!! @ $i @ (^[Y15 : $i]: (((Y12 @ Y14 @ Y15) & (Y12 @ Y13 @ Y14)) => (Y12 @ Y13 @ Y15))))))))) @ Y11)) => (Y11 @ Y9 @ Y10))))))))) @ Y7))) @ Y3 @ Y4 @ Y6))))))))) @ Y0 @ Y2 @ Y1)))))))
% 0.86/0.38 for all inputs,
% 0.86/0.38 define confl := (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((^[Y4 : $i > $i > $o]: ((^[Y5 : $i > $i > $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (Y6 = Y7))))))) @ ((^[Y5 : $i > $i > $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: (!! @ ($i > $i > $o) @ (^[Y8 : $i > $i > $o]: ((((^[Y9 : $i > $i > $o]: ((^[Y10 : $i > $i > $o]: (!! @ $i @ (^[Y11 : $i]: (!! @ $i @ (^[Y12 : $i]: ((Y9 @ Y11 @ Y12) => (Y10 @ Y11 @ Y12))))))))) @ Y5 @ Y8) & ((^[Y9 : $i > $i > $o]: (!! @ $i @ (^[Y10 : $i]: (!! @ $i @ (^[Y11 : $i]: (!! @ $i @ (^[Y12 : $i]: (((Y9 @ Y11 @ Y12) & (Y9 @ Y10 @ Y11)) => (Y9 @ Y10 @ Y12))))))))) @ Y8)) => (Y8 @ Y6 @ Y7))))))))) @ Y4))) @ Y0 @ Y3 @ Y2) & ((^[Y4 : $i > $i > $o]: ((^[Y5 : $i > $i > $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (Y6 = Y7))))))) @ ((^[Y5 : $i > $i > $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: (!! @ ($i > $i > $o) @ (^[Y8 : $i > $i > $o]: ((((^[Y9 : $i > $i > $o]: ((^[Y10 : $i > $i > $o]: (!! @ $i @ (^[Y11 : $i]: (!! @ $i @ (^[Y12 : $i]: ((Y9 @ Y11 @ Y12) => (Y10 @ Y11 @ Y12))))))))) @ Y5 @ Y8) & ((^[Y9 : $i > $i > $o]: (!! @ $i @ (^[Y10 : $i]: (!! @ $i @ (^[Y11 : $i]: (!! @ $i @ (^[Y12 : $i]: (((Y9 @ Y11 @ Y12) & (Y9 @ Y10 @ Y11)) => (Y9 @ Y10 @ Y12))))))))) @ Y8)) => (Y8 @ Y6 @ Y7))))))))) @ Y4))) @ Y0 @ Y3 @ Y1)) => ((^[Y4 : $i > $i > $o]: ((^[Y5 : $i]: ((^[Y6 : $i]: (?? @ $i @ (^[Y7 : $i]: (((^[Y8 : $i > $i > $o]: ((^[Y9 : $i > $i > $o]: ((^[Y10 : $i]: ((^[Y11 : $i]: ((Y9 @ Y10 @ Y11) | (Y10 = Y11))))))) @ ((^[Y9 : $i > $i > $o]: ((^[Y10 : $i]: ((^[Y11 : $i]: (!! @ ($i > $i > $o) @ (^[Y12 : $i > $i > $o]: ((((^[Y13 : $i > $i > $o]: ((^[Y14 : $i > $i > $o]: (!! @ $i @ (^[Y15 : $i]: (!! @ $i @ (^[Y16 : $i]: ((Y13 @ Y15 @ Y16) => (Y14 @ Y15 @ Y16))))))))) @ Y9 @ Y12) & ((^[Y13 : $i > $i > $o]: (!! @ $i @ (^[Y14 : $i]: (!! @ $i @ (^[Y15 : $i]: (!! @ $i @ (^[Y16 : $i]: (((Y13 @ Y15 @ Y16) & (Y13 @ Y14 @ Y15)) => (Y13 @ Y14 @ Y16))))))))) @ Y12)) => (Y12 @ Y10 @ Y11))))))))) @ Y8))) @ Y4 @ Y6 @ Y7) & ((^[Y8 : $i > $i > $o]: ((^[Y9 : $i > $i > $o]: ((^[Y10 : $i]: ((^[Y11 : $i]: ((Y9 @ Y10 @ Y11) | (Y10 = Y11))))))) @ ((^[Y9 : $i > $i > $o]: ((^[Y10 : $i]: ((^[Y11 : $i]: (!! @ ($i > $i > $o) @ (^[Y12 : $i > $i > $o]: ((((^[Y13 : $i > $i > $o]: ((^[Y14 : $i > $i > $o]: (!! @ $i @ (^[Y15 : $i]: (!! @ $i @ (^[Y16 : $i]: ((Y13 @ Y15 @ Y16) => (Y14 @ Y15 @ Y16))))))))) @ Y9 @ Y12) & ((^[Y13 : $i > $i > $o]: (!! @ $i @ (^[Y14 : $i]: (!! @ $i @ (^[Y15 : $i]: (!! @ $i @ (^[Y16 : $i]: (((Y13 @ Y15 @ Y16) & (Y13 @ Y14 @ Y15)) => (Y13 @ Y14 @ Y16))))))))) @ Y12)) => (Y12 @ Y10 @ Y11))))))))) @ Y8))) @ Y4 @ Y5 @ Y7))))))))) @ Y0 @ Y2 @ Y1)))))))))
% 0.86/0.38 for all inputs,
% 0.86/0.38 define sconfl := (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((^[Y4 : $i > $i > $o]: ((^[Y5 : $i > $i > $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (Y6 = Y7))))))) @ ((^[Y5 : $i > $i > $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: (!! @ ($i > $i > $o) @ (^[Y8 : $i > $i > $o]: ((((^[Y9 : $i > $i > $o]: ((^[Y10 : $i > $i > $o]: (!! @ $i @ (^[Y11 : $i]: (!! @ $i @ (^[Y12 : $i]: ((Y9 @ Y11 @ Y12) => (Y10 @ Y11 @ Y12))))))))) @ Y5 @ Y8) & ((^[Y9 : $i > $i > $o]: (!! @ $i @ (^[Y10 : $i]: (!! @ $i @ (^[Y11 : $i]: (!! @ $i @ (^[Y12 : $i]: (((Y9 @ Y11 @ Y12) & (Y9 @ Y10 @ Y11)) => (Y9 @ Y10 @ Y12))))))))) @ Y8)) => (Y8 @ Y6 @ Y7))))))))) @ Y4))) @ Y0 @ Y1 @ Y3) & (Y0 @ Y1 @ Y2)) => ((^[Y4 : $i > $i > $o]: ((^[Y5 : $i]: ((^[Y6 : $i]: (?? @ $i @ (^[Y7 : $i]: (((^[Y8 : $i > $i > $o]: ((^[Y9 : $i > $i > $o]: ((^[Y10 : $i]: ((^[Y11 : $i]: ((Y9 @ Y10 @ Y11) | (Y10 = Y11))))))) @ ((^[Y9 : $i > $i > $o]: ((^[Y10 : $i]: ((^[Y11 : $i]: (!! @ ($i > $i > $o) @ (^[Y12 : $i > $i > $o]: ((((^[Y13 : $i > $i > $o]: ((^[Y14 : $i > $i > $o]: (!! @ $i @ (^[Y15 : $i]: (!! @ $i @ (^[Y16 : $i]: ((Y13 @ Y15 @ Y16) => (Y14 @ Y15 @ Y16))))))))) @ Y9 @ Y12) & ((^[Y13 : $i > $i > $o]: (!! @ $i @ (^[Y14 : $i]: (!! @ $i @ (^[Y15 : $i]: (!! @ $i @ (^[Y16 : $i]: (((Y13 @ Y15 @ Y16) & (Y13 @ Y14 @ Y15)) => (Y13 @ Y14 @ Y16))))))))) @ Y12)) => (Y12 @ Y10 @ Y11))))))))) @ Y8))) @ Y4 @ Y6 @ Y7) & ((^[Y8 : $i > $i > $o]: ((^[Y9 : $i > $i > $o]: ((^[Y10 : $i]: ((^[Y11 : $i]: ((Y9 @ Y10 @ Y11) | (Y10 = Y11))))))) @ ((^[Y9 : $i > $i > $o]: ((^[Y10 : $i]: ((^[Y11 : $i]: (!! @ ($i > $i > $o) @ (^[Y12 : $i > $i > $o]: ((((^[Y13 : $i > $i > $o]: ((^[Y14 : $i > $i > $o]: (!! @ $i @ (^[Y15 : $i]: (!! @ $i @ (^[Y16 : $i]: ((Y13 @ Y15 @ Y16) => (Y14 @ Y15 @ Y16))))))))) @ Y9 @ Y12) & ((^[Y13 : $i > $i > $o]: (!! @ $i @ (^[Y14 : $i]: (!! @ $i @ (^[Y15 : $i]: (!! @ $i @ (^[Y16 : $i]: (((Y13 @ Y15 @ Y16) & (Y13 @ Y14 @ Y15)) => (Y13 @ Y14 @ Y16))))))))) @ Y12)) => (Y12 @ Y10 @ Y11))))))))) @ Y8))) @ Y4 @ Y5 @ Y7))))))))) @ Y0 @ Y2 @ Y3)))))))))
% 0.86/0.38 for all inputs,
% 0.86/0.38 define lconfl := (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y2 @ Y3)) => ((^[Y4 : $i > $i > $o]: ((^[Y5 : $i]: ((^[Y6 : $i]: (?? @ $i @ (^[Y7 : $i]: (((^[Y8 : $i > $i > $o]: ((^[Y9 : $i > $i > $o]: ((^[Y10 : $i]: ((^[Y11 : $i]: ((Y9 @ Y10 @ Y11) | (Y10 = Y11))))))) @ ((^[Y9 : $i > $i > $o]: ((^[Y10 : $i]: ((^[Y11 : $i]: (!! @ ($i > $i > $o) @ (^[Y12 : $i > $i > $o]: ((((^[Y13 : $i > $i > $o]: ((^[Y14 : $i > $i > $o]: (!! @ $i @ (^[Y15 : $i]: (!! @ $i @ (^[Y16 : $i]: ((Y13 @ Y15 @ Y16) => (Y14 @ Y15 @ Y16))))))))) @ Y9 @ Y12) & ((^[Y13 : $i > $i > $o]: (!! @ $i @ (^[Y14 : $i]: (!! @ $i @ (^[Y15 : $i]: (!! @ $i @ (^[Y16 : $i]: (((Y13 @ Y15 @ Y16) & (Y13 @ Y14 @ Y15)) => (Y13 @ Y14 @ Y16))))))))) @ Y12)) => (Y12 @ Y10 @ Y11))))))))) @ Y8))) @ Y4 @ Y6 @ Y7) & ((^[Y8 : $i > $i > $o]: ((^[Y9 : $i > $i > $o]: ((^[Y10 : $i]: ((^[Y11 : $i]: ((Y9 @ Y10 @ Y11) | (Y10 = Y11))))))) @ ((^[Y9 : $i > $i > $o]: ((^[Y10 : $i]: ((^[Y11 : $i]: (!! @ ($i > $i > $o) @ (^[Y12 : $i > $i > $o]: ((((^[Y13 : $i > $i > $o]: ((^[Y14 : $i > $i > $o]: (!! @ $i @ (^[Y15 : $i]: (!! @ $i @ (^[Y16 : $i]: ((Y13 @ Y15 @ Y16) => (Y14 @ Y15 @ Y16))))))))) @ Y9 @ Y12) & ((^[Y13 : $i > $i > $o]: (!! @ $i @ (^[Y14 : $i]: (!! @ $i @ (^[Y15 : $i]: (!! @ $i @ (^[Y16 : $i]: (((Y13 @ Y15 @ Y16) & (Y13 @ Y14 @ Y15)) => (Y13 @ Y14 @ Y16))))))))) @ Y12)) => (Y12 @ Y10 @ Y11))))))))) @ Y8))) @ Y4 @ Y5 @ Y7))))))))) @ Y0 @ Y1 @ Y3)))))))))
% 0.86/0.38 for all inputs,
% 0.86/0.38 define join := (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: (((^[Y4 : $i > $i > $o]: ((^[Y5 : $i > $i > $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (Y6 = Y7))))))) @ ((^[Y5 : $i > $i > $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: (!! @ ($i > $i > $o) @ (^[Y8 : $i > $i > $o]: ((((^[Y9 : $i > $i > $o]: ((^[Y10 : $i > $i > $o]: (!! @ $i @ (^[Y11 : $i]: (!! @ $i @ (^[Y12 : $i]: ((Y9 @ Y11 @ Y12) => (Y10 @ Y11 @ Y12))))))))) @ Y5 @ Y8) & ((^[Y9 : $i > $i > $o]: (!! @ $i @ (^[Y10 : $i]: (!! @ $i @ (^[Y11 : $i]: (!! @ $i @ (^[Y12 : $i]: (((Y9 @ Y11 @ Y12) & (Y9 @ Y10 @ Y11)) => (Y9 @ Y10 @ Y12))))))))) @ Y8)) => (Y8 @ Y6 @ Y7))))))))) @ Y4))) @ Y0 @ Y2 @ Y3) & ((^[Y4 : $i > $i > $o]: ((^[Y5 : $i > $i > $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (Y6 = Y7))))))) @ ((^[Y5 : $i > $i > $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: (!! @ ($i > $i > $o) @ (^[Y8 : $i > $i > $o]: ((((^[Y9 : $i > $i > $o]: ((^[Y10 : $i > $i > $o]: (!! @ $i @ (^[Y11 : $i]: (!! @ $i @ (^[Y12 : $i]: ((Y9 @ Y11 @ Y12) => (Y10 @ Y11 @ Y12))))))))) @ Y5 @ Y8) & ((^[Y9 : $i > $i > $o]: (!! @ $i @ (^[Y10 : $i]: (!! @ $i @ (^[Y11 : $i]: (!! @ $i @ (^[Y12 : $i]: (((Y9 @ Y11 @ Y12) & (Y9 @ Y10 @ Y11)) => (Y9 @ Y10 @ Y12))))))))) @ Y8)) => (Y8 @ Y6 @ Y7))))))))) @ Y4))) @ Y0 @ Y1 @ Y3)))))))))
% 0.86/0.38 for all inputs,
% 0.86/0.38 define norm := (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: ((^[Y5 : $i]: (((^[Y6 : $i > $i > $o]: ((^[Y7 : $i > $i > $o]: ((^[Y8 : $i]: ((^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (Y8 = Y9))))))) @ ((^[Y7 : $i > $i > $o]: ((^[Y8 : $i]: ((^[Y9 : $i]: (!! @ ($i > $i > $o) @ (^[Y10 : $i > $i > $o]: ((((^[Y11 : $i > $i > $o]: ((^[Y12 : $i > $i > $o]: (!! @ $i @ (^[Y13 : $i]: (!! @ $i @ (^[Y14 : $i]: ((Y11 @ Y13 @ Y14) => (Y12 @ Y13 @ Y14))))))))) @ Y7 @ Y10) & ((^[Y11 : $i > $i > $o]: (!! @ $i @ (^[Y12 : $i]: (!! @ $i @ (^[Y13 : $i]: (!! @ $i @ (^[Y14 : $i]: (((Y11 @ Y13 @ Y14) & (Y11 @ Y12 @ Y13)) => (Y11 @ Y12 @ Y14))))))))) @ Y10)) => (Y10 @ Y8 @ Y9))))))))) @ Y6))) @ Y3 @ Y5 @ Y4) & ((^[Y6 : $i > $i > $o]: ((^[Y7 : $i]: (~ (?? @ $i @ (^[Y8 : $i]: (Y6 @ Y7 @ Y8))))))) @ Y3 @ Y4))))))) @ Y0 @ Y2 @ Y1))))))
% 0.86/0.38 for all inputs,
% 0.86/0.38 define nfof := (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((^[Y3 : $i > $i > $o]: ((^[Y4 : $i > $i > $o]: ((^[Y5 : $i]: ((^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (Y5 = Y6))))))) @ ((^[Y4 : $i > $i > $o]: ((^[Y5 : $i]: ((^[Y6 : $i]: (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: ((((^[Y8 : $i > $i > $o]: ((^[Y9 : $i > $i > $o]: (!! @ $i @ (^[Y10 : $i]: (!! @ $i @ (^[Y11 : $i]: ((Y8 @ Y10 @ Y11) => (Y9 @ Y10 @ Y11))))))))) @ Y4 @ Y7) & ((^[Y8 : $i > $i > $o]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (!! @ $i @ (^[Y11 : $i]: (((Y8 @ Y10 @ Y11) & (Y8 @ Y9 @ Y10)) => (Y8 @ Y9 @ Y11))))))))) @ Y7)) => (Y7 @ Y5 @ Y6))))))))) @ Y3))) @ Y0 @ Y2 @ Y1) & ((^[Y3 : $i > $i > $o]: ((^[Y4 : $i]: (~ (?? @ $i @ (^[Y5 : $i]: (Y3 @ Y4 @ Y5))))))) @ Y0 @ Y1)))))))
% 0.86/0.38 for all inputs,
% 0.86/0.38 define innf := (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (~ (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y1 @ Y2)))))))
% 0.86/0.38 for all inputs,
% 0.86/0.38 define ind := (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (((^[Y4 : $i > $i > $o]: ((^[Y5 : $i]: ((^[Y6 : $i]: (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: ((((^[Y8 : $i > $i > $o]: ((^[Y9 : $i > $i > $o]: (!! @ $i @ (^[Y10 : $i]: (!! @ $i @ (^[Y11 : $i]: ((Y8 @ Y10 @ Y11) => (Y9 @ Y10 @ Y11))))))))) @ Y4 @ Y7) & ((^[Y8 : $i > $i > $o]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (!! @ $i @ (^[Y11 : $i]: (((Y8 @ Y10 @ Y11) & (Y8 @ Y9 @ Y10)) => (Y8 @ Y9 @ Y11))))))))) @ Y7)) => (Y7 @ Y5 @ Y6))))))))) @ Y0 @ Y2 @ Y3) => (Y1 @ Y3)))) => (Y1 @ Y2)))) => (!! @ $i @ (^[Y2 : $i]: (Y1 @ Y2)))))))
% 0.86/0.38 for all inputs,
% 0.86/0.38 define term := (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: (Y1 @ Y2))) => (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (~ (Y0 @ Y2 @ Y3))))))))))))
% 0.86/0.38 for all inputs,
% 0.86/0.38 define total := (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y0 @ Y2 @ Y1) | (Y0 @ Y1 @ Y2)) | (Y2 = Y1)))))))
% 0.86/0.38 for all inputs,
% 0.86/0.38 define so := (^[Y0 : $i > $i > $o]: (((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y4) & (Y1 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y4))))))))) @ Y0) & ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) => (~ (Y1 @ Y3 @ Y2)))))))) @ Y0)))
% 0.86/0.38 for all inputs,
% 0.86/0.38 define po := (^[Y0 : $i > $i > $o]: ((((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (Y1 @ Y2 @ Y2)))) @ Y0) & ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y1 @ Y3 @ Y2) & (Y1 @ Y2 @ Y3)) => (Y3 = Y2))))))) @ Y0)) & ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y4) & (Y1 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y4))))))))) @ Y0)))
% 0.86/0.38 for all inputs,
% 0.86/0.38 define trsc := (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((Y1 @ Y2 @ Y3) | (Y1 @ Y3 @ Y2))))))) @ ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((Y1 @ Y2 @ Y3) | (Y2 = Y3))))))) @ ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: ((^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: ((((^[Y5 : $i > $i > $o]: ((^[Y6 : $i > $i > $o]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y5 @ Y7 @ Y8) => (Y6 @ Y7 @ Y8))))))))) @ Y1 @ Y4) & ((^[Y5 : $i > $i > $o]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y7 @ Y8) & (Y5 @ Y6 @ Y7)) => (Y5 @ Y6 @ Y8))))))))) @ Y4)) => (Y4 @ Y2 @ Y3))))))))) @ Y0))))
% 0.86/0.38 for all inputs,
% 0.86/0.38 define trc := (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((Y1 @ Y2 @ Y3) | (Y2 = Y3))))))) @ ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: ((^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: ((((^[Y5 : $i > $i > $o]: ((^[Y6 : $i > $i > $o]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y5 @ Y7 @ Y8) => (Y6 @ Y7 @ Y8))))))))) @ Y1 @ Y4) & ((^[Y5 : $i > $i > $o]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y7 @ Y8) & (Y5 @ Y6 @ Y7)) => (Y5 @ Y6 @ Y8))))))))) @ Y4)) => (Y4 @ Y2 @ Y3))))))))) @ Y0)))
% 0.86/0.38 for all inputs,
% 0.86/0.38 define tc := (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: ((((^[Y4 : $i > $i > $o]: ((^[Y5 : $i > $i > $o]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y6 @ Y7) => (Y5 @ Y6 @ Y7))))))))) @ Y0 @ Y3) & ((^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y6 @ Y7) & (Y4 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y7))))))))) @ Y3)) => (Y3 @ Y1 @ Y2)))))))))
% 0.86/0.38 for all inputs,
% 0.86/0.38 define trans := (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y3)))))))))
% 0.86/0.38 for all inputs,
% 0.86/0.38 define sc := (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1)))))))
% 0.86/0.38 for all inputs,
% 0.86/0.38 define asymm := (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (~ (Y0 @ Y2 @ Y1))))))))
% 0.86/0.38 for all inputs,
% 0.86/0.38 define antisymm := (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y2 = Y1)))))))
% 0.86/0.38 for all inputs,
% 0.86/0.38 define symm := (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1)))))))
% 0.86/0.38 for all inputs,
% 0.86/0.38 define rc := (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y1 = Y2)))))))
% 0.86/0.38 for all inputs,
% 0.86/0.38 define irrefl := (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1)))))
% 0.86/0.38 for all inputs,
% 0.86/0.38 define refl := (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))
% 0.86/0.38 for all inputs,
% 0.86/0.38 define mono := (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((^[Y3 : $i > $i > $o]: ((^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y3 @ Y5 @ Y6) => (Y4 @ Y5 @ Y6))))))))) @ Y1 @ Y2) => ((^[Y3 : $i > $i > $o]: ((^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y3 @ Y5 @ Y6) => (Y4 @ Y5 @ Y6))))))))) @ (Y0 @ Y1) @ (Y0 @ Y2))))))))
% 0.86/0.38 for all inputs,
% 0.86/0.38 define infl := (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y2 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5))))))))) @ Y1 @ (Y0 @ Y1)))))
% 0.86/0.38 for all inputs,
% 0.86/0.38 define idem := (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ Y1) = (Y0 @ (Y0 @ Y1))))))
% 0.86/0.38 for all inputs,
% 0.86/0.38 define inv := (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y0 @ Y2 @ Y1))))))
% 0.86/0.38 for all inputs,
% 0.86/0.38 define subrel := (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3)))))))))
% 0.86/0.38 % SZS output end Definitions and Model Updates.
% 0.86/0.38 % (252314)------------------------------
% 0.86/0.38 % (252314)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.86/0.38 % (252314)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.86/0.38 % (252314)CaDiCaL version: 2.1.3
% 0.86/0.38 % (252314)Termination reason: Satisfiable
% 0.86/0.38 % (252314)Time elapsed: 0.006 s
% 0.86/0.38 % (252314)Peak memory usage: 12 MB
% 0.86/0.38 % (252314)Instructions burned: 12 (million)
% 0.86/0.38 % (252224)Success in time 0.146 s
% 0.86/0.38 % Vampire exiting
%------------------------------------------------------------------------------