%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT179^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 07:48:29 AM UTC 2026
% Result : Theorem 1.42s 0.56s
% Output : Refutation 1.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT179^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n020.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 18:07:20 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.22/0.27 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
% 0.63/0.42 % (1406321)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.63/0.42 % (1406327)lrs+10_16_si=on:nwc=1.5:random_seed=972273327:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.63/0.42 % (1406332)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.63/0.42 % (1406332)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.63/0.42 % (1406327)Instruction limit reached!
% 0.63/0.42 % (1406327)------------------------------
% 0.63/0.42 % (1406327)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.42 % (1406327)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.42 % (1406327)CaDiCaL version: 2.1.3
% 0.63/0.42 % (1406327)Termination reason: Instruction limit
% 0.63/0.42 % (1406327)Termination phase: Property scanning
% 0.63/0.42 % (1406327)Time elapsed: 0.006 s
% 0.63/0.42 % (1406327)Peak memory usage: 10 MB
% 0.63/0.42 % (1406327)Instructions burned: 23 (million)
% 0.63/0.42 % (1406331)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=544593498:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.63/0.42 % (1406326)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1016254065:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.63/0.42 % (1406328)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3119814786:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.63/0.42 % (1406330)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1550757791:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.63/0.42 % (1406329)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=800578111:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.63/0.42 % (1406332)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=553248308:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.63/0.42 % (1406328)Instruction limit reached!
% 0.63/0.42 % (1406328)------------------------------
% 0.63/0.42 % (1406328)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.42 % (1406328)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.42 % (1406328)CaDiCaL version: 2.1.3
% 0.63/0.42 % (1406328)Termination reason: Instruction limit
% 0.63/0.42 % (1406328)Termination phase: shuffling
% 0.63/0.42 % (1406328)Time elapsed: 0.002 s
% 0.63/0.42 % (1406328)Peak memory usage: 10 MB
% 0.63/0.42 % (1406328)Instructions burned: 4 (million)
% 0.63/0.42 % (1406334)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=141508591:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.63/0.42 % (1406330)Instruction limit reached!
% 0.63/0.42 % (1406330)------------------------------
% 0.63/0.42 % (1406330)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.42 % (1406330)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.42 % (1406330)CaDiCaL version: 2.1.3
% 0.63/0.42 % (1406330)Termination reason: Instruction limit
% 0.63/0.42 % (1406330)Termination phase: Preprocessing 2
% 0.63/0.42 % (1406330)Time elapsed: 0.013 s
% 0.63/0.42 % (1406330)Peak memory usage: 10 MB
% 0.63/0.42 % (1406330)Instructions burned: 25 (million)
% 0.63/0.42 % (1406334)Instruction limit reached!
% 0.63/0.42 % (1406334)------------------------------
% 0.63/0.42 % (1406334)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.42 % (1406334)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.42 % (1406334)CaDiCaL version: 2.1.3
% 0.63/0.42 % (1406334)Termination reason: Instruction limit
% 0.63/0.42 % (1406334)Termination phase: shuffling
% 0.63/0.42 % (1406334)Time elapsed: 0.001 s
% 0.63/0.42 % (1406334)Peak memory usage: 10 MB
% 0.63/0.42 % (1406334)Instructions burned: 5 (million)
% 0.63/0.42 % (1406341)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=837164987:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.63/0.45 % (1406344)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=267805187:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.63/0.45 % (1406341)Instruction limit reached!
% 0.63/0.45 % (1406341)------------------------------
% 0.63/0.45 % (1406341)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.45 % (1406341)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.45 % (1406341)CaDiCaL version: 2.1.3
% 0.63/0.45 % (1406341)Termination reason: Instruction limit
% 0.63/0.45 % (1406341)Termination phase: shuffling
% 0.63/0.45 % (1406341)Time elapsed: 0.004 s
% 0.63/0.45 % (1406341)Peak memory usage: 10 MB
% 0.63/0.45 % (1406341)Instructions burned: 6 (million)
% 0.63/0.45 % (1406344)Instruction limit reached!
% 0.63/0.45 % (1406344)------------------------------
% 0.63/0.45 % (1406344)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.45 % (1406344)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.45 % (1406344)CaDiCaL version: 2.1.3
% 0.63/0.45 % (1406344)Termination reason: Instruction limit
% 0.63/0.45 % (1406344)Termination phase: shuffling
% 0.63/0.45 % (1406344)Time elapsed: 0.003 s
% 0.63/0.45 % (1406344)Peak memory usage: 10 MB
% 0.63/0.45 % (1406344)Instructions burned: 12 (million)
% 0.63/0.45 % (1406343)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.63/0.45 % (1406343)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2018389879:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.63/0.45 % (1406331)Instruction limit reached!
% 0.63/0.45 % (1406331)------------------------------
% 0.63/0.45 % (1406331)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.45 % (1406331)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.45 % (1406331)CaDiCaL version: 2.1.3
% 0.63/0.45 % (1406331)Termination reason: Instruction limit
% 0.63/0.45 % (1406331)Termination phase: Property scanning
% 0.63/0.45 % (1406331)Time elapsed: 0.037 s
% 0.63/0.45 % (1406331)Peak memory usage: 12 MB
% 0.63/0.45 % (1406331)Instructions burned: 75 (million)
% 0.63/0.45 % (1406343)Instruction limit reached!
% 0.63/0.45 % (1406343)------------------------------
% 0.63/0.45 % (1406343)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.45 % (1406343)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.45 % (1406343)CaDiCaL version: 2.1.3
% 0.63/0.45 % (1406343)Termination reason: Instruction limit
% 0.63/0.45 % (1406343)Termination phase: shuffling
% 0.63/0.45 % (1406343)Time elapsed: 0.007 s
% 0.63/0.45 % (1406343)Peak memory usage: 10 MB
% 0.63/0.45 % (1406343)Instructions burned: 15 (million)
% 0.63/0.45 % (1406348)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=885672842:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.63/0.45 % (1406347)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.63/0.45 % (1406347)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.63/0.45 % (1406347)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3673028017:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.63/0.45 % (1406350)lrs+10_1_si=on:cs=on:random_seed=781453481:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.63/0.45 % (1406351)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.63/0.45 % (1406350)Instruction limit reached!
% 0.63/0.45 % (1406350)------------------------------
% 0.63/0.45 % (1406350)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.45 % (1406350)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.45 % (1406350)CaDiCaL version: 2.1.3
% 0.63/0.45 % (1406350)Termination reason: Instruction limit
% 0.63/0.45 % (1406350)Termination phase: shuffling
% 0.63/0.48 % (1406350)Time elapsed: 0.004 s
% 0.63/0.48 % (1406350)Peak memory usage: 10 MB
% 0.63/0.48 % (1406350)Instructions burned: 8 (million)
% 0.63/0.48 % (1406351)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=1372797720:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.63/0.48 % (1406347)Instruction limit reached!
% 0.63/0.48 % (1406347)------------------------------
% 0.63/0.48 % (1406347)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.48 % (1406347)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.48 % (1406347)CaDiCaL version: 2.1.3
% 0.63/0.48 % (1406347)Termination reason: Instruction limit
% 0.63/0.48 % (1406347)Termination phase: Property scanning
% 0.63/0.48 % (1406347)Time elapsed: 0.014 s
% 0.63/0.48 % (1406347)Peak memory usage: 11 MB
% 0.63/0.48 % (1406347)Instructions burned: 29 (million)
% 0.63/0.48 % (1406351)Instruction limit reached!
% 0.63/0.48 % (1406351)------------------------------
% 0.63/0.48 % (1406351)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.48 % (1406351)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.48 % (1406351)CaDiCaL version: 2.1.3
% 0.63/0.48 % (1406351)Termination reason: Instruction limit
% 0.63/0.48 % (1406351)Termination phase: shuffling
% 0.63/0.48 % (1406351)Time elapsed: 0.002 s
% 0.63/0.48 % (1406351)Peak memory usage: 10 MB
% 0.63/0.48 % (1406351)Instructions burned: 3 (million)
% 0.63/0.48 % (1406348)Instruction limit reached!
% 0.63/0.48 % (1406348)------------------------------
% 0.63/0.48 % (1406348)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.48 % (1406348)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.48 % (1406348)CaDiCaL version: 2.1.3
% 0.63/0.48 % (1406348)Termination reason: Instruction limit
% 0.63/0.48 % (1406348)Termination phase: Saturation
% 0.63/0.48 % (1406348)Time elapsed: 0.024 s
% 0.63/0.48 % (1406348)Peak memory usage: 12 MB
% 0.63/0.48 % (1406348)Instructions burned: 99 (million)
% 0.63/0.48 % (1406359)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=4070162032:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.63/0.48 % (1406326)Instruction limit reached!
% 0.63/0.48 % (1406326)------------------------------
% 0.63/0.48 % (1406326)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.48 % (1406326)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.48 % (1406326)CaDiCaL version: 2.1.3
% 0.63/0.48 % (1406326)Termination reason: Instruction limit
% 0.63/0.48 % (1406326)Termination phase: Saturation
% 0.63/0.48 % (1406326)Time elapsed: 0.079 s
% 0.63/0.48 % (1406326)Peak memory usage: 13 MB
% 0.63/0.48 % (1406326)Instructions burned: 87 (million)
% 0.63/0.48 % (1406356)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=3997231230:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 0.63/0.48 % (1406332)Instruction limit reached!
% 0.63/0.48 % (1406332)------------------------------
% 0.63/0.48 % (1406332)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.48 % (1406332)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.48 % (1406332)CaDiCaL version: 2.1.3
% 0.63/0.48 % (1406332)Termination reason: Instruction limit
% 0.63/0.48 % (1406332)Termination phase: Saturation
% 0.63/0.48 % (1406332)Time elapsed: 0.079 s
% 0.63/0.48 % (1406332)Peak memory usage: 13 MB
% 0.63/0.48 % (1406332)Instructions burned: 158 (million)
% 0.63/0.48 % (1406357)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=23861313:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.63/0.48 % (1406359)Instruction limit reached!
% 0.63/0.48 % (1406359)------------------------------
% 0.63/0.48 % (1406359)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.48 % (1406359)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.48 % (1406359)CaDiCaL version: 2.1.3
% 0.63/0.48 % (1406359)Termination reason: Instruction limit
% 0.63/0.48 % (1406359)Termination phase: Property scanning
% 0.63/0.48 % (1406359)Time elapsed: 0.004 s
% 0.63/0.48 % (1406359)Peak memory usage: 10 MB
% 0.63/0.48 % (1406359)Instructions burned: 17 (million)
% 0.63/0.48 % (1406358)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2207987003:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.42/0.53 % (1406365)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=2771182458: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)
% 1.42/0.53 % (1406365)Instruction limit reached!
% 1.42/0.53 % (1406365)------------------------------
% 1.42/0.53 % (1406365)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.53 % (1406365)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.53 % (1406365)CaDiCaL version: 2.1.3
% 1.42/0.53 % (1406365)Termination reason: Instruction limit
% 1.42/0.53 % (1406365)Termination phase: shuffling
% 1.42/0.53 % (1406365)Time elapsed: 0.001 s
% 1.42/0.53 % (1406365)Peak memory usage: 10 MB
% 1.42/0.53 % (1406365)Instructions burned: 5 (million)
% 1.42/0.53 % (1406357)Refutation not found, incomplete strategy
% 1.42/0.53 % (1406357)------------------------------
% 1.42/0.53 % (1406357)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.53 % (1406357)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.53 % (1406357)CaDiCaL version: 2.1.3
% 1.42/0.53 % (1406357)Termination reason: Refutation not found, incomplete strategy
% 1.42/0.53 % (1406357)Time elapsed: 0.016 s
% 1.42/0.53 % (1406357)Peak memory usage: 13 MB
% 1.42/0.53 % (1406357)Instructions burned: 30 (million)
% 1.42/0.53 % (1406362)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=3690485227:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.42/0.53 % (1406358)Instruction limit reached!
% 1.42/0.53 % (1406358)------------------------------
% 1.42/0.53 % (1406358)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.53 % (1406358)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.53 % (1406358)CaDiCaL version: 2.1.3
% 1.42/0.53 % (1406358)Termination reason: Instruction limit
% 1.42/0.53 % (1406358)Termination phase: SInE selection
% 1.42/0.53 % (1406358)Time elapsed: 0.013 s
% 1.42/0.53 % (1406358)Peak memory usage: 11 MB
% 1.42/0.53 % (1406358)Instructions burned: 25 (million)
% 1.42/0.53 % (1406363)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=4147818300:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.42/0.53 % (1406357)------------------------------
% 1.42/0.53 % (1406357)------------------------------
% 1.42/0.53 % (1406356)Instruction limit reached!
% 1.42/0.53 % (1406356)------------------------------
% 1.42/0.53 % (1406356)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.53 % (1406356)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.53 % (1406356)CaDiCaL version: 2.1.3
% 1.42/0.53 % (1406356)Termination reason: Instruction limit
% 1.42/0.53 % (1406356)Termination phase: Saturation
% 1.42/0.53 % (1406356)Time elapsed: 0.020 s
% 1.42/0.53 % (1406356)Peak memory usage: 12 MB
% 1.42/0.53 % (1406356)Instructions burned: 39 (million)
% 1.42/0.53 % (1406368)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=3891442781:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.42/0.53 % (1406363)Instruction limit reached!
% 1.42/0.53 % (1406363)------------------------------
% 1.42/0.53 % (1406363)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.53 % (1406363)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.53 % (1406363)CaDiCaL version: 2.1.3
% 1.42/0.53 % (1406363)Termination reason: Instruction limit
% 1.42/0.53 % (1406363)Termination phase: Property scanning
% 1.42/0.53 % (1406363)Time elapsed: 0.007 s
% 1.42/0.53 % (1406363)Peak memory usage: 10 MB
% 1.42/0.53 % (1406363)Instructions burned: 14 (million)
% 1.42/0.53 % (1406368)Instruction limit reached!
% 1.42/0.53 % (1406368)------------------------------
% 1.42/0.53 % (1406368)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.53 % (1406368)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.53 % (1406368)CaDiCaL version: 2.1.3
% 1.42/0.53 % (1406368)Termination reason: Instruction limit
% 1.42/0.53 % (1406368)Termination phase: Property scanning
% 1.42/0.53 % (1406368)Time elapsed: 0.007 s
% 1.42/0.53 % (1406368)Peak memory usage: 11 MB
% 1.42/0.53 % (1406368)Instructions burned: 30 (million)
% 1.42/0.53 % (1406373)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
% 1.42/0.55 % (1406373)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.42/0.55 % (1406372)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=2526462799:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.42/0.55 % (1406371)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=3298460626:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.42/0.55 % (1406373)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=89960453:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.42/0.55 % (1406375)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.42/0.55 % (1406376)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=4127193170:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 1.42/0.55 % (1406375)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=1186456765:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.42/0.55 % (1406373)Instruction limit reached!
% 1.42/0.55 % (1406373)------------------------------
% 1.42/0.55 % (1406373)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.55 % (1406373)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.55 % (1406373)CaDiCaL version: 2.1.3
% 1.42/0.55 % (1406373)Termination reason: Instruction limit
% 1.42/0.55 % (1406373)Termination phase: shuffling
% 1.42/0.55 % (1406373)Time elapsed: 0.007 s
% 1.42/0.55 % (1406373)Peak memory usage: 10 MB
% 1.42/0.55 % (1406373)Instructions burned: 15 (million)
% 1.42/0.55 % (1406371)Instruction limit reached!
% 1.42/0.55 % (1406371)------------------------------
% 1.42/0.55 % (1406371)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.55 % (1406371)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.55 % (1406371)CaDiCaL version: 2.1.3
% 1.42/0.55 % (1406371)Termination reason: Instruction limit
% 1.42/0.55 % (1406371)Termination phase: Property scanning
% 1.42/0.55 % (1406371)Time elapsed: 0.011 s
% 1.42/0.55 % (1406371)Peak memory usage: 10 MB
% 1.42/0.55 % (1406371)Instructions burned: 24 (million)
% 1.42/0.55 % (1406375)Instruction limit reached!
% 1.42/0.55 % (1406375)------------------------------
% 1.42/0.55 % (1406375)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.55 % (1406375)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.55 % (1406375)CaDiCaL version: 2.1.3
% 1.42/0.55 % (1406375)Termination reason: Instruction limit
% 1.42/0.55 % (1406375)Termination phase: shuffling
% 1.42/0.55 % (1406375)Time elapsed: 0.004 s
% 1.42/0.55 % (1406375)Peak memory usage: 10 MB
% 1.42/0.55 % (1406375)Instructions burned: 8 (million)
% 1.42/0.55 % (1406376)Instruction limit reached!
% 1.42/0.55 % (1406376)------------------------------
% 1.42/0.55 % (1406376)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.55 % (1406376)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.55 % (1406376)CaDiCaL version: 2.1.3
% 1.42/0.55 % (1406376)Termination reason: Instruction limit
% 1.42/0.55 % (1406376)Termination phase: Property scanning
% 1.42/0.55 % (1406376)Time elapsed: 0.008 s
% 1.42/0.55 % (1406376)Peak memory usage: 10 MB
% 1.42/0.55 % (1406376)Instructions burned: 34 (million)
% 1.42/0.55 % (1406382)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=499118046:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 1.42/0.55 % (1406372)Instruction limit reached!
% 1.42/0.55 % (1406372)------------------------------
% 1.42/0.55 % (1406372)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.55 % (1406372)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.55 % (1406372)CaDiCaL version: 2.1.3
% 1.42/0.55 % (1406372)Termination reason: Instruction limit
% 1.42/0.55 % (1406372)Termination phase: Property scanning
% 1.42/0.55 % (1406372)Time elapsed: 0.028 s
% 1.42/0.55 % (1406372)Peak memory usage: 11 MB
% 1.42/0.55 % (1406372)Instructions burned: 61 (million)
% 1.42/0.55 % (1406383)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=3587116944:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.42/0.55 % (1406384)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=2861009296:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 1.42/0.55 % (1406382)Instruction limit reached!
% 1.42/0.55 % (1406382)------------------------------
% 1.42/0.55 % (1406382)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.55 % (1406382)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.55 % (1406382)CaDiCaL version: 2.1.3
% 1.42/0.55 % (1406382)Termination reason: Instruction limit
% 1.42/0.55 % (1406382)Termination phase: shuffling
% 1.42/0.55 % (1406382)Time elapsed: 0.005 s
% 1.42/0.55 % (1406382)Peak memory usage: 10 MB
% 1.42/0.55 % (1406382)Instructions burned: 8 (million)
% 1.42/0.55 % (1406385)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=44613264:i=1240:rtra=on:ixr=off_2998 on theBenchmark for (2998ds/1240Mi)
% 1.42/0.55 % (1406387)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=3540555134:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/143Mi)
% 1.42/0.55 % (1406384)Instruction limit reached!
% 1.42/0.55 % (1406384)------------------------------
% 1.42/0.55 % (1406384)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.55 % (1406384)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.55 % (1406384)CaDiCaL version: 2.1.3
% 1.42/0.55 % (1406384)Termination reason: Instruction limit
% 1.42/0.55 % (1406384)Termination phase: Property scanning
% 1.42/0.55 % (1406384)Time elapsed: 0.010 s
% 1.42/0.55 % (1406384)Peak memory usage: 10 MB
% 1.42/0.55 % (1406384)Instructions burned: 20 (million)
% 1.42/0.55 % (1406383)Instruction limit reached!
% 1.42/0.55 % (1406383)------------------------------
% 1.42/0.55 % (1406383)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.55 % (1406383)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.55 % (1406383)CaDiCaL version: 2.1.3
% 1.42/0.55 % (1406383)Termination reason: Instruction limit
% 1.42/0.55 % (1406383)Termination phase: shuffling
% 1.42/0.55 % (1406383)Time elapsed: 0.011 s
% 1.42/0.55 % (1406383)Peak memory usage: 10 MB
% 1.42/0.55 % (1406383)Instructions burned: 24 (million)
% 1.42/0.55 % (1406390)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=834661194:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 1.42/0.55 % (1406394)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.42/0.55 % (1406393)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2275840638:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 1.42/0.55 % (1406394)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=382756162:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 1.42/0.55 % (1406394)Instruction limit reached!
% 1.42/0.55 % (1406394)------------------------------
% 1.42/0.55 % (1406394)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.55 % (1406394)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.55 % (1406394)CaDiCaL version: 2.1.3
% 1.42/0.55 % (1406394)Termination reason: Instruction limit
% 1.42/0.55 % (1406394)Termination phase: shuffling
% 1.42/0.55 % (1406394)Time elapsed: 0.004 s
% 1.42/0.55 % (1406394)Peak memory usage: 10 MB
% 1.42/0.55 % (1406394)Instructions burned: 8 (million)
% 1.42/0.55 % (1406387)Instruction limit reached!
% 1.42/0.55 % (1406387)------------------------------
% 1.42/0.55 % (1406387)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.55 % (1406387)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.55 % (1406387)CaDiCaL version: 2.1.3
% 1.42/0.55 % (1406387)Termination reason: Instruction limit
% 1.42/0.55 % (1406387)Termination phase: Saturation
% 1.42/0.55 % (1406387)Time elapsed: 0.039 s
% 1.42/0.55 % (1406387)Peak memory usage: 14 MB
% 1.42/0.55 % (1406387)Instructions burned: 144 (million)
% 1.42/0.55 % (1406393)Instruction limit reached!
% 1.42/0.55 % (1406393)------------------------------
% 1.42/0.55 % (1406393)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.55 % (1406393)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.55 % (1406393)CaDiCaL version: 2.1.3
% 1.42/0.55 % (1406393)Termination reason: Instruction limit
% 1.42/0.55 % (1406393)Termination phase: Property scanning
% 1.42/0.55 % (1406393)Time elapsed: 0.021 s
% 1.42/0.55 % (1406393)Peak memory usage: 11 MB
% 1.42/0.55 % (1406393)Instructions burned: 44 (million)
% 1.42/0.55 % (1406398)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=1427515006:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 1.42/0.55 % (1406399)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=2426630491:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2997 on theBenchmark for (2997ds/169Mi)
% 1.42/0.55 % (1406400)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 1.42/0.56 % (1406400)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=801225849:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2997 on theBenchmark for (2997ds/6Mi)
% 1.42/0.56 % (1406399) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1406321-1406399"...
% 1.42/0.56 % (1406399)...printing done.
% 1.42/0.56 % (1406399)Refutation found. Thanks to Tanya!
% 1.42/0.56 % SZS status Theorem for theBenchmark
% 1.42/0.56 % SZS output start Proof for theBenchmark
% 1.42/0.56 thf(type_def_5, type, coinductive_llist: $tType > $tType).
% 1.42/0.56 thf(type_def_6, type, option: $tType > $tType).
% 1.42/0.56 thf(type_def_7, type, set: $tType > $tType).
% 1.42/0.56 thf(type_def_8, type, num: $tType).
% 1.42/0.56 thf(type_def_9, type, nat: $tType).
% 1.42/0.56 thf(type_def_10, type, int: $tType).
% 1.42/0.56 thf(type_def_11, type, itself: $tType > $tType).
% 1.42/0.56 thf(type_def_12, type, a: $tType).
% 1.42/0.56 thf(type_def_13, type, sTfun: ($tType * $tType) > $tType).
% 1.42/0.56 thf(func_def_0, type, type: !>[X0: $tType]:((itself @ X0 > $o))).
% 1.42/0.56 thf(func_def_1, type, ord: !>[X0: $tType]:((itself @ X0 > $o))).
% 1.42/0.56 thf(func_def_2, type, order: !>[X0: $tType]:((itself @ X0 > $o))).
% 1.42/0.56 thf(func_def_3, type, semiring_1: !>[X0: $tType]:((itself @ X0 > $o))).
% 1.42/0.56 thf(func_def_4, type, linorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 1.42/0.56 thf(func_def_5, type, preorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 1.42/0.56 thf(func_def_6, type, semiring_char_0: !>[X0: $tType]:((itself @ X0 > $o))).
% 1.42/0.56 thf(func_def_7, type, linordered_semidom: !>[X0: $tType]:((itself @ X0 > $o))).
% 1.42/0.56 thf(func_def_8, type, linord219039673up_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 1.42/0.56 thf(func_def_9, type, archim1727834104eiling: !>[X0: $tType]:((itself @ X0 > $o))).
% 1.42/0.56 thf(func_def_10, type, comple187826305attice: !>[X0: $tType]:((itself @ X0 > $o))).
% 1.42/0.56 thf(func_def_11, type, archim1804426504_field: !>[X0: $tType]:((itself @ X0 > $o))).
% 1.42/0.56 thf(func_def_12, type, canoni770627133id_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 1.42/0.56 thf(func_def_13, type, ordere236663937imp_le: !>[X0: $tType]:((itself @ X0 > $o))).
% 1.42/0.56 thf(func_def_14, type, ordere516151231imp_le: !>[X0: $tType]:((itself @ X0 > $o))).
% 1.42/0.56 thf(func_def_15, type, archimedean_round: !>[X0: $tType]:((X0 > int))).
% 1.42/0.56 thf(func_def_16, type, coinductive_LNil: !>[X0: $tType]:(coinductive_llist @ X0)).
% 1.42/0.56 thf(func_def_17, type, plus_plus: !>[X0: $tType]:((X0 > X0 > X0))).
% 1.42/0.56 thf(func_def_18, type, zero_zero: !>[X0: $tType]:(X0)).
% 1.42/0.56 thf(func_def_19, type, hilbert_GreatestM: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > $o) > X0))).
% 1.42/0.56 thf(func_def_20, type, hilbert_LeastM: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > $o) > X0))).
% 1.42/0.56 thf(func_def_21, type, if: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 1.42/0.56 thf(func_def_22, type, nat2: (int > nat)).
% 1.42/0.56 thf(func_def_23, type, lList2435255213lllsts: !>[X0: $tType]:((set @ X0 > set @ coinductive_llist @ X0))).
% 1.42/0.56 thf(func_def_24, type, lList22096119349pslsts: !>[X0: $tType]:((set @ X0 > set @ coinductive_llist @ X0))).
% 1.42/0.56 thf(func_def_25, type, lList21612149805nflsts: !>[X0: $tType]:((set @ X0 > set @ coinductive_llist @ X0))).
% 1.42/0.56 thf(func_def_26, type, lList2370560421utlast: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.42/0.56 thf(func_def_27, type, lList2228235758e_ll2f: !>[X0: $tType]:((coinductive_llist @ X0 > nat > option @ X0))).
% 1.42/0.56 thf(func_def_28, type, lList21232602520length: !>[X0: $tType]:((coinductive_llist @ X0 > nat))).
% 1.42/0.56 thf(func_def_29, type, lList22119844313_ltake: !>[X0: $tType]:((coinductive_llist @ X0 > nat > coinductive_llist @ X0))).
% 1.42/0.56 thf(func_def_30, type, lList21148268032oslsts: !>[X0: $tType]:((set @ X0 > set @ coinductive_llist @ X0))).
% 1.42/0.56 thf(func_def_31, type, suc: (nat > nat)).
% 1.42/0.56 thf(func_def_32, type, semiring_1_of_nat: !>[X0: $tType]:((nat > X0))).
% 1.42/0.56 thf(func_def_33, type, semiri532925092at_aux: !>[X0: $tType]:(((X0 > X0) > nat > X0 > X0))).
% 1.42/0.56 thf(func_def_34, type, size_size: !>[X0: $tType]:((X0 > nat))).
% 1.42/0.56 thf(func_def_35, type, nat_tr1645093318rphism: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > $o) > $o))).
% 1.42/0.56 thf(func_def_36, type, nat_tsub: (int > int > int)).
% 1.42/0.56 thf(func_def_37, type, numeral_numeral: !>[X0: $tType]:((num > X0))).
% 1.42/0.56 thf(func_def_38, type, bind: !>[X0: $tType, X1: $tType]:((option @ X0 > (X0 > option @ X1) > option @ X1))).
% 1.42/0.56 thf(func_def_39, type, combine_options: !>[X0: $tType]:(((X0 > X0 > X0) > option @ X0 > option @ X0 > option @ X0))).
% 1.42/0.56 thf(func_def_40, type, is_none: !>[X0: $tType]:((option @ X0 > $o))).
% 1.42/0.56 thf(func_def_41, type, none: !>[X0: $tType]:(option @ X0)).
% 1.42/0.56 thf(func_def_42, type, some: !>[X0: $tType]:((X0 > option @ X0))).
% 1.42/0.56 thf(func_def_43, type, case_option: !>[X0: $tType, X1: $tType]:((X0 > (X1 > X0) > option @ X1 > X0))).
% 1.42/0.56 thf(func_def_44, type, pred_option: !>[X0: $tType]:(((X0 > $o) > option @ X0 > $o))).
% 1.42/0.56 thf(func_def_45, type, rec_option: !>[X0: $tType, X1: $tType]:((X0 > (X1 > X0) > option @ X1 > X0))).
% 1.42/0.56 thf(func_def_46, type, set_option: !>[X0: $tType]:((option @ X0 > set @ X0))).
% 1.42/0.56 thf(func_def_47, type, size_option: !>[X0: $tType]:(((X0 > nat) > option @ X0 > nat))).
% 1.42/0.56 thf(func_def_48, type, the: !>[X0: $tType]:((option @ X0 > X0))).
% 1.42/0.56 thf(func_def_49, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 1.42/0.56 thf(func_def_50, type, type2: !>[X0: $tType]:(itself @ X0)).
% 1.42/0.56 thf(func_def_51, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 1.42/0.56 thf(func_def_52, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 1.42/0.56 thf(func_def_53, type, q: $o).
% 1.42/0.56 thf(func_def_54, type, i: nat).
% 1.42/0.56 thf(func_def_55, type, j: nat).
% 1.42/0.56 thf(func_def_56, type, t: coinductive_llist @ a).
% 1.42/0.56 thf(func_def_57, type, x: a).
% 1.42/0.56 thf(func_def_61, type, vAND: ($o > $o > $o)).
% 1.42/0.56 thf(func_def_62, type, db1: !>[X0: $tType]:(X0)).
% 1.42/0.56 thf(func_def_63, type, db0: !>[X0: $tType]:(X0)).
% 1.42/0.56 thf(func_def_64, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 1.42/0.56 thf(func_def_65, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 1.42/0.56 thf(func_def_66, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 1.42/0.56 thf(func_def_67, type, vNOT: ($o > $o)).
% 1.42/0.56 thf(func_def_68, type, vIMP: ($o > $o > $o)).
% 1.42/0.56 thf(func_def_69, type, vOR: ($o > $o > $o)).
% 1.42/0.56 thf(func_def_70, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 1.42/0.56 thf(func_def_71, type, db2: !>[X0: $tType]:(X0)).
% 1.42/0.56 thf(func_def_72, type, sP0: !>[X0: $tType, X1: $tType]:(((option @ X1 > option @ X0 > $o) > option @ X1 > option @ X0 > $o))).
% 1.42/0.56 thf(func_def_73, type, sK1: (int > nat)).
% 1.42/0.56 thf(func_def_74, type, sK2: (nat > nat)).
% 1.42/0.56 thf(func_def_75, type, sK3: ((nat > $o) > nat)).
% 1.42/0.56 thf(func_def_76, type, sK4: ((nat > nat > $o) > nat)).
% 1.42/0.56 thf(func_def_77, type, sK5: ((nat > nat > $o) > nat)).
% 1.42/0.56 thf(func_def_78, type, sK6: ((nat > nat > $o) > nat)).
% 1.42/0.56 thf(func_def_79, type, sK7: ((nat > nat > $o) > nat)).
% 1.42/0.56 thf(func_def_80, type, sK8: ((nat > $o) > nat)).
% 1.42/0.56 thf(func_def_81, type, sK9: !>[X0: $tType]:((option @ X0 > X0))).
% 1.42/0.56 thf(func_def_82, type, sK10: (nat > nat)).
% 1.42/0.56 thf(func_def_83, type, sK11: !>[X0: $tType, X1: $tType]:(((option @ X1 > option @ X0 > $o) > option @ X1 > option @ X0 > X1))).
% 1.42/0.56 thf(func_def_84, type, sK12: !>[X0: $tType, X1: $tType]:(((option @ X1 > option @ X0 > $o) > option @ X1 > option @ X0 > X0))).
% 1.42/0.56 thf(func_def_85, type, sK13: (int > nat)).
% 1.42/0.56 thf(func_def_86, type, sK14: !>[X0: $tType]:((nat > coinductive_llist @ X0 > X0))).
% 1.42/0.56 thf(func_def_87, type, sK15: !>[X0: $tType]:((nat > coinductive_llist @ X0 > X0))).
% 1.42/0.56 thf(func_def_88, type, sK16: !>[X0: $tType]:(((option @ X0 > $o) > X0))).
% 1.42/0.56 thf(func_def_89, type, sK17: !>[X0: $tType]:(((nat > X0 > X0 > $o) > (nat > X0 > $o) > nat > X0))).
% 1.42/0.56 thf(func_def_90, type, sK18: !>[X0: $tType]:(((nat > X0 > X0 > $o) > (nat > X0 > $o) > nat))).
% 1.42/0.56 thf(func_def_91, type, sK19: !>[X0: $tType]:(((nat > X0 > X0 > $o) > (nat > X0 > $o) > X0))).
% 1.42/0.56 thf(func_def_92, type, sK20: ((nat > $o) > nat)).
% 1.42/0.56 thf(func_def_93, type, sK21: !>[X0: $tType]:((nat > coinductive_llist @ X0 > X0))).
% 1.42/0.56 thf(func_def_94, type, sK22: (nat > nat)).
% 1.42/0.56 thf(func_def_95, type, sK23: !>[X0: $tType]:((coinductive_llist @ X0 > nat > X0))).
% 1.42/0.56 thf(func_def_96, type, sK24: ((nat > $o) > nat)).
% 1.42/0.56 thf(func_def_97, type, sK25: (nat > nat)).
% 1.42/0.56 thf(func_def_98, type, sK26: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > X0))).
% 1.42/0.56 thf(func_def_99, type, sK27: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 1.42/0.56 thf(func_def_100, type, sK28: (int > nat)).
% 1.42/0.56 thf(func_def_101, type, sK29: ((nat > $o) > nat)).
% 1.42/0.56 thf(f1,axiom,(
% 1.42/0.56 ! [X3 : a] : ((((lList2228235758e_ll2f @ a @ t @ j)) = ((some @ a @ X3))) => q)),
% 1.42/0.56 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_H)).
% 1.42/0.56 thf(f2,axiom,(
% 1.42/0.56 (ord_less_eq @ nat @ j @ i)),
% 1.42/0.56 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_jlei)).
% 1.42/0.56 thf(f3,axiom,(
% 1.42/0.56 (((lList2228235758e_ll2f @ a @ t @ i)) = ((some @ a @ x)))),
% 1.42/0.56 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_tisome)).
% 1.42/0.56 thf(f57,axiom,(
% 1.42/0.56 ! [X0 : $tType,X3 : nat,X1 : coinductive_llist @ X0,X2 : nat] : ((((lList2228235758e_ll2f @ X0 @ X1 @ X2)) = none @ X0) => ((ord_less_eq @ nat @ X2 @ X3) => (((lList2228235758e_ll2f @ X0 @ X1 @ X3)) = none @ X0)))),
% 1.42/0.56 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_ll2f__None__le)).
% 1.42/0.56 thf(f93,axiom,(
% 1.42/0.56 ! [X0 : $tType,X1 : option @ X0] : ((X1 != none @ X0) => ~ ! [X2 : X0] : (X1 != ((some @ X0 @ X2))))),
% 1.42/0.56 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_option_Oexhaust)).
% 1.42/0.56 thf(f95,axiom,(
% 1.42/0.56 ! [X0 : $tType,X1 : X0] : (none @ X0 != ((some @ X0 @ X1)))),
% 1.42/0.56 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_option_Odistinct_I1_J)).
% 1.42/0.56 thf(f294,conjecture,(
% 1.42/0.56 q),
% 1.42/0.56 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 1.42/0.56 thf(f295,negated_conjecture,(
% 1.42/0.56 ~q),
% 1.42/0.56 inference(negated_conjecture,[status(cth)],[f294])).
% 1.42/0.56 thf(f312,plain,(
% 1.42/0.56 ! [X0 : $tType,X1 : nat,X2 : coinductive_llist @ X0,X3 : nat] : ((none @ X0 = ((lList2228235758e_ll2f @ X0 @ X2 @ X3))) => ((ord_less_eq @ nat @ X3 @ X1) => (none @ X0 = ((lList2228235758e_ll2f @ X0 @ X2 @ X1)))))),
% 1.42/0.56 inference(rectify,[],[f57])).
% 1.42/0.56 thf(f313,plain,(
% 1.42/0.56 ! [X0 : $tType,X2 : coinductive_llist @ X0,X3 : nat,X1 : nat] : ((none @ X0 = ((lList2228235758e_ll2f @ X0 @ X2 @ X3))) => (($true = ((ord_less_eq @ nat @ X3 @ X1))) => (none @ X0 = ((lList2228235758e_ll2f @ X0 @ X2 @ X1)))))),
% 1.42/0.56 inference(fool_elimination,[],[f312])).
% 1.42/0.56 thf(f348,plain,(
% 1.42/0.56 ! [X0 : a] : ((((lList2228235758e_ll2f @ a @ t @ j)) = ((some @ a @ X0))) => q)),
% 1.42/0.56 inference(rectify,[],[f1])).
% 1.42/0.56 thf(f349,plain,(
% 1.42/0.56 ! [X0 : a] : ((((lList2228235758e_ll2f @ a @ t @ j)) = ((some @ a @ X0))) => (q = $true))),
% 1.42/0.56 inference(fool_elimination,[],[f348])).
% 1.42/0.56 thf(f506,plain,(
% 1.42/0.56 (ord_less_eq @ nat @ j @ i)),
% 1.42/0.56 inference(rectify,[],[f2])).
% 1.42/0.56 thf(f507,plain,(
% 1.42/0.56 (((ord_less_eq @ nat @ j @ i)) = $true)),
% 1.42/0.56 inference(fool_elimination,[],[f506])).
% 1.42/0.56 thf(f615,plain,(
% 1.42/0.56 ~q),
% 1.42/0.56 inference(rectify,[],[f295])).
% 1.42/0.56 thf(f616,plain,(
% 1.42/0.56 ~ (q = $true)),
% 1.42/0.56 inference(fool_elimination,[],[f615])).
% 1.42/0.56 thf(f750,plain,(
% 1.42/0.56 (q != $true)),
% 1.42/0.56 inference(flattening,[],[f616])).
% 1.42/0.56 thf(f759,plain,(
% 1.42/0.56 ! [X0 : $tType,X2 : coinductive_llist @ X0,X3 : nat,X1 : nat] : (((none @ X0 = ((lList2228235758e_ll2f @ X0 @ X2 @ X1))) | ($true != ((ord_less_eq @ nat @ X3 @ X1)))) | (none @ X0 != ((lList2228235758e_ll2f @ X0 @ X2 @ X3))))),
% 1.42/0.56 inference(ennf_transformation,[],[f313])).
% 1.42/0.56 thf(f760,plain,(
% 1.42/0.56 ! [X0 : $tType,X2 : coinductive_llist @ X0,X3 : nat,X1 : nat] : ((none @ X0 = ((lList2228235758e_ll2f @ X0 @ X2 @ X1))) | ($true != ((ord_less_eq @ nat @ X3 @ X1))) | (none @ X0 != ((lList2228235758e_ll2f @ X0 @ X2 @ X3))))),
% 1.42/0.56 inference(flattening,[],[f759])).
% 1.42/0.56 thf(f768,plain,(
% 1.42/0.56 ! [X0 : $tType,X1 : option @ X0] : (? [X2 : X0] : (((some @ X0 @ X2)) = X1) | (none @ X0 = X1))),
% 1.42/0.56 inference(ennf_transformation,[],[f93])).
% 1.42/0.56 thf(f803,plain,(
% 1.42/0.56 ! [X0 : a] : ((((lList2228235758e_ll2f @ a @ t @ j)) != ((some @ a @ X0))) | (q = $true))),
% 1.42/0.56 inference(ennf_transformation,[],[f349])).
% 1.42/0.56 thf(f815,plain,(
% 1.42/0.56 ! [X0 : $tType,X1 : option @ X0] : ((((some @ X0 @ (sK9 @ X0 @ X1))) = X1) | (none @ X0 = X1))),
% 1.42/0.56 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X1,sK1 @ X0)],[f768])).
% 1.42/0.56 thf(f851,plain,(
% 1.42/0.56 ! [X0 : $tType,X1 : coinductive_llist @ X0,X2 : nat,X3 : nat] : ((((lList2228235758e_ll2f @ X0 @ X1 @ X3)) = none @ X0) | (((ord_less_eq @ nat @ X2 @ X3)) != $true) | (((lList2228235758e_ll2f @ X0 @ X1 @ X2)) != none @ X0))),
% 1.42/0.56 inference(rectify,[],[f760])).
% 1.42/0.56 thf(f868,plain,(
% 1.42/0.56 ( ! [X0 : $tType,X1 : option @ X0] : ((((some @ X0 @ (sK9 @ X0 @ X1))) = X1) | (none @ X0 = X1)) )),
% 1.42/0.56 inference(cnf_transformation,[],[f815])).
% 1.42/0.56 thf(f889,plain,(
% 1.42/0.56 (((lList2228235758e_ll2f @ a @ t @ i)) = ((some @ a @ x)))),
% 1.42/0.56 inference(cnf_transformation,[],[f3])).
% 1.42/0.56 thf(f905,plain,(
% 1.42/0.56 (((ord_less_eq @ nat @ j @ i)) = $true)),
% 1.42/0.56 inference(cnf_transformation,[],[f507])).
% 1.42/0.56 thf(f915,plain,(
% 1.42/0.56 ( ! [X0 : a] : ((((lList2228235758e_ll2f @ a @ t @ j)) != ((some @ a @ X0))) | (q = $true)) )),
% 1.42/0.56 inference(cnf_transformation,[],[f803])).
% 1.42/0.56 thf(f918,plain,(
% 1.42/0.56 (q != $true)),
% 1.42/0.56 inference(cnf_transformation,[],[f750])).
% 1.42/0.56 thf(f922,plain,(
% 1.42/0.56 ( ! [X0 : $tType,X1 : X0] : ((((some @ X0 @ X1)) != none @ X0)) )),
% 1.42/0.56 inference(cnf_transformation,[],[f95])).
% 1.42/0.56 thf(f925,plain,(
% 1.42/0.56 ( ! [X0 : $tType,X2 : nat,X3 : nat,X1 : coinductive_llist @ X0] : ((((lList2228235758e_ll2f @ X0 @ X1 @ X2)) != none @ X0) | (((ord_less_eq @ nat @ X2 @ X3)) != $true) | (((lList2228235758e_ll2f @ X0 @ X1 @ X3)) = none @ X0)) )),
% 1.42/0.56 inference(cnf_transformation,[],[f851])).
% 1.42/0.56 thf(f934,plain,(
% 1.42/0.56 ($true != $true) | (q = $false)),
% 1.42/0.56 inference(fool_paramodulation,[],[f918])).
% 1.42/0.56 thf(f935,plain,(
% 1.42/0.56 (q = $false)),
% 1.42/0.56 inference(trivial_inequality_removal,[],[f934])).
% 1.42/0.56 thf(f937,plain,(
% 1.42/0.56 ( ! [X0 : a] : (($true = $false) | (((lList2228235758e_ll2f @ a @ t @ j)) != ((some @ a @ X0)))) )),
% 1.42/0.56 inference(backward_demodulation,[],[f915,f935])).
% 1.42/0.56 thf(f938,plain,(
% 1.42/0.56 ( ! [X0 : a] : ((((lList2228235758e_ll2f @ a @ t @ j)) != ((some @ a @ X0)))) )),
% 1.42/0.56 inference(trivial_inequality_removal,[],[f937])).
% 1.42/0.56 thf(f939,plain,(
% 1.42/0.56 ( ! [X0 : option @ a] : ((((lList2228235758e_ll2f @ a @ t @ j)) != X0) | (none @ a = X0)) )),
% 1.42/0.56 inference(constrained_superposition,[],[f938,f868])).
% 1.42/0.56 thf(f941,plain,(
% 1.42/0.56 (((lList2228235758e_ll2f @ a @ t @ j)) = none @ a)),
% 1.42/0.56 inference(equality_resolution,[],[f939])).
% 1.42/0.56 thf(f944,plain,(
% 1.42/0.56 ( ! [X0 : nat] : ((((ord_less_eq @ nat @ j @ X0)) != $true) | (((lList2228235758e_ll2f @ a @ t @ X0)) = none @ a) | (none @ a != none @ a)) )),
% 1.42/0.56 inference(constrained_superposition,[],[f925,f941])).
% 1.42/0.56 thf(f947,plain,(
% 1.42/0.56 ( ! [X0 : nat] : ((((ord_less_eq @ nat @ j @ X0)) != $true) | (((lList2228235758e_ll2f @ a @ t @ X0)) = none @ a)) )),
% 1.42/0.56 inference(trivial_inequality_removal,[],[f944])).
% 1.42/0.56 thf(f966,plain,(
% 1.42/0.56 (((lList2228235758e_ll2f @ a @ t @ i)) = none @ a) | ($true != $true)),
% 1.42/0.56 inference(constrained_superposition,[],[f947,f905])).
% 1.42/0.56 thf(f971,plain,(
% 1.42/0.56 (((lList2228235758e_ll2f @ a @ t @ i)) = none @ a)),
% 1.42/0.56 inference(trivial_inequality_removal,[],[f966])).
% 1.42/0.56 thf(f976,plain,(
% 1.42/0.56 (((some @ a @ x)) = none @ a)),
% 1.42/0.56 inference(backward_demodulation,[],[f889,f971])).
% 1.42/0.56 thf(f981,plain,(
% 1.42/0.56 $false),
% 1.42/0.56 inference(forward_subsumption_resolution,[],[f976,f922])).
% 1.42/0.56 % SZS output end Proof for theBenchmark
% 1.42/0.56 % (1406399)------------------------------
% 1.42/0.56 % (1406399)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.56 % (1406399)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.56 % (1406399)CaDiCaL version: 2.1.3
% 1.42/0.56 % (1406399)Termination reason: Refutation
% 1.42/0.56 % (1406399)Time elapsed: 0.014 s
% 1.42/0.56 % (1406399)Peak memory usage: 13 MB
% 1.42/0.56 % (1406399)Instructions burned: 50 (million)
% 1.42/0.56 % (1406321)Success in time 0.277 s
% 1.42/0.56 % Vampire exiting
%------------------------------------------------------------------------------