%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP132^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:08:29 AM UTC 2026
% Result : Theorem 1.35s 0.53s
% Output : Refutation 1.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP132^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n004.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 19:58:37 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.25 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.64/0.39 % (1768186)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.64/0.39 % (1768193)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3791482357:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.64/0.39 % (1768193)Instruction limit reached!
% 0.64/0.39 % (1768193)------------------------------
% 0.64/0.39 % (1768193)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.39 % (1768193)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.39 % (1768193)CaDiCaL version: 2.1.3
% 0.64/0.39 % (1768193)Termination reason: Instruction limit
% 0.64/0.39 % (1768193)Termination phase: shuffling
% 0.64/0.39 % (1768193)Time elapsed: 0.002 s
% 0.64/0.39 % (1768193)Peak memory usage: 10 MB
% 0.64/0.39 % (1768193)Instructions burned: 7 (million)
% 0.64/0.39 % (1768197)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.64/0.39 % (1768197)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
% 0.64/0.39 % (1768191)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3699080347:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.64/0.39 % (1768192)lrs+10_16_si=on:nwc=1.5:random_seed=2706994337:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.64/0.39 % (1768194)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=4102779231: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)
% 0.64/0.39 % (1768195)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2739476396:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.64/0.39 % (1768196)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=553131843:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.64/0.39 % (1768197)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=468680148:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.64/0.39 % (1768199)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1673140452:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.64/0.39 % (1768199)Instruction limit reached!
% 0.64/0.39 % (1768199)------------------------------
% 0.64/0.39 % (1768199)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.39 % (1768199)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.39 % (1768199)CaDiCaL version: 2.1.3
% 0.64/0.39 % (1768199)Termination reason: Instruction limit
% 0.64/0.39 % (1768199)Termination phase: shuffling
% 0.64/0.39 % (1768199)Time elapsed: 0.001 s
% 0.64/0.39 % (1768199)Peak memory usage: 10 MB
% 0.64/0.39 % (1768199)Instructions burned: 4 (million)
% 0.64/0.39 % (1768192)Instruction limit reached!
% 0.64/0.39 % (1768192)------------------------------
% 0.64/0.39 % (1768192)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.39 % (1768192)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.39 % (1768192)CaDiCaL version: 2.1.3
% 0.64/0.39 % (1768192)Termination reason: Instruction limit
% 0.64/0.39 % (1768192)Termination phase: Property scanning
% 0.64/0.39 % (1768192)Time elapsed: 0.008 s
% 0.64/0.39 % (1768192)Peak memory usage: 10 MB
% 0.64/0.39 % (1768192)Instructions burned: 18 (million)
% 0.64/0.39 % (1768195)Instruction limit reached!
% 0.64/0.39 % (1768195)------------------------------
% 0.64/0.39 % (1768195)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.39 % (1768195)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.39 % (1768195)CaDiCaL version: 2.1.3
% 0.64/0.39 % (1768195)Termination reason: Instruction limit
% 0.64/0.39 % (1768195)Termination phase: Preprocessing 1
% 0.64/0.39 % (1768195)Time elapsed: 0.011 s
% 0.64/0.39 % (1768195)Peak memory usage: 10 MB
% 0.64/0.39 % (1768195)Instructions burned: 24 (million)
% 0.64/0.39 % (1768208)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.64/0.41 % (1768208)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2740429847:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.64/0.41 % (1768207)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2875282867:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.64/0.41 % (1768208)Instruction limit reached!
% 0.64/0.41 % (1768208)------------------------------
% 0.64/0.41 % (1768208)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.41 % (1768208)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.41 % (1768208)CaDiCaL version: 2.1.3
% 0.64/0.41 % (1768208)Termination reason: Instruction limit
% 0.64/0.41 % (1768208)Termination phase: shuffling
% 0.64/0.41 % (1768208)Time elapsed: 0.002 s
% 0.64/0.41 % (1768208)Peak memory usage: 10 MB
% 0.64/0.41 % (1768208)Instructions burned: 9 (million)
% 0.64/0.41 % (1768209)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2262358918:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.64/0.41 % (1768207)Instruction limit reached!
% 0.64/0.41 % (1768207)------------------------------
% 0.64/0.41 % (1768207)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.41 % (1768207)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.41 % (1768207)CaDiCaL version: 2.1.3
% 0.64/0.41 % (1768207)Termination reason: Instruction limit
% 0.64/0.41 % (1768207)Termination phase: shuffling
% 0.64/0.41 % (1768207)Time elapsed: 0.003 s
% 0.64/0.41 % (1768207)Peak memory usage: 10 MB
% 0.64/0.41 % (1768207)Instructions burned: 6 (million)
% 0.64/0.41 % (1768196)Instruction limit reached!
% 0.64/0.41 % (1768196)------------------------------
% 0.64/0.41 % (1768196)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.41 % (1768196)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.41 % (1768196)CaDiCaL version: 2.1.3
% 0.64/0.41 % (1768196)Termination reason: Instruction limit
% 0.64/0.41 % (1768196)Termination phase: Property scanning
% 0.64/0.41 % (1768196)Time elapsed: 0.034 s
% 0.64/0.41 % (1768196)Peak memory usage: 11 MB
% 0.64/0.41 % (1768196)Instructions burned: 76 (million)
% 0.64/0.41 % (1768209)Instruction limit reached!
% 0.64/0.41 % (1768209)------------------------------
% 0.64/0.41 % (1768209)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.41 % (1768209)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.41 % (1768209)CaDiCaL version: 2.1.3
% 0.64/0.41 % (1768209)Termination reason: Instruction limit
% 0.64/0.41 % (1768209)Termination phase: Property scanning
% 0.64/0.41 % (1768209)Time elapsed: 0.006 s
% 0.64/0.41 % (1768209)Peak memory usage: 10 MB
% 0.64/0.41 % (1768209)Instructions burned: 14 (million)
% 0.64/0.41 % (1768212)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
% 0.64/0.41 % (1768212)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.64/0.41 % (1768191)Instruction limit reached!
% 0.64/0.41 % (1768191)------------------------------
% 0.64/0.41 % (1768191)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.41 % (1768191)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.41 % (1768191)CaDiCaL version: 2.1.3
% 0.64/0.41 % (1768191)Termination reason: Instruction limit
% 0.64/0.41 % (1768191)Termination phase: Saturation
% 0.64/0.41 % (1768191)Time elapsed: 0.039 s
% 0.64/0.41 % (1768191)Peak memory usage: 12 MB
% 0.64/0.41 % (1768191)Instructions burned: 87 (million)
% 0.64/0.41 % (1768212)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3355188844:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.64/0.41 % (1768212)Instruction limit reached!
% 0.64/0.41 % (1768212)------------------------------
% 0.64/0.41 % (1768212)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.41 % (1768212)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.41 % (1768212)CaDiCaL version: 2.1.3
% 0.64/0.41 % (1768212)Termination reason: Instruction limit
% 0.64/0.44 % (1768212)Termination phase: Property scanning
% 0.64/0.44 % (1768212)Time elapsed: 0.007 s
% 0.64/0.44 % (1768212)Peak memory usage: 11 MB
% 0.64/0.44 % (1768212)Instructions burned: 31 (million)
% 0.64/0.44 % (1768214)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=4126343145:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.64/0.44 % (1768216)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.64/0.44 % (1768215)lrs+10_1_si=on:cs=on:random_seed=2062452945:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.64/0.44 % (1768216)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=3323017001:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.64/0.44 % (1768217)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=753625161:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.64/0.44 % (1768219)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=2124209066:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.64/0.44 % (1768216)Instruction limit reached!
% 0.64/0.44 % (1768216)------------------------------
% 0.64/0.44 % (1768216)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.44 % (1768216)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.44 % (1768216)CaDiCaL version: 2.1.3
% 0.64/0.44 % (1768216)Termination reason: Instruction limit
% 0.64/0.44 % (1768216)Termination phase: shuffling
% 0.64/0.44 % (1768216)Time elapsed: 0.002 s
% 0.64/0.44 % (1768216)Peak memory usage: 10 MB
% 0.64/0.44 % (1768216)Instructions burned: 4 (million)
% 0.64/0.44 % (1768215)Instruction limit reached!
% 0.64/0.44 % (1768215)------------------------------
% 0.64/0.44 % (1768215)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.44 % (1768215)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.44 % (1768215)CaDiCaL version: 2.1.3
% 0.64/0.44 % (1768215)Termination reason: Instruction limit
% 0.64/0.44 % (1768215)Termination phase: shuffling
% 0.64/0.44 % (1768215)Time elapsed: 0.004 s
% 0.64/0.44 % (1768215)Peak memory usage: 10 MB
% 0.64/0.44 % (1768215)Instructions burned: 8 (million)
% 0.64/0.44 % (1768217)Instruction limit reached!
% 0.64/0.44 % (1768217)------------------------------
% 0.64/0.44 % (1768217)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.44 % (1768217)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.44 % (1768217)CaDiCaL version: 2.1.3
% 0.64/0.44 % (1768217)Termination reason: Instruction limit
% 0.64/0.44 % (1768217)Termination phase: Preprocessing 3
% 0.64/0.44 % (1768217)Time elapsed: 0.017 s
% 0.64/0.44 % (1768217)Peak memory usage: 11 MB
% 0.64/0.44 % (1768217)Instructions burned: 38 (million)
% 0.64/0.44 % (1768219)Refutation not found, incomplete strategy
% 0.64/0.44 % (1768219)------------------------------
% 0.64/0.44 % (1768219)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.44 % (1768219)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.44 % (1768219)CaDiCaL version: 2.1.3
% 0.64/0.44 % (1768219)Termination reason: Refutation not found, incomplete strategy
% 0.64/0.44 % (1768219)Time elapsed: 0.018 s
% 0.64/0.44 % (1768219)Peak memory usage: 13 MB
% 0.64/0.44 % (1768219)Instructions burned: 71 (million)
% 0.64/0.44 % (1768219)------------------------------
% 0.64/0.44 % (1768219)------------------------------
% 0.64/0.44 % (1768197)Instruction limit reached!
% 0.64/0.44 % (1768197)------------------------------
% 0.64/0.44 % (1768197)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.44 % (1768197)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.44 % (1768197)CaDiCaL version: 2.1.3
% 0.64/0.44 % (1768197)Termination reason: Instruction limit
% 0.64/0.44 % (1768197)Termination phase: Saturation
% 0.64/0.44 % (1768197)Time elapsed: 0.078 s
% 0.64/0.44 % (1768197)Peak memory usage: 13 MB
% 0.64/0.44 % (1768197)Instructions burned: 157 (million)
% 0.64/0.44 % (1768225)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2511681460:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.35/0.49 % (1768226)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=1678430995:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.35/0.49 % (1768214)Instruction limit reached!
% 1.35/0.49 % (1768214)------------------------------
% 1.35/0.49 % (1768214)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.35/0.49 % (1768214)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.35/0.49 % (1768214)CaDiCaL version: 2.1.3
% 1.35/0.49 % (1768214)Termination reason: Instruction limit
% 1.35/0.49 % (1768214)Termination phase: Property scanning
% 1.35/0.49 % (1768214)Time elapsed: 0.036 s
% 1.35/0.49 % (1768214)Peak memory usage: 11 MB
% 1.35/0.49 % (1768214)Instructions burned: 88 (million)
% 1.35/0.49 % (1768226)Instruction limit reached!
% 1.35/0.49 % (1768226)------------------------------
% 1.35/0.49 % (1768226)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.35/0.49 % (1768226)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.35/0.49 % (1768226)CaDiCaL version: 2.1.3
% 1.35/0.49 % (1768226)Termination reason: Instruction limit
% 1.35/0.49 % (1768226)Termination phase: Property scanning
% 1.35/0.49 % (1768226)Time elapsed: 0.007 s
% 1.35/0.49 % (1768226)Peak memory usage: 10 MB
% 1.35/0.49 % (1768226)Instructions burned: 16 (million)
% 1.35/0.49 % (1768228)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=1833081381:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.35/0.49 % (1768225)Instruction limit reached!
% 1.35/0.49 % (1768225)------------------------------
% 1.35/0.49 % (1768225)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.35/0.49 % (1768225)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.35/0.49 % (1768225)CaDiCaL version: 2.1.3
% 1.35/0.49 % (1768225)Termination reason: Instruction limit
% 1.35/0.49 % (1768225)Termination phase: SInE selection
% 1.35/0.49 % (1768225)Time elapsed: 0.012 s
% 1.35/0.49 % (1768225)Peak memory usage: 10 MB
% 1.35/0.49 % (1768225)Instructions burned: 26 (million)
% 1.35/0.49 % (1768228)Instruction limit reached!
% 1.35/0.49 % (1768228)------------------------------
% 1.35/0.49 % (1768228)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.35/0.49 % (1768228)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.35/0.49 % (1768228)CaDiCaL version: 2.1.3
% 1.35/0.49 % (1768228)Termination reason: Instruction limit
% 1.35/0.49 % (1768228)Termination phase: Property scanning
% 1.35/0.49 % (1768228)Time elapsed: 0.004 s
% 1.35/0.49 % (1768228)Peak memory usage: 10 MB
% 1.35/0.49 % (1768228)Instructions burned: 18 (million)
% 1.35/0.49 % (1768227)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=4163281057:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.35/0.49 % (1768229)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=699407767: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)
% 1.35/0.49 % (1768229)Instruction limit reached!
% 1.35/0.49 % (1768229)------------------------------
% 1.35/0.49 % (1768229)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.35/0.49 % (1768229)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.35/0.49 % (1768229)CaDiCaL version: 2.1.3
% 1.35/0.49 % (1768229)Termination reason: Instruction limit
% 1.35/0.49 % (1768229)Termination phase: shuffling
% 1.35/0.49 % (1768229)Time elapsed: 0.002 s
% 1.35/0.49 % (1768229)Peak memory usage: 10 MB
% 1.35/0.49 % (1768229)Instructions burned: 4 (million)
% 1.35/0.49 % (1768236)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
% 1.35/0.49 % (1768236)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.35/0.49 % (1768236)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=274851478:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.35/0.49 % (1768232)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=4190303063:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.35/0.53 % (1768234)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=1907220780:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.35/0.53 % (1768236)Instruction limit reached!
% 1.35/0.53 % (1768236)------------------------------
% 1.35/0.53 % (1768236)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.35/0.53 % (1768236)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.35/0.53 % (1768236)CaDiCaL version: 2.1.3
% 1.35/0.53 % (1768236)Termination reason: Instruction limit
% 1.35/0.53 % (1768236)Termination phase: shuffling
% 1.35/0.53 % (1768236)Time elapsed: 0.004 s
% 1.35/0.53 % (1768236)Peak memory usage: 10 MB
% 1.35/0.53 % (1768236)Instructions burned: 18 (million)
% 1.35/0.53 % (1768235)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=2698677864:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.35/0.53 % (1768239)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.35/0.53 % (1768234)Instruction limit reached!
% 1.35/0.53 % (1768234)------------------------------
% 1.35/0.53 % (1768234)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.35/0.53 % (1768234)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.35/0.53 % (1768234)CaDiCaL version: 2.1.3
% 1.35/0.53 % (1768234)Termination reason: Instruction limit
% 1.35/0.53 % (1768234)Termination phase: Preprocessing 1
% 1.35/0.53 % (1768234)Time elapsed: 0.010 s
% 1.35/0.53 % (1768234)Peak memory usage: 10 MB
% 1.35/0.53 % (1768234)Instructions burned: 24 (million)
% 1.35/0.53 % (1768232)Instruction limit reached!
% 1.35/0.53 % (1768232)------------------------------
% 1.35/0.53 % (1768232)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.35/0.53 % (1768232)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.35/0.53 % (1768232)CaDiCaL version: 2.1.3
% 1.35/0.53 % (1768232)Termination reason: Instruction limit
% 1.35/0.53 % (1768232)Termination phase: Property scanning
% 1.35/0.53 % (1768232)Time elapsed: 0.012 s
% 1.35/0.53 % (1768232)Peak memory usage: 10 MB
% 1.35/0.53 % (1768232)Instructions burned: 27 (million)
% 1.35/0.53 % (1768243)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=1297341191:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 1.35/0.53 % (1768239)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=1407091072:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.35/0.53 % (1768239)Instruction limit reached!
% 1.35/0.53 % (1768239)------------------------------
% 1.35/0.53 % (1768239)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.35/0.53 % (1768239)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.35/0.53 % (1768239)CaDiCaL version: 2.1.3
% 1.35/0.53 % (1768239)Termination reason: Instruction limit
% 1.35/0.53 % (1768239)Termination phase: shuffling
% 1.35/0.53 % (1768239)Time elapsed: 0.005 s
% 1.35/0.53 % (1768239)Peak memory usage: 10 MB
% 1.35/0.53 % (1768239)Instructions burned: 10 (million)
% 1.35/0.53 % (1768243)Instruction limit reached!
% 1.35/0.53 % (1768243)------------------------------
% 1.35/0.53 % (1768243)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.35/0.53 % (1768243)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.35/0.53 % (1768243)CaDiCaL version: 2.1.3
% 1.35/0.53 % (1768243)Termination reason: Instruction limit
% 1.35/0.53 % (1768243)Termination phase: Property scanning
% 1.35/0.53 % (1768243)Time elapsed: 0.007 s
% 1.35/0.53 % (1768243)Peak memory usage: 10 MB
% 1.35/0.53 % (1768243)Instructions burned: 34 (million)
% 1.35/0.53 % (1768250)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=763071043:i=1240:rtra=on:ixr=off_2998 on theBenchmark for (2998ds/1240Mi)
% 1.35/0.53 % (1768245)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=811641367:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 1.35/0.53 % (1768247)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=3237146042:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.35/0.53 % (1768235)Instruction limit reached!
% 1.35/0.53 % (1768235)------------------------------
% 1.35/0.53 % (1768235)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.35/0.53 % (1768235)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.35/0.53 % (1768235)CaDiCaL version: 2.1.3
% 1.35/0.53 % (1768235)Termination reason: Instruction limit
% 1.35/0.53 % (1768235)Termination phase: Property scanning
% 1.35/0.53 % (1768235)Time elapsed: 0.026 s
% 1.35/0.53 % (1768235)Peak memory usage: 11 MB
% 1.35/0.53 % (1768235)Instructions burned: 60 (million)
% 1.35/0.53 % (1768245)Instruction limit reached!
% 1.35/0.53 % (1768245)------------------------------
% 1.35/0.53 % (1768245)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.35/0.53 % (1768245)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.35/0.53 % (1768245)CaDiCaL version: 2.1.3
% 1.35/0.53 % (1768245)Termination reason: Instruction limit
% 1.35/0.53 % (1768245)Termination phase: shuffling
% 1.35/0.53 % (1768245)Time elapsed: 0.005 s
% 1.35/0.53 % (1768245)Peak memory usage: 10 MB
% 1.35/0.53 % (1768245)Instructions burned: 11 (million)
% 1.35/0.53 % (1768249)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=1726749079:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 1.35/0.53 % (1768247)Instruction limit reached!
% 1.35/0.53 % (1768247)------------------------------
% 1.35/0.53 % (1768247)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.35/0.53 % (1768247)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.35/0.53 % (1768247)CaDiCaL version: 2.1.3
% 1.35/0.53 % (1768247)Termination reason: Instruction limit
% 1.35/0.53 % (1768247)Termination phase: shuffling
% 1.35/0.53 % (1768247)Time elapsed: 0.010 s
% 1.35/0.53 % (1768247)Peak memory usage: 10 MB
% 1.35/0.53 % (1768247)Instructions burned: 23 (million)
% 1.35/0.53 % (1768249)Instruction limit reached!
% 1.35/0.53 % (1768249)------------------------------
% 1.35/0.53 % (1768249)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.35/0.53 % (1768249)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.35/0.53 % (1768249)CaDiCaL version: 2.1.3
% 1.35/0.53 % (1768249)Termination reason: Instruction limit
% 1.35/0.53 % (1768249)Termination phase: Property scanning
% 1.35/0.53 % (1768249)Time elapsed: 0.009 s
% 1.35/0.53 % (1768249)Peak memory usage: 10 MB
% 1.35/0.53 % (1768249)Instructions burned: 20 (million)
% 1.35/0.53 % (1768254)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=3970786852:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/143Mi)
% 1.35/0.53 % (1768255)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=1898125654:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/193Mi)
% 1.35/0.53 % (1768257)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2983267432:i=42:hud=10:rtra=on_2998 on theBenchmark for (2998ds/42Mi)
% 1.35/0.53 % (1768258)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.35/0.53 % (1768258)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3705661848:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2998 on theBenchmark for (2998ds/7Mi)
% 1.35/0.53 % (1768258)Instruction limit reached!
% 1.35/0.53 % (1768258)------------------------------
% 1.35/0.53 % (1768258)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.35/0.53 % (1768258)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.35/0.53 % (1768258)CaDiCaL version: 2.1.3
% 1.35/0.53 % (1768258)Termination reason: Instruction limit
% 1.35/0.53 % (1768258)Termination phase: shuffling
% 1.35/0.53 % (1768258)Time elapsed: 0.003 s
% 1.35/0.53 % (1768258)Peak memory usage: 10 MB
% 1.35/0.53 % (1768258)Instructions burned: 7 (million)
% 1.35/0.53 % (1768257)Instruction limit reached!
% 1.35/0.53 % (1768257)------------------------------
% 1.35/0.53 % (1768257)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.35/0.53 % (1768257)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.35/0.53 % (1768257)CaDiCaL version: 2.1.3
% 1.35/0.53 % (1768257)Termination reason: Instruction limit
% 1.35/0.53 % (1768257)Termination phase: Property scanning
% 1.35/0.53 % (1768257)Time elapsed: 0.019 s
% 1.35/0.53 % (1768257)Peak memory usage: 11 MB
% 1.35/0.53 % (1768257)Instructions burned: 44 (million)
% 1.35/0.53 % (1768263)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=2480646907:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 1.35/0.53 % (1768264)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=3622288588: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)
% 1.35/0.53 % (1768254) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1768186-1768254"...
% 1.35/0.53 % (1768254)...printing done.
% 1.35/0.53 % (1768254)Refutation found. Thanks to Tanya!
% 1.35/0.53 % SZS status Theorem for theBenchmark
% 1.35/0.53 % SZS output start Proof for theBenchmark
% 1.35/0.53 thf(type_def_5, type, set_set_nat: $tType).
% 1.35/0.53 thf(type_def_6, type, set_nat: $tType).
% 1.35/0.53 thf(type_def_7, type, nat: $tType).
% 1.35/0.53 thf(type_def_8, type, sTfun: ($tType * $tType) > $tType).
% 1.35/0.53 thf(func_def_0, type, fun_upd_nat_nat: ((nat > nat) > nat > nat > nat > nat)).
% 1.35/0.53 thf(func_def_1, type, minus_minus_nat: (nat > nat > nat)).
% 1.35/0.53 thf(func_def_2, type, one_one_nat: nat).
% 1.35/0.53 thf(func_def_3, type, times_times_nat: (nat > nat > nat)).
% 1.35/0.53 thf(func_def_4, type, zero_zero_nat: nat).
% 1.35/0.53 thf(func_def_5, type, groups1842438620at_nat: ((nat > nat) > set_nat > nat)).
% 1.35/0.53 thf(func_def_6, type, if_nat: ($o > nat > nat > nat)).
% 1.35/0.53 thf(func_def_7, type, number1551313001itions: ((nat > nat) > nat > $o)).
% 1.35/0.53 thf(func_def_8, type, ord_less_nat: (nat > nat > $o)).
% 1.35/0.53 thf(func_def_9, type, ord_less_eq_nat: (nat > nat > $o)).
% 1.35/0.53 thf(func_def_10, type, ord_less_eq_set_nat: (set_nat > set_nat > $o)).
% 1.35/0.53 thf(func_def_11, type, ord_le1613022364et_nat: (set_set_nat > set_set_nat > $o)).
% 1.35/0.53 thf(func_def_12, type, collect_nat: ((nat > $o) > set_nat)).
% 1.35/0.53 thf(func_def_13, type, collect_set_nat: ((set_nat > $o) > set_set_nat)).
% 1.35/0.53 thf(func_def_14, type, set_ord_atMost_nat: (nat > set_nat)).
% 1.35/0.53 thf(func_def_15, type, set_or1086813439et_nat: (set_nat > set_set_nat)).
% 1.35/0.53 thf(func_def_16, type, member_nat: (nat > set_nat > $o)).
% 1.35/0.53 thf(func_def_17, type, member_set_nat: (set_nat > set_set_nat > $o)).
% 1.35/0.53 thf(func_def_18, type, k: nat).
% 1.35/0.53 thf(func_def_19, type, n: nat).
% 1.35/0.53 thf(func_def_20, type, p: (nat > nat)).
% 1.35/0.53 thf(func_def_24, type, vAND: ($o > $o > $o)).
% 1.35/0.53 thf(func_def_25, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 1.35/0.53 thf(func_def_26, type, vOR: ($o > $o > $o)).
% 1.35/0.53 thf(func_def_27, type, db0: !>[X0: $tType]:(X0)).
% 1.35/0.53 thf(func_def_28, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 1.35/0.53 thf(func_def_29, type, vNOT: ($o > $o)).
% 1.35/0.53 thf(func_def_30, type, db1: !>[X0: $tType]:(X0)).
% 1.35/0.53 thf(func_def_31, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 1.35/0.53 thf(func_def_32, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 1.35/0.53 thf(func_def_33, type, vIMP: ($o > $o > $o)).
% 1.35/0.53 thf(func_def_34, type, db2: !>[X0: $tType]:(X0)).
% 1.35/0.53 thf(func_def_35, type, db3: !>[X0: $tType]:(X0)).
% 1.35/0.53 thf(func_def_36, type, sP0: (set_nat > (nat > nat) > (nat > nat) > $o)).
% 1.35/0.53 thf(func_def_37, type, sP1: (set_nat > (nat > nat) > (nat > nat) > $o)).
% 1.35/0.53 thf(func_def_38, type, sP2: (nat > nat > nat > $o)).
% 1.35/0.53 thf(func_def_39, type, sP3: (nat > nat > nat > $o)).
% 1.35/0.53 thf(func_def_40, type, sP4: (nat > nat > nat > $o)).
% 1.35/0.53 thf(func_def_41, type, sK5: ((nat > nat) > set_nat > nat)).
% 1.35/0.53 thf(func_def_42, type, sK6: ((set_nat > nat) > set_nat)).
% 1.35/0.53 thf(func_def_43, type, sK7: ((set_nat > nat) > set_nat)).
% 1.35/0.53 thf(func_def_44, type, sK8: ((set_nat > nat) > set_nat)).
% 1.35/0.53 thf(func_def_45, type, sK9: ((set_nat > nat) > set_nat)).
% 1.35/0.53 thf(func_def_46, type, sK10: ((nat > set_nat) > nat)).
% 1.35/0.53 thf(func_def_47, type, sK11: ((nat > set_nat) > nat)).
% 1.35/0.53 thf(func_def_48, type, sK12: ((set_nat > set_nat) > set_nat)).
% 1.35/0.53 thf(func_def_49, type, sK13: ((set_nat > set_nat) > set_nat)).
% 1.35/0.53 thf(func_def_50, type, sK14: (set_nat > (nat > nat) > (nat > nat) > nat)).
% 1.35/0.53 thf(func_def_51, type, sK15: (set_nat > (nat > nat) > (nat > nat) > nat)).
% 1.35/0.53 thf(func_def_52, type, sK16: ((nat > nat) > set_nat > set_nat > nat)).
% 1.35/0.53 thf(func_def_53, type, sK17: ((nat > nat) > set_nat > (nat > nat) > (nat > nat) > nat)).
% 1.35/0.53 thf(func_def_54, type, sK18: (set_nat > set_nat > (nat > nat) > nat)).
% 1.35/0.53 thf(func_def_55, type, sK19: (set_nat > (nat > nat) > (nat > nat) > nat)).
% 1.35/0.53 thf(func_def_56, type, sK20: ((set_nat > nat) > set_nat)).
% 1.35/0.53 thf(func_def_57, type, sK21: ((set_nat > nat) > set_nat)).
% 1.35/0.53 thf(func_def_58, type, sK22: ((nat > nat) > (nat > nat) > (nat > nat) > set_nat > set_nat > nat)).
% 1.35/0.53 thf(func_def_59, type, sK23: ((nat > nat) > set_nat > set_nat > nat)).
% 1.35/0.53 thf(func_def_60, type, sK24: (nat > (nat > nat) > set_nat > set_nat > nat)).
% 1.35/0.53 thf(func_def_61, type, sK25: ((nat > nat > $o) > nat)).
% 1.35/0.53 thf(func_def_62, type, sK26: ((nat > nat > $o) > nat)).
% 1.35/0.53 thf(func_def_63, type, sK27: ((nat > nat > $o) > nat)).
% 1.35/0.53 thf(func_def_64, type, sK28: ((nat > nat > $o) > nat)).
% 1.35/0.53 thf(func_def_65, type, sK29: ((set_nat > nat) > set_nat)).
% 1.35/0.53 thf(func_def_66, type, sK30: ((set_nat > nat) > set_nat)).
% 1.35/0.53 thf(func_def_67, type, sK31: ((nat > nat) > nat)).
% 1.35/0.53 thf(func_def_68, type, sK32: ((nat > nat) > nat)).
% 1.35/0.53 thf(func_def_69, type, sK33: ((nat > nat) > nat)).
% 1.35/0.53 thf(func_def_70, type, sK34: ((nat > nat) > nat)).
% 1.35/0.53 thf(func_def_71, type, sK35: ((nat > nat > $o) > nat)).
% 1.35/0.53 thf(func_def_72, type, sK36: ((nat > nat > $o) > nat)).
% 1.35/0.53 thf(func_def_73, type, sK37: ((nat > nat > $o) > nat)).
% 1.35/0.53 thf(func_def_74, type, sK38: ((nat > nat > $o) > nat)).
% 1.35/0.53 thf(func_def_75, type, sK39: ((nat > nat > $o) > nat)).
% 1.35/0.53 thf(func_def_76, type, sK40: ((nat > nat) > (nat > nat) > set_nat > set_nat > (nat > nat) > (nat > nat) > nat)).
% 1.35/0.53 thf(func_def_77, type, sK41: ((nat > nat) > set_nat > set_nat > (nat > nat) > nat)).
% 1.35/0.53 thf(func_def_78, type, sK42: ((nat > nat) > nat)).
% 1.35/0.53 thf(func_def_79, type, sK43: ((nat > nat) > nat)).
% 1.35/0.53 thf(func_def_80, type, sK44: (nat > nat)).
% 1.35/0.53 thf(func_def_81, type, sK45: ((nat > set_nat) > nat)).
% 1.35/0.53 thf(func_def_82, type, sK46: ((nat > set_nat) > nat)).
% 1.35/0.53 thf(func_def_83, type, sK47: ((set_nat > set_nat) > set_nat)).
% 1.35/0.53 thf(func_def_84, type, sK48: ((set_nat > set_nat) > set_nat)).
% 1.35/0.53 thf(func_def_85, type, sK49: ((nat > nat) > nat)).
% 1.35/0.53 thf(func_def_86, type, sK50: ((nat > nat) > nat)).
% 1.35/0.53 thf(func_def_87, type, sK51: ((nat > nat) > nat > nat)).
% 1.35/0.53 thf(func_def_88, type, sK52: ((nat > set_nat) > nat)).
% 1.35/0.53 thf(func_def_89, type, sK53: ((nat > set_nat) > nat)).
% 1.35/0.53 thf(func_def_90, type, sK54: ((nat > nat) > set_nat > (nat > nat) > nat)).
% 1.35/0.53 thf(func_def_91, type, sK55: ((nat > nat) > nat)).
% 1.35/0.53 thf(func_def_92, type, sK56: ((nat > nat) > nat)).
% 1.35/0.53 thf(func_def_93, type, sK57: ((nat > set_nat) > nat)).
% 1.35/0.53 thf(func_def_94, type, sK58: ((nat > set_nat) > nat)).
% 1.35/0.53 thf(func_def_95, type, sK59: ((nat > nat) > nat)).
% 1.35/0.53 thf(func_def_96, type, sK60: ((nat > nat) > nat)).
% 1.35/0.53 thf(func_def_97, type, sK61: ((nat > $o) > nat > nat)).
% 1.35/0.53 thf(func_def_98, type, sK62: ((nat > $o) > nat)).
% 1.35/0.53 thf(func_def_99, type, sK63: ((nat > nat) > nat)).
% 1.35/0.53 thf(func_def_100, type, sK64: ((nat > nat) > nat)).
% 1.35/0.53 thf(func_def_101, type, sK65: (set_nat > set_nat > nat)).
% 1.35/0.53 thf(func_def_102, type, sK66: ((nat > nat) > set_nat > nat)).
% 1.35/0.53 thf(func_def_103, type, sK67: ((nat > nat) > set_nat > nat)).
% 1.35/0.53 thf(func_def_104, type, sK68: ((nat > nat) > nat)).
% 1.35/0.53 thf(func_def_105, type, sK69: ((nat > nat) > nat)).
% 1.35/0.53 thf(func_def_106, type, sK70: ((nat > $o) > nat)).
% 1.35/0.53 thf(func_def_107, type, sK71: (set_nat > (nat > nat) > (nat > nat) > nat)).
% 1.35/0.53 thf(func_def_108, type, sK72: ((nat > $o) > nat)).
% 1.35/0.53 thf(func_def_109, type, sK73: ((nat > $o) > nat)).
% 1.35/0.53 thf(func_def_110, type, sK74: ((set_nat > set_nat) > set_nat)).
% 1.35/0.53 thf(func_def_111, type, sK75: ((set_nat > set_nat) > set_nat)).
% 1.35/0.53 thf(func_def_112, type, sK76: (nat > (nat > $o) > nat)).
% 1.35/0.53 thf(func_def_113, type, sK77: ((nat > $o) > nat)).
% 1.35/0.53 thf(func_def_114, type, sK78: ((set_nat > set_nat) > set_nat)).
% 1.35/0.53 thf(func_def_115, type, sK79: ((set_nat > set_nat) > set_nat)).
% 1.35/0.53 thf(func_def_116, type, sK80: ((nat > nat) > set_nat > nat)).
% 1.35/0.53 thf(func_def_117, type, sK81: ((nat > $o) > (nat > $o) > nat)).
% 1.35/0.53 thf(func_def_118, type, sF82: nat).
% 1.35/0.53 thf(func_def_119, type, sF83: set_nat).
% 1.35/0.53 thf(func_def_120, type, sF84: nat).
% 1.35/0.53 thf(func_def_121, type, sF85: nat).
% 1.35/0.53 thf(func_def_122, type, sK86: ((nat > nat) > nat > nat)).
% 1.35/0.53 thf(func_def_123, type, sK87: (nat > (nat > nat) > nat)).
% 1.35/0.53 thf(func_def_124, type, sK88: (nat > (nat > nat) > nat)).
% 1.35/0.53 thf(func_def_125, type, sK89: (nat > (nat > nat) > nat)).
% 1.35/0.53 thf(func_def_126, type, sK90: ((nat > nat) > nat)).
% 1.35/0.53 thf(func_def_127, type, sK91: ((nat > nat) > nat > nat)).
% 1.35/0.53 thf(func_def_128, type, sK92: ((nat > nat) > nat > nat)).
% 1.35/0.53 thf(func_def_129, type, sK93: ((nat > nat) > nat > nat)).
% 1.35/0.53 thf(f1,axiom,(
% 1.35/0.53 (number1551313001itions @ p @ n)),
% 1.35/0.53 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_partitions)).
% 1.35/0.53 thf(f42,axiom,(
% 1.35/0.53 ((^[X0 : nat] : ((collect_nat @ (^[X1 : nat] : ((ord_less_eq_nat @ X1 @ X0)))))) = set_ord_atMost_nat)),
% 1.35/0.53 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_atMost__def)).
% 1.35/0.53 thf(f62,axiom,(
% 1.35/0.53 ((^[X0 : (nat > nat), X1 : nat] : ((((groups1842438620at_nat @ (^[X2 : nat] : ((times_times_nat @ (X0 @ X2) @ X2))) @ (set_ord_atMost_nat @ X1))) = X1) & ! [X2 : nat] : ((((X0 @ X2)) != zero_zero_nat) => ((ord_less_eq_nat @ one_one_nat @ X2) & (ord_less_eq_nat @ X2 @ X1))))) = number1551313001itions)),
% 1.35/0.53 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_partitions__def)).
% 1.35/0.53 thf(f245,conjecture,(
% 1.35/0.53 (((minus_minus_nat @ (groups1842438620at_nat @ (^[X0 : nat] : ((times_times_nat @ (p @ X0) @ X0))) @ (set_ord_atMost_nat @ n)) @ k)) = ((minus_minus_nat @ n @ k)))),
% 1.35/0.53 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 1.35/0.53 thf(f246,negated_conjecture,(
% 1.35/0.53 ~ (((minus_minus_nat @ (groups1842438620at_nat @ (^[X0 : nat] : ((times_times_nat @ (p @ X0) @ X0))) @ (set_ord_atMost_nat @ n)) @ k)) = ((minus_minus_nat @ n @ k)))),
% 1.35/0.53 inference(negated_conjecture,[status(cth)],[f245])).
% 1.35/0.53 thf(f434,plain,(
% 1.35/0.53 (number1551313001itions @ p @ n)),
% 1.35/0.53 inference(rectify,[],[f1])).
% 1.35/0.53 thf(f435,plain,(
% 1.35/0.53 (((number1551313001itions @ p @ n)) = $true)),
% 1.35/0.53 inference(fool_elimination,[],[f434])).
% 1.35/0.53 thf(f511,plain,(
% 1.35/0.53 ((^[X0 : (nat > nat), X1 : nat] : ((((groups1842438620at_nat @ (^[X2 : nat] : ((times_times_nat @ (X0 @ X2) @ X2))) @ (set_ord_atMost_nat @ X1))) = X1) & ! [X3 : nat] : ((((X0 @ X3)) != zero_zero_nat) => ((ord_less_eq_nat @ one_one_nat @ X3) & (ord_less_eq_nat @ X3 @ X1))))) = number1551313001itions)),
% 1.35/0.53 inference(rectify,[],[f62])).
% 1.35/0.53 thf(f512,plain,(
% 1.35/0.53 (number1551313001itions = (^[Y0 : nat > nat]: ((^[Y1 : nat]: ((!! @ nat @ (^[Y2 : nat]: ((~ ((Y0 @ Y2) = zero_zero_nat)) => ((ord_less_eq_nat @ Y2 @ Y1) & (ord_less_eq_nat @ one_one_nat @ Y2))))) & ((groups1842438620at_nat @ (^[Y2 : nat]: (times_times_nat @ (Y0 @ Y2) @ Y2)) @ (set_ord_atMost_nat @ Y1)) = Y1))))))),
% 1.35/0.53 inference(fool_elimination,[],[f511])).
% 1.35/0.53 thf(f549,plain,(
% 1.35/0.53 ((^[X0 : nat] : ((collect_nat @ (^[X1 : nat] : ((ord_less_eq_nat @ X1 @ X0)))))) = set_ord_atMost_nat)),
% 1.35/0.53 inference(rectify,[],[f42])).
% 1.35/0.53 thf(f550,plain,(
% 1.35/0.53 (set_ord_atMost_nat = (^[Y0 : nat]: (collect_nat @ (^[Y1 : nat]: (ord_less_eq_nat @ Y1 @ Y0)))))),
% 1.35/0.53 inference(fool_elimination,[],[f549])).
% 1.35/0.53 thf(f572,plain,(
% 1.35/0.53 ~ (((minus_minus_nat @ (groups1842438620at_nat @ (^[X0 : nat] : ((times_times_nat @ (p @ X0) @ X0))) @ (set_ord_atMost_nat @ n)) @ k)) = ((minus_minus_nat @ n @ k)))),
% 1.35/0.53 inference(rectify,[],[f246])).
% 1.35/0.53 thf(f573,plain,(
% 1.35/0.53 ~ (((minus_minus_nat @ n @ k)) = ((minus_minus_nat @ (groups1842438620at_nat @ (^[Y0 : nat]: (times_times_nat @ (p @ Y0) @ Y0)) @ (set_ord_atMost_nat @ n)) @ k)))),
% 1.35/0.53 inference(fool_elimination,[],[f572])).
% 1.35/0.53 thf(f660,plain,(
% 1.35/0.53 (((minus_minus_nat @ n @ k)) != ((minus_minus_nat @ (groups1842438620at_nat @ (^[Y0 : nat]: (times_times_nat @ (p @ Y0) @ Y0)) @ (set_ord_atMost_nat @ n)) @ k)))),
% 1.35/0.53 inference(flattening,[],[f573])).
% 1.35/0.53 thf(f1106,plain,(
% 1.35/0.53 (((number1551313001itions @ p @ n)) = $true)),
% 1.35/0.53 inference(cnf_transformation,[],[f435])).
% 1.35/0.53 thf(f1138,plain,(
% 1.35/0.53 (set_ord_atMost_nat = (^[Y0 : nat]: (collect_nat @ (^[Y1 : nat]: (ord_less_eq_nat @ Y1 @ Y0)))))),
% 1.35/0.53 inference(cnf_transformation,[],[f550])).
% 1.35/0.53 thf(f1162,plain,(
% 1.35/0.53 (number1551313001itions = (^[Y0 : nat > nat]: ((^[Y1 : nat]: ((!! @ nat @ (^[Y2 : nat]: ((~ ((Y0 @ Y2) = zero_zero_nat)) => ((ord_less_eq_nat @ Y2 @ Y1) & (ord_less_eq_nat @ one_one_nat @ Y2))))) & ((groups1842438620at_nat @ (^[Y2 : nat]: (times_times_nat @ (Y0 @ Y2) @ Y2)) @ (set_ord_atMost_nat @ Y1)) = Y1))))))),
% 1.35/0.53 inference(cnf_transformation,[],[f512])).
% 1.35/0.53 thf(f1307,plain,(
% 1.35/0.53 (((minus_minus_nat @ n @ k)) != ((minus_minus_nat @ (groups1842438620at_nat @ (^[Y0 : nat]: (times_times_nat @ (p @ Y0) @ Y0)) @ (set_ord_atMost_nat @ n)) @ k)))),
% 1.35/0.53 inference(cnf_transformation,[],[f660])).
% 1.35/0.53 thf(f1387,plain,(
% 1.35/0.53 (number1551313001itions = (^[Y0 : nat > nat]: ((^[Y1 : nat]: ((!! @ nat @ (^[Y2 : nat]: ((~ ((Y0 @ Y2) = zero_zero_nat)) => ((ord_less_eq_nat @ Y2 @ Y1) & (ord_less_eq_nat @ one_one_nat @ Y2))))) & ((groups1842438620at_nat @ (^[Y2 : nat]: (times_times_nat @ (Y0 @ Y2) @ Y2)) @ ((^[Y2 : nat]: (collect_nat @ (^[Y3 : nat]: (ord_less_eq_nat @ Y3 @ Y2)))) @ Y1)) = Y1))))))),
% 1.35/0.53 inference(definition_unfolding,[],[f1162,f1138])).
% 1.35/0.53 thf(f1390,plain,(
% 1.35/0.53 ($true = (((^[Y0 : nat > nat]: ((^[Y1 : nat]: ((!! @ nat @ (^[Y2 : nat]: ((~ ((Y0 @ Y2) = zero_zero_nat)) => ((ord_less_eq_nat @ Y2 @ Y1) & (ord_less_eq_nat @ one_one_nat @ Y2))))) & ((groups1842438620at_nat @ (^[Y2 : nat]: (times_times_nat @ (Y0 @ Y2) @ Y2)) @ ((^[Y2 : nat]: (collect_nat @ (^[Y3 : nat]: (ord_less_eq_nat @ Y3 @ Y2)))) @ Y1)) = Y1))))) @ p @ n)))),
% 1.35/0.53 inference(definition_unfolding,[],[f1106,f1387])).
% 1.35/0.53 thf(f1406,plain,(
% 1.35/0.53 (((minus_minus_nat @ n @ k)) != ((minus_minus_nat @ (groups1842438620at_nat @ (^[Y0 : nat]: (times_times_nat @ (p @ Y0) @ Y0)) @ ((^[Y0 : nat]: (collect_nat @ (^[Y1 : nat]: (ord_less_eq_nat @ Y1 @ Y0)))) @ n)) @ k)))),
% 1.35/0.53 inference(definition_unfolding,[],[f1307,f1138])).
% 1.35/0.53 thf(f1455,definition,(
% 1.35/0.53 (sF82 = ((minus_minus_nat @ n @ k)))),
% 1.35/0.53 introduced(definition,[new_symbols(definition,[sF82])],[function_definition])).
% 1.35/0.53 thf(f1456,plain,(
% 1.35/0.53 (((minus_minus_nat @ n @ k)) = sF82)),
% 1.35/0.53 inference(reorient_equations,[],[f1455])).
% 1.35/0.53 thf(f1457,definition,(
% 1.35/0.53 (sF83 = (((^[Y0 : nat]: (collect_nat @ (^[Y1 : nat]: (ord_less_eq_nat @ Y1 @ Y0)))) @ n)))),
% 1.35/0.53 introduced(definition,[new_symbols(definition,[sF83])],[function_definition])).
% 1.35/0.53 thf(f1458,plain,(
% 1.35/0.53 ((((^[Y0 : nat]: (collect_nat @ (^[Y1 : nat]: (ord_less_eq_nat @ Y1 @ Y0)))) @ n)) = sF83)),
% 1.35/0.53 inference(reorient_equations,[],[f1457])).
% 1.35/0.53 thf(f1459,definition,(
% 1.35/0.53 (sF84 = ((groups1842438620at_nat @ (^[Y0 : nat]: (times_times_nat @ (p @ Y0) @ Y0)) @ sF83)))),
% 1.35/0.53 introduced(definition,[new_symbols(definition,[sF84])],[function_definition])).
% 1.35/0.53 thf(f1460,plain,(
% 1.35/0.53 (((groups1842438620at_nat @ (^[Y0 : nat]: (times_times_nat @ (p @ Y0) @ Y0)) @ sF83)) = sF84)),
% 1.35/0.53 inference(reorient_equations,[],[f1459])).
% 1.35/0.53 thf(f1461,definition,(
% 1.35/0.53 (sF85 = ((minus_minus_nat @ sF84 @ k)))),
% 1.35/0.53 introduced(definition,[new_symbols(definition,[sF85])],[function_definition])).
% 1.35/0.53 thf(f1462,plain,(
% 1.35/0.53 (((minus_minus_nat @ sF84 @ k)) = sF85)),
% 1.35/0.53 inference(reorient_equations,[],[f1461])).
% 1.35/0.53 thf(f1463,plain,(
% 1.35/0.53 (sF82 != sF85)),
% 1.35/0.53 inference(definition_folding,[],[f1406,f1462,f1460,f1458,f1456])).
% 1.35/0.53 thf(f1813,plain,(
% 1.35/0.53 ((((!! @ nat @ (^[Y0 : nat]: ((~ ((p @ Y0) = zero_zero_nat)) => ((ord_less_eq_nat @ Y0 @ n) & (ord_less_eq_nat @ one_one_nat @ Y0))))) & ((groups1842438620at_nat @ (^[Y0 : nat]: (times_times_nat @ (p @ Y0) @ Y0)) @ (collect_nat @ (^[Y0 : nat]: (ord_less_eq_nat @ Y0 @ n)))) = n))) = $true)),
% 1.35/0.53 inference(beta-eta_normalization,[],[f1390])).
% 1.35/0.53 thf(f1814,plain,(
% 1.35/0.53 ($true = (((groups1842438620at_nat @ (^[Y0 : nat]: (times_times_nat @ (p @ Y0) @ Y0)) @ (collect_nat @ (^[Y0 : nat]: (ord_less_eq_nat @ Y0 @ n)))) = n)))),
% 1.35/0.53 inference(and_proxy_clausification,[],[f1813])).
% 1.35/0.53 thf(f1825,plain,(
% 1.35/0.53 (n = ((groups1842438620at_nat @ (^[Y0 : nat]: (times_times_nat @ (p @ Y0) @ Y0)) @ (collect_nat @ (^[Y0 : nat]: (ord_less_eq_nat @ Y0 @ n))))))),
% 1.35/0.53 inference(equality_proxy_clausification,[],[f1814])).
% 1.35/0.53 thf(f1855,plain,(
% 1.35/0.53 (((collect_nat @ (^[Y0 : nat]: (ord_less_eq_nat @ Y0 @ n)))) = sF83)),
% 1.35/0.53 inference(beta-eta_normalization,[],[f1458])).
% 1.35/0.53 thf(f1887,definition,(
% 1.35/0.53 spl94_2 <=> (((minus_minus_nat @ n @ k)) = sF82)),
% 1.35/0.53 introduced(definition,[new_symbols(definition,[spl94_2])],[avatar_definition])).
% 1.35/0.53 thf(f1890,plain,(
% 1.35/0.53 spl94_2),
% 1.35/0.53 inference(avatar_split_clause,[],[f1456,f1887])).
% 1.35/0.53 thf(f1915,definition,(
% 1.35/0.53 spl94_8 <=> (sF82 = sF85)),
% 1.35/0.53 introduced(definition,[new_symbols(definition,[spl94_8])],[avatar_definition])).
% 1.35/0.53 thf(f1918,plain,(
% 1.35/0.53 ~spl94_8),
% 1.35/0.53 inference(avatar_split_clause,[],[f1463,f1915])).
% 1.35/0.53 thf(f1952,definition,(
% 1.35/0.53 spl94_14 <=> (((minus_minus_nat @ sF84 @ k)) = sF85)),
% 1.35/0.53 introduced(definition,[new_symbols(definition,[spl94_14])],[avatar_definition])).
% 1.35/0.53 thf(f1955,plain,(
% 1.35/0.53 spl94_14),
% 1.35/0.53 inference(avatar_split_clause,[],[f1462,f1952])).
% 1.35/0.53 thf(f1972,definition,(
% 1.35/0.53 spl94_18 <=> (((groups1842438620at_nat @ (^[Y0 : nat]: (times_times_nat @ (p @ Y0) @ Y0)) @ sF83)) = sF84)),
% 1.35/0.53 introduced(definition,[new_symbols(definition,[spl94_18])],[avatar_definition])).
% 1.35/0.53 thf(f1975,plain,(
% 1.35/0.53 spl94_18),
% 1.35/0.53 inference(avatar_split_clause,[],[f1460,f1972])).
% 1.35/0.53 thf(f1983,definition,(
% 1.35/0.53 spl94_20 <=> (n = ((groups1842438620at_nat @ (^[Y0 : nat]: (times_times_nat @ (p @ Y0) @ Y0)) @ (collect_nat @ (^[Y0 : nat]: (ord_less_eq_nat @ Y0 @ n))))))),
% 1.35/0.53 introduced(definition,[new_symbols(definition,[spl94_20])],[avatar_definition])).
% 1.35/0.53 thf(f1986,plain,(
% 1.35/0.53 spl94_20),
% 1.35/0.53 inference(avatar_split_clause,[],[f1825,f1983])).
% 1.35/0.53 thf(f1993,definition,(
% 1.35/0.53 spl94_22 <=> (((collect_nat @ (^[Y0 : nat]: (ord_less_eq_nat @ Y0 @ n)))) = sF83)),
% 1.35/0.53 introduced(definition,[new_symbols(definition,[spl94_22])],[avatar_definition])).
% 1.35/0.53 thf(f1996,plain,(
% 1.35/0.53 spl94_22),
% 1.35/0.53 inference(avatar_split_clause,[],[f1855,f1993])).
% 1.35/0.53 thf(f2011,definition,(
% 1.35/0.53 (((collect_nat @ (^[Y0 : nat]: (ord_less_eq_nat @ Y0 @ n)))) != sF83) | (((groups1842438620at_nat @ (^[Y0 : nat]: (times_times_nat @ (p @ Y0) @ Y0)) @ sF83)) != sF84) | (n != ((groups1842438620at_nat @ (^[Y0 : nat]: (times_times_nat @ (p @ Y0) @ Y0)) @ (collect_nat @ (^[Y0 : nat]: (ord_less_eq_nat @ Y0 @ n)))))) | (((minus_minus_nat @ n @ k)) != sF82) | (((minus_minus_nat @ sF84 @ k)) != sF85) | (sF82 = sF85)),
% 1.35/0.53 introduced(theory,[theory_tautology_sat_conflict])).
% 1.35/0.53 cnf(s2, plain, spl94_2, inference(sat_conversion,[],[f1890])).
% 1.35/0.53 cnf(s8, plain, ~spl94_8, inference(sat_conversion,[],[f1918])).
% 1.35/0.53 cnf(s15, plain, spl94_14, inference(sat_conversion,[],[f1955])).
% 1.35/0.53 cnf(s21, plain, spl94_18, inference(sat_conversion,[],[f1975])).
% 1.35/0.53 cnf(s25, plain, spl94_20, inference(sat_conversion,[],[f1986])).
% 1.35/0.53 cnf(s27, plain, spl94_22, inference(sat_conversion,[],[f1996])).
% 1.35/0.53 cnf(s32, plain, ~spl94_2 | spl94_8 | ~spl94_14 | ~spl94_18 | ~spl94_20 | ~spl94_22, inference(sat_conversion,[],[f2011])).
% 1.35/0.53 cnf(s33, plain, ~spl94_2, inference(rat,[],[s32,s27,s25,s21,s15,s8])).
% 1.35/0.53 cnf(s34, plain, $false, inference(rat,[],[s2,s33])).
% 1.35/0.53 thf(f2012,plain,(
% 1.35/0.53 $false),
% 1.35/0.53 inference(avatar_sat_refutation,[],[s34])).
% 1.35/0.53 % SZS output end Proof for theBenchmark
% 1.35/0.53 % (1768254)------------------------------
% 1.35/0.53 % (1768254)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.35/0.53 % (1768254)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.35/0.53 % (1768254)CaDiCaL version: 2.1.3
% 1.35/0.53 % (1768254)Termination reason: Refutation
% 1.35/0.53 % (1768254)Time elapsed: 0.061 s
% 1.35/0.53 % (1768254)Peak memory usage: 14 MB
% 1.35/0.53 % (1768254)Instructions burned: 128 (million)
% 1.35/0.53 % (1768186)Success in time 0.269 s
% 1.35/0.53 % Vampire exiting
%------------------------------------------------------------------------------