%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU698^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 08:30:50 AM UTC 2026
% Result : Theorem 2.69s 0.74s
% Output : Refutation 2.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU698^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n007.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 14:09:41 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running higher-order theorem proving
% 0.21/0.26 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
% 0.66/0.40 % (3425148)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.66/0.40 % (3425162)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.66/0.40 % (3425162)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
% 0.66/0.40 % (3425162)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=2306996959:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.66/0.40 % (3425157)lrs+10_16_si=on:nwc=1.5:random_seed=1828426070:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.66/0.40 % (3425158)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=4139676742:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.66/0.40 % (3425156)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4256654578:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.66/0.40 % (3425160)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1025607642:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.66/0.40 % (3425159)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=2119647446: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)
% 0.66/0.40 % (3425161)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=200047565:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.66/0.40 % (3425158)Instruction limit reached!
% 0.66/0.40 % (3425158)------------------------------
% 0.66/0.40 % (3425158)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.40 % (3425158)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.40 % (3425158)CaDiCaL version: 2.1.3
% 0.66/0.40 % (3425158)Termination reason: Instruction limit
% 0.66/0.40 % (3425158)Termination phase: shuffling
% 0.66/0.40 % (3425158)Time elapsed: 0.002 s
% 0.66/0.40 % (3425158)Peak memory usage: 10 MB
% 0.66/0.40 % (3425158)Instructions burned: 3 (million)
% 0.66/0.40 % (3425157)Instruction limit reached!
% 0.66/0.40 % (3425157)------------------------------
% 0.66/0.40 % (3425157)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.40 % (3425157)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.40 % (3425157)CaDiCaL version: 2.1.3
% 0.66/0.40 % (3425157)Termination reason: Instruction limit
% 0.66/0.40 % (3425157)Termination phase: shuffling
% 0.66/0.40 % (3425157)Time elapsed: 0.008 s
% 0.66/0.40 % (3425157)Peak memory usage: 10 MB
% 0.66/0.40 % (3425157)Instructions burned: 18 (million)
% 0.66/0.40 % (3425160)Instruction limit reached!
% 0.66/0.40 % (3425160)------------------------------
% 0.66/0.40 % (3425160)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.40 % (3425160)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.40 % (3425160)CaDiCaL version: 2.1.3
% 0.66/0.40 % (3425160)Termination reason: Instruction limit
% 0.66/0.40 % (3425160)Termination phase: Property scanning
% 0.66/0.40 % (3425160)Time elapsed: 0.012 s
% 0.66/0.40 % (3425160)Peak memory usage: 10 MB
% 0.66/0.40 % (3425160)Instructions burned: 26 (million)
% 0.66/0.40 % (3425174)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1924321294:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.66/0.40 % (3425174)Instruction limit reached!
% 0.66/0.40 % (3425174)------------------------------
% 0.66/0.40 % (3425174)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.40 % (3425174)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.40 % (3425174)CaDiCaL version: 2.1.3
% 0.66/0.40 % (3425174)Termination reason: Instruction limit
% 0.66/0.40 % (3425174)Termination phase: shuffling
% 0.66/0.40 % (3425174)Time elapsed: 0.002 s
% 0.66/0.40 % (3425174)Peak memory usage: 10 MB
% 0.66/0.40 % (3425174)Instructions burned: 3 (million)
% 0.66/0.40 % (3425178)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=655462518:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.66/0.44 % (3425182)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.66/0.44 % (3425162)Instruction limit reached!
% 0.66/0.44 % (3425162)------------------------------
% 0.66/0.44 % (3425162)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.44 % (3425162)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.44 % (3425162)CaDiCaL version: 2.1.3
% 0.66/0.44 % (3425162)Termination reason: Instruction limit
% 0.66/0.44 % (3425162)Termination phase: Saturation
% 0.66/0.44 % (3425162)Time elapsed: 0.037 s
% 0.66/0.44 % (3425162)Peak memory usage: 13 MB
% 0.66/0.44 % (3425162)Instructions burned: 160 (million)
% 0.66/0.44 % (3425178)Instruction limit reached!
% 0.66/0.44 % (3425178)------------------------------
% 0.66/0.44 % (3425178)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.44 % (3425178)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.44 % (3425178)CaDiCaL version: 2.1.3
% 0.66/0.44 % (3425178)Termination reason: Instruction limit
% 0.66/0.44 % (3425178)Termination phase: shuffling
% 0.66/0.44 % (3425178)Time elapsed: 0.003 s
% 0.66/0.44 % (3425178)Peak memory usage: 10 MB
% 0.66/0.44 % (3425178)Instructions burned: 6 (million)
% 0.66/0.44 % (3425182)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=922242559:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.66/0.44 % (3425161)Instruction limit reached!
% 0.66/0.44 % (3425161)------------------------------
% 0.66/0.44 % (3425161)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.44 % (3425161)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.44 % (3425161)CaDiCaL version: 2.1.3
% 0.66/0.44 % (3425161)Termination reason: Instruction limit
% 0.66/0.44 % (3425161)Termination phase: Preprocessing 3
% 0.66/0.44 % (3425161)Time elapsed: 0.035 s
% 0.66/0.44 % (3425161)Peak memory usage: 12 MB
% 0.66/0.44 % (3425161)Instructions burned: 77 (million)
% 0.66/0.44 % (3425182)Instruction limit reached!
% 0.66/0.44 % (3425182)------------------------------
% 0.66/0.44 % (3425182)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.44 % (3425182)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.44 % (3425182)CaDiCaL version: 2.1.3
% 0.66/0.44 % (3425182)Termination reason: Instruction limit
% 0.66/0.44 % (3425182)Termination phase: shuffling
% 0.66/0.44 % (3425182)Time elapsed: 0.004 s
% 0.66/0.44 % (3425182)Peak memory usage: 10 MB
% 0.66/0.44 % (3425182)Instructions burned: 9 (million)
% 0.66/0.44 % (3425187)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
% 0.66/0.44 % (3425187)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.66/0.44 % (3425187)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2267838310:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.66/0.44 % (3425156)Instruction limit reached!
% 0.66/0.44 % (3425156)------------------------------
% 0.66/0.44 % (3425156)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.44 % (3425156)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.44 % (3425156)CaDiCaL version: 2.1.3
% 0.66/0.44 % (3425156)Termination reason: Instruction limit
% 0.66/0.44 % (3425156)Termination phase: Property scanning
% 0.66/0.44 % (3425156)Time elapsed: 0.044 s
% 0.66/0.44 % (3425156)Peak memory usage: 13 MB
% 0.66/0.44 % (3425156)Instructions burned: 96 (million)
% 0.66/0.44 % (3425185)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2796926754:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.66/0.44 % (3425187)Instruction limit reached!
% 0.66/0.44 % (3425187)------------------------------
% 0.66/0.44 % (3425187)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.44 % (3425187)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.44 % (3425187)CaDiCaL version: 2.1.3
% 0.66/0.44 % (3425187)Termination reason: Instruction limit
% 1.31/0.47 % (3425187)Termination phase: shuffling
% 1.31/0.47 % (3425187)Time elapsed: 0.007 s
% 1.31/0.47 % (3425187)Peak memory usage: 10 MB
% 1.31/0.47 % (3425187)Instructions burned: 30 (million)
% 1.31/0.47 % (3425185)Instruction limit reached!
% 1.31/0.47 % (3425185)------------------------------
% 1.31/0.47 % (3425185)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.31/0.47 % (3425185)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.31/0.47 % (3425185)CaDiCaL version: 2.1.3
% 1.31/0.47 % (3425185)Termination reason: Instruction limit
% 1.31/0.47 % (3425185)Termination phase: shuffling
% 1.31/0.47 % (3425185)Time elapsed: 0.006 s
% 1.31/0.47 % (3425185)Peak memory usage: 10 MB
% 1.31/0.47 % (3425185)Instructions burned: 12 (million)
% 1.31/0.47 % (3425189)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=830812731:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 1.31/0.47 % (3425192)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.31/0.47 % (3425195)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=435215533:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 1.31/0.47 % (3425192)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=3453774470:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 1.31/0.47 % (3425191)lrs+10_1_si=on:cs=on:random_seed=2567210064:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 1.31/0.47 % (3425192)Instruction limit reached!
% 1.31/0.47 % (3425192)------------------------------
% 1.31/0.47 % (3425192)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.31/0.47 % (3425192)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.31/0.47 % (3425192)CaDiCaL version: 2.1.3
% 1.31/0.47 % (3425192)Termination reason: Instruction limit
% 1.31/0.47 % (3425192)Termination phase: shuffling
% 1.31/0.47 % (3425192)Time elapsed: 0.002 s
% 1.31/0.47 % (3425192)Peak memory usage: 10 MB
% 1.31/0.47 % (3425192)Instructions burned: 3 (million)
% 1.31/0.47 % (3425194)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=476982518:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 1.31/0.47 % (3425191)Instruction limit reached!
% 1.31/0.47 % (3425191)------------------------------
% 1.31/0.47 % (3425191)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.31/0.47 % (3425191)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.31/0.47 % (3425191)CaDiCaL version: 2.1.3
% 1.31/0.47 % (3425191)Termination reason: Instruction limit
% 1.31/0.47 % (3425191)Termination phase: Property scanning
% 1.31/0.47 % (3425191)Time elapsed: 0.020 s
% 1.31/0.47 % (3425191)Peak memory usage: 10 MB
% 1.31/0.47 % (3425191)Instructions burned: 29 (million)
% 1.31/0.47 % (3425201)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=229637174:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2999 on theBenchmark for (2999ds/14Mi)
% 1.31/0.47 % (3425196)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=1090815860:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 1.31/0.47 % (3425194)Instruction limit reached!
% 1.31/0.47 % (3425194)------------------------------
% 1.31/0.47 % (3425194)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.31/0.47 % (3425194)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.31/0.47 % (3425194)CaDiCaL version: 2.1.3
% 1.31/0.47 % (3425194)Termination reason: Instruction limit
% 1.31/0.47 % (3425194)Termination phase: SInE selection
% 1.31/0.47 % (3425194)Time elapsed: 0.026 s
% 1.31/0.47 % (3425194)Peak memory usage: 10 MB
% 1.31/0.47 % (3425194)Instructions burned: 39 (million)
% 1.31/0.47 % (3425201)Instruction limit reached!
% 1.31/0.47 % (3425201)------------------------------
% 1.31/0.47 % (3425201)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.31/0.47 % (3425201)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.31/0.47 % (3425201)CaDiCaL version: 2.1.3
% 1.31/0.47 % (3425201)Termination reason: Instruction limit
% 1.31/0.47 % (3425201)Termination phase: shuffling
% 1.31/0.52 % (3425201)Time elapsed: 0.007 s
% 1.31/0.52 % (3425201)Peak memory usage: 10 MB
% 1.31/0.52 % (3425201)Instructions burned: 16 (million)
% 1.31/0.52 % (3425196)Instruction limit reached!
% 1.31/0.52 % (3425196)------------------------------
% 1.31/0.52 % (3425196)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.31/0.52 % (3425196)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.31/0.52 % (3425196)CaDiCaL version: 2.1.3
% 1.31/0.52 % (3425196)Termination reason: Instruction limit
% 1.31/0.52 % (3425196)Termination phase: Property scanning
% 1.31/0.52 % (3425196)Time elapsed: 0.012 s
% 1.31/0.52 % (3425196)Peak memory usage: 10 MB
% 1.31/0.52 % (3425196)Instructions burned: 26 (million)
% 1.31/0.52 % (3425203)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=2847968415:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.31/0.52 % (3425189)Instruction limit reached!
% 1.31/0.52 % (3425189)------------------------------
% 1.31/0.52 % (3425189)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.31/0.52 % (3425189)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.31/0.52 % (3425189)CaDiCaL version: 2.1.3
% 1.31/0.52 % (3425189)Termination reason: Instruction limit
% 1.31/0.52 % (3425189)Termination phase: Function definition elimination
% 1.31/0.52 % (3425189)Time elapsed: 0.052 s
% 1.31/0.52 % (3425189)Peak memory usage: 11 MB
% 1.31/0.52 % (3425189)Instructions burned: 86 (million)
% 1.31/0.52 % (3425206)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=3505463673:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.31/0.52 % (3425207)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=1617372838: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)
% 1.31/0.52 % (3425207)Instruction limit reached!
% 1.31/0.52 % (3425207)------------------------------
% 1.31/0.52 % (3425207)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.31/0.52 % (3425207)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.31/0.52 % (3425207)CaDiCaL version: 2.1.3
% 1.31/0.52 % (3425207)Termination reason: Instruction limit
% 1.31/0.52 % (3425207)Termination phase: shuffling
% 1.31/0.52 % (3425207)Time elapsed: 0.002 s
% 1.31/0.52 % (3425207)Peak memory usage: 10 MB
% 1.31/0.52 % (3425207)Instructions burned: 3 (million)
% 1.31/0.52 % (3425206)Instruction limit reached!
% 1.31/0.52 % (3425206)------------------------------
% 1.31/0.52 % (3425206)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.31/0.52 % (3425206)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.31/0.52 % (3425206)CaDiCaL version: 2.1.3
% 1.31/0.52 % (3425206)Termination reason: Instruction limit
% 1.31/0.52 % (3425206)Termination phase: shuffling
% 1.31/0.52 % (3425206)Time elapsed: 0.007 s
% 1.31/0.52 % (3425206)Peak memory usage: 10 MB
% 1.31/0.52 % (3425206)Instructions burned: 16 (million)
% 1.31/0.52 % (3425208)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2436965218:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.31/0.52 % (3425210)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=3858728828:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.31/0.52 % (3425208)Instruction limit reached!
% 1.31/0.52 % (3425208)------------------------------
% 1.31/0.52 % (3425208)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.31/0.52 % (3425208)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.31/0.52 % (3425208)CaDiCaL version: 2.1.3
% 1.31/0.52 % (3425208)Termination reason: Instruction limit
% 1.31/0.52 % (3425208)Termination phase: shuffling
% 1.31/0.52 % (3425208)Time elapsed: 0.011 s
% 1.31/0.52 % (3425208)Peak memory usage: 10 MB
% 1.31/0.52 % (3425208)Instructions burned: 26 (million)
% 1.31/0.52 % (3425215)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
% 1.31/0.52 % (3425215)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.31/0.52 % (3425210)Instruction limit reached!
% 1.31/0.52 % (3425210)------------------------------
% 1.31/0.52 % (3425210)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.06/0.57 % (3425210)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.06/0.57 % (3425210)CaDiCaL version: 2.1.3
% 2.06/0.57 % (3425210)Termination reason: Instruction limit
% 2.06/0.57 % (3425210)Termination phase: shuffling
% 2.06/0.57 % (3425210)Time elapsed: 0.010 s
% 2.06/0.57 % (3425210)Peak memory usage: 10 MB
% 2.06/0.57 % (3425210)Instructions burned: 23 (million)
% 2.06/0.57 % (3425213)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=2569111916:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 2.06/0.57 % (3425195)Instruction limit reached!
% 2.06/0.57 % (3425195)------------------------------
% 2.06/0.57 % (3425195)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.06/0.57 % (3425195)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.06/0.57 % (3425215)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=735754640:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 2.06/0.57 % (3425195)CaDiCaL version: 2.1.3
% 2.06/0.57 % (3425195)Termination reason: Instruction limit
% 2.06/0.57 % (3425195)Termination phase: Saturation
% 2.06/0.57 % (3425195)Time elapsed: 0.077 s
% 2.06/0.57 % (3425195)Peak memory usage: 14 MB
% 2.06/0.57 % (3425195)Instructions burned: 249 (million)
% 2.06/0.57 % (3425215)Instruction limit reached!
% 2.06/0.57 % (3425215)------------------------------
% 2.06/0.57 % (3425215)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.06/0.57 % (3425215)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.06/0.57 % (3425215)CaDiCaL version: 2.1.3
% 2.06/0.57 % (3425215)Termination reason: Instruction limit
% 2.06/0.57 % (3425215)Termination phase: shuffling
% 2.06/0.57 % (3425215)Time elapsed: 0.007 s
% 2.06/0.57 % (3425215)Peak memory usage: 10 MB
% 2.06/0.57 % (3425215)Instructions burned: 16 (million)
% 2.06/0.57 % (3425217)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 2.06/0.57 % (3425221)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=1128126943:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 2.06/0.57 % (3425217)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=4135693242:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 2.06/0.57 % (3425221)Instruction limit reached!
% 2.06/0.57 % (3425221)------------------------------
% 2.06/0.57 % (3425221)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.06/0.57 % (3425221)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.06/0.57 % (3425221)CaDiCaL version: 2.1.3
% 2.06/0.57 % (3425221)Termination reason: Instruction limit
% 2.06/0.57 % (3425221)Termination phase: shuffling
% 2.06/0.57 % (3425221)Time elapsed: 0.002 s
% 2.06/0.57 % (3425221)Peak memory usage: 10 MB
% 2.06/0.57 % (3425221)Instructions burned: 9 (million)
% 2.06/0.57 % (3425219)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=3594714968:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 2.06/0.57 % (3425217)Instruction limit reached!
% 2.06/0.57 % (3425217)------------------------------
% 2.06/0.57 % (3425217)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.06/0.57 % (3425217)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.06/0.57 % (3425217)CaDiCaL version: 2.1.3
% 2.06/0.57 % (3425217)Termination reason: Instruction limit
% 2.06/0.57 % (3425217)Termination phase: shuffling
% 2.06/0.57 % (3425217)Time elapsed: 0.004 s
% 2.06/0.57 % (3425217)Peak memory usage: 10 MB
% 2.06/0.57 % (3425217)Instructions burned: 9 (million)
% 2.06/0.57 % (3425227)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=2081568517:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 2.06/0.57 % (3425222)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=1807186962:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 2.06/0.57 % (3425213)Instruction limit reached!
% 2.06/0.57 % (3425213)------------------------------
% 2.06/0.57 % (3425213)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.38/0.64 % (3425213)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.38/0.64 % (3425213)CaDiCaL version: 2.1.3
% 2.38/0.64 % (3425213)Termination reason: Instruction limit
% 2.38/0.64 % (3425213)Termination phase: Preprocessing 3
% 2.38/0.64 % (3425213)Time elapsed: 0.028 s
% 2.38/0.64 % (3425213)Peak memory usage: 12 MB
% 2.38/0.64 % (3425213)Instructions burned: 61 (million)
% 2.38/0.64 % (3425227)Instruction limit reached!
% 2.38/0.64 % (3425227)------------------------------
% 2.38/0.64 % (3425227)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.38/0.64 % (3425227)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.38/0.64 % (3425227)CaDiCaL version: 2.1.3
% 2.38/0.64 % (3425227)Termination reason: Instruction limit
% 2.38/0.64 % (3425227)Termination phase: shuffling
% 2.38/0.64 % (3425227)Time elapsed: 0.005 s
% 2.38/0.64 % (3425227)Peak memory usage: 10 MB
% 2.38/0.64 % (3425227)Instructions burned: 22 (million)
% 2.38/0.64 % (3425219)Instruction limit reached!
% 2.38/0.64 % (3425219)------------------------------
% 2.38/0.64 % (3425219)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.38/0.64 % (3425219)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.38/0.64 % (3425219)CaDiCaL version: 2.1.3
% 2.38/0.64 % (3425219)Termination reason: Instruction limit
% 2.38/0.64 % (3425219)Termination phase: Property scanning
% 2.38/0.64 % (3425219)Time elapsed: 0.014 s
% 2.38/0.64 % (3425219)Peak memory usage: 11 MB
% 2.38/0.64 % (3425219)Instructions burned: 32 (million)
% 2.38/0.64 % (3425232)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=506248089:i=1240:rtra=on:ixr=off_2998 on theBenchmark for (2998ds/1240Mi)
% 2.38/0.64 % (3425222)Instruction limit reached!
% 2.38/0.64 % (3425222)------------------------------
% 2.38/0.64 % (3425222)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.38/0.64 % (3425222)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.38/0.64 % (3425222)CaDiCaL version: 2.1.3
% 2.38/0.64 % (3425222)Termination reason: Instruction limit
% 2.38/0.64 % (3425222)Termination phase: shuffling
% 2.38/0.64 % (3425222)Time elapsed: 0.011 s
% 2.38/0.64 % (3425222)Peak memory usage: 10 MB
% 2.38/0.64 % (3425222)Instructions burned: 24 (million)
% 2.38/0.64 % (3425236)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=3117471744:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 2.38/0.64 % (3425235)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=1846242846:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/143Mi)
% 2.38/0.64 % (3425237)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3139845718:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 2.38/0.64 % (3425239)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 2.38/0.64 % (3425239)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1770973698:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 2.38/0.64 % (3425239)Instruction limit reached!
% 2.38/0.64 % (3425239)------------------------------
% 2.38/0.64 % (3425239)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.38/0.64 % (3425239)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.38/0.64 % (3425239)CaDiCaL version: 2.1.3
% 2.38/0.64 % (3425239)Termination reason: Instruction limit
% 2.38/0.64 % (3425239)Termination phase: shuffling
% 2.38/0.64 % (3425239)Time elapsed: 0.004 s
% 2.38/0.64 % (3425239)Peak memory usage: 10 MB
% 2.38/0.64 % (3425239)Instructions burned: 9 (million)
% 2.38/0.64 % (3425237)Instruction limit reached!
% 2.38/0.64 % (3425237)------------------------------
% 2.38/0.64 % (3425237)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.38/0.64 % (3425237)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.38/0.64 % (3425237)CaDiCaL version: 2.1.3
% 2.38/0.64 % (3425237)Termination reason: Instruction limit
% 2.38/0.64 % (3425237)Termination phase: Property scanning
% 2.38/0.64 % (3425237)Time elapsed: 0.018 s
% 2.38/0.64 % (3425237)Peak memory usage: 10 MB
% 2.38/0.64 % (3425237)Instructions burned: 42 (million)
% 2.38/0.64 % (3425253)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=1316250596:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 2.69/0.71 % (3425236)Instruction limit reached!
% 2.69/0.71 % (3425236)------------------------------
% 2.69/0.71 % (3425236)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.69/0.71 % (3425236)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/0.71 % (3425236)CaDiCaL version: 2.1.3
% 2.69/0.71 % (3425236)Termination reason: Instruction limit
% 2.69/0.71 % (3425236)Termination phase: Saturation
% 2.69/0.71 % (3425236)Time elapsed: 0.044 s
% 2.69/0.71 % (3425236)Peak memory usage: 14 MB
% 2.69/0.71 % (3425236)Instructions burned: 193 (million)
% 2.69/0.71 % (3425257)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=979789820: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)
% 2.69/0.71 % (3425269)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 2.69/0.71 % (3425269)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=2227332937:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2997 on theBenchmark for (2997ds/6Mi)
% 2.69/0.71 % (3425269)Instruction limit reached!
% 2.69/0.71 % (3425269)------------------------------
% 2.69/0.71 % (3425269)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.69/0.71 % (3425269)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/0.71 % (3425269)CaDiCaL version: 2.1.3
% 2.69/0.71 % (3425269)Termination reason: Instruction limit
% 2.69/0.71 % (3425269)Termination phase: shuffling
% 2.69/0.71 % (3425269)Time elapsed: 0.002 s
% 2.69/0.71 % (3425269)Peak memory usage: 10 MB
% 2.69/0.71 % (3425269)Instructions burned: 8 (million)
% 2.69/0.71 % (3425235)Instruction limit reached!
% 2.69/0.71 % (3425235)------------------------------
% 2.69/0.71 % (3425235)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.69/0.71 % (3425235)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/0.71 % (3425235)CaDiCaL version: 2.1.3
% 2.69/0.71 % (3425235)Termination reason: Instruction limit
% 2.69/0.71 % (3425235)Termination phase: Saturation
% 2.69/0.71 % (3425235)Time elapsed: 0.060 s
% 2.69/0.71 % (3425235)Peak memory usage: 13 MB
% 2.69/0.71 % (3425235)Instructions burned: 144 (million)
% 2.69/0.71 % (3425279)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=2880106218:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2997 on theBenchmark for (2997ds/22Mi)
% 2.69/0.71 % (3425279)Instruction limit reached!
% 2.69/0.71 % (3425279)------------------------------
% 2.69/0.71 % (3425279)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.69/0.71 % (3425279)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/0.71 % (3425279)CaDiCaL version: 2.1.3
% 2.69/0.71 % (3425279)Termination reason: Instruction limit
% 2.69/0.71 % (3425279)Termination phase: shuffling
% 2.69/0.71 % (3425279)Time elapsed: 0.005 s
% 2.69/0.71 % (3425279)Peak memory usage: 10 MB
% 2.69/0.71 % (3425279)Instructions burned: 22 (million)
% 2.69/0.71 % (3425203)Instruction limit reached!
% 2.69/0.71 % (3425203)------------------------------
% 2.69/0.71 % (3425203)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.69/0.71 % (3425203)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/0.71 % (3425203)CaDiCaL version: 2.1.3
% 2.69/0.71 % (3425203)Termination reason: Instruction limit
% 2.69/0.71 % (3425203)Termination phase: Saturation
% 2.69/0.71 % (3425203)Time elapsed: 0.156 s
% 2.69/0.71 % (3425203)Peak memory usage: 15 MB
% 2.69/0.71 % (3425203)Instructions burned: 327 (million)
% 2.69/0.71 % (3425289)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=1136689303:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/316Mi)
% 2.69/0.71 % (3425284)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=3899361728:i=19:add=on:rtra=on_2997 on theBenchmark for (2997ds/19Mi)
% 2.69/0.71 % (3425284)Instruction limit reached!
% 2.69/0.71 % (3425284)------------------------------
% 2.69/0.71 % (3425284)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.69/0.74 % (3425284)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/0.74 % (3425284)CaDiCaL version: 2.1.3
% 2.69/0.74 % (3425284)Termination reason: Instruction limit
% 2.69/0.74 % (3425284)Termination phase: shuffling
% 2.69/0.74 % (3425284)Time elapsed: 0.010 s
% 2.69/0.74 % (3425284)Peak memory usage: 10 MB
% 2.69/0.74 % (3425284)Instructions burned: 22 (million)
% 2.69/0.74 % (3425293)dis+1004_4:1_slsqr=1,2:to=lpo:plsq=on:fde=unused:e2e=on:si=on:spb=goal_then_units:acc=on:urr=on:uwa=off:fd=preordered:s2agt=16:slsqc=1:slsq=on:random_seed=2658500310:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2997 on theBenchmark for (2997ds/853Mi)
% 2.69/0.74 % (3425298)dis+1003_3:4_to=kbo:plsq=on:prc=on:sims=off:e2e=on:si=on:spb=intro:acc=on:urr=on:uwa=off:foolp=on:s2agt=32:slsqc=3:slsq=on:random_seed=274628207:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2996 on theBenchmark for (2996ds/45Mi)
% 2.69/0.74 % (3425253)Instruction limit reached!
% 2.69/0.74 % (3425253)------------------------------
% 2.69/0.74 % (3425253)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.69/0.74 % (3425253)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/0.74 % (3425253)CaDiCaL version: 2.1.3
% 2.69/0.74 % (3425253)Termination reason: Instruction limit
% 2.69/0.74 % (3425253)Termination phase: Saturation
% 2.69/0.74 % (3425253)Time elapsed: 0.077 s
% 2.69/0.74 % (3425253)Peak memory usage: 13 MB
% 2.69/0.74 % (3425253)Instructions burned: 181 (million)
% 2.69/0.74 % (3425257)Instruction limit reached!
% 2.69/0.74 % (3425257)------------------------------
% 2.69/0.74 % (3425257)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.69/0.74 % (3425257)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/0.74 % (3425257)CaDiCaL version: 2.1.3
% 2.69/0.74 % (3425257)Termination reason: Instruction limit
% 2.69/0.74 % (3425257)Termination phase: Saturation
% 2.69/0.74 % (3425257)Time elapsed: 0.073 s
% 2.69/0.74 % (3425257)Peak memory usage: 13 MB
% 2.69/0.74 % (3425257)Instructions burned: 171 (million)
% 2.69/0.74 % (3425298)Instruction limit reached!
% 2.69/0.74 % (3425298)------------------------------
% 2.69/0.74 % (3425298)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.69/0.74 % (3425298)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/0.74 % (3425298)CaDiCaL version: 2.1.3
% 2.69/0.74 % (3425298)Termination reason: Instruction limit
% 2.69/0.74 % (3425298)Termination phase: SInE selection
% 2.69/0.74 % (3425298)Time elapsed: 0.020 s
% 2.69/0.74 % (3425298)Peak memory usage: 10 MB
% 2.69/0.74 % (3425298)Instructions burned: 47 (million)
% 2.69/0.74 % (3425302)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=1620951932:i=480:rtra=on_2996 on theBenchmark for (2996ds/480Mi)
% 2.69/0.74 % (3425303)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=432577678:avsq=on:i=21:avsqr=8,1:kws=frequency:fgj=on:bd=all:rtra=on:fe=axiom:ntd=on_2996 on theBenchmark for (2996ds/21Mi)
% 2.69/0.74 % (3425304)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 2.69/0.74 % (3425303)Instruction limit reached!
% 2.69/0.74 % (3425303)------------------------------
% 2.69/0.74 % (3425303)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.69/0.74 % (3425303)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/0.74 % (3425303)CaDiCaL version: 2.1.3
% 2.69/0.74 % (3425303)Termination reason: Instruction limit
% 2.69/0.74 % (3425303)Termination phase: shuffling
% 2.69/0.74 % (3425303)Time elapsed: 0.009 s
% 2.69/0.74 % (3425303)Peak memory usage: 10 MB
% 2.69/0.74 % (3425303)Instructions burned: 21 (million)
% 2.69/0.74 % (3425304)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=2327188462:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/200Mi)
% 2.69/0.74 % (3425289)Instruction limit reached!
% 2.69/0.74 % (3425289)------------------------------
% 2.69/0.74 % (3425289)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.69/0.74 % (3425289)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/0.74 % (3425289)CaDiCaL version: 2.1.3
% 2.69/0.74 % (3425289)Termination reason: Instruction limit
% 2.69/0.74 % (3425289)Termination phase: Saturation
% 2.69/0.74 % (3425289)Time elapsed: 0.079 s
% 2.69/0.74 % (3425289)Peak memory usage: 16 MB
% 2.69/0.74 % (3425289)Instructions burned: 317 (million)
% 2.69/0.74 % (3425307)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=2322911003:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_2996 on theBenchmark for (2996ds/13Mi)
% 2.69/0.74 % (3425159)Instruction limit reached!
% 2.69/0.74 % (3425159)------------------------------
% 2.69/0.74 % (3425159)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.69/0.74 % (3425159)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/0.74 % (3425159)CaDiCaL version: 2.1.3
% 2.69/0.74 % (3425159)Termination reason: Instruction limit
% 2.69/0.74 % (3425159)Termination phase: Saturation
% 2.69/0.74 % (3425159)Time elapsed: 0.345 s
% 2.69/0.74 % (3425159)Peak memory usage: 20 MB
% 2.69/0.74 % (3425159)Instructions burned: 635 (million)
% 2.69/0.74 % (3425309)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=668514069:i=66:s2at=3:nm=2:rtra=on:rawr=on_2996 on theBenchmark for (2996ds/66Mi)
% 2.69/0.74 % (3425307)Instruction limit reached!
% 2.69/0.74 % (3425307)------------------------------
% 2.69/0.74 % (3425307)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.69/0.74 % (3425307)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/0.74 % (3425307)CaDiCaL version: 2.1.3
% 2.69/0.74 % (3425307)Termination reason: Instruction limit
% 2.69/0.74 % (3425307)Termination phase: shuffling
% 2.69/0.74 % (3425307)Time elapsed: 0.006 s
% 2.69/0.74 % (3425307)Peak memory usage: 10 MB
% 2.69/0.74 % (3425307)Instructions burned: 13 (million)
% 2.69/0.74 % (3425311)lrs+1004_128_si=on:sos=all:uwa=off:random_seed=2872196914:i=51:fsr=off:rtra=on_2996 on theBenchmark for (2996ds/51Mi)
% 2.69/0.74 % (3425309)Instruction limit reached!
% 2.69/0.74 % (3425309)------------------------------
% 2.69/0.74 % (3425309)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.69/0.74 % (3425309)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/0.74 % (3425309)CaDiCaL version: 2.1.3
% 2.69/0.74 % (3425309)Termination reason: Instruction limit
% 2.69/0.74 % (3425309)Termination phase: Preprocessing 1
% 2.69/0.74 % (3425309)Time elapsed: 0.015 s
% 2.69/0.74 % (3425309)Peak memory usage: 11 MB
% 2.69/0.74 % (3425309)Instructions burned: 67 (million)
% 2.69/0.74 % (3425313)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=3185371263:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/31Mi)
% 2.69/0.74 % (3425315)dis+1010_40_to=kbo:tgt=full:fde=unused:si=on:sp=const_frequency:lma=off:cbe=off:uwa=interpreted_only:random_seed=4205845747:i=137:kws=precedence:bd=all:rtra=on:c=on:ntd=on_2995 on theBenchmark for (2995ds/137Mi)
% 2.69/0.74 % (3425313)Instruction limit reached!
% 2.69/0.74 % (3425313)------------------------------
% 2.69/0.74 % (3425313)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.69/0.74 % (3425313)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/0.74 % (3425313)CaDiCaL version: 2.1.3
% 2.69/0.74 % (3425313)Termination reason: Instruction limit
% 2.69/0.74 % (3425313)Termination phase: Property scanning
% 2.69/0.74 % (3425313)Time elapsed: 0.014 s
% 2.69/0.74 % (3425313)Peak memory usage: 10 MB
% 2.69/0.74 % (3425313)Instructions burned: 31 (million)
% 2.69/0.74 % (3425311)Instruction limit reached!
% 2.69/0.74 % (3425311)------------------------------
% 2.69/0.74 % (3425311)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.69/0.74 % (3425311)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/0.74 % (3425311)CaDiCaL version: 2.1.3
% 2.69/0.74 % (3425311)Termination reason: Instruction limit
% 2.69/0.74 % (3425311)Termination phase: Preprocessing 1
% 2.69/0.74 % (3425311)Time elapsed: 0.022 s
% 2.69/0.74 % (3425311)Peak memory usage: 10 MB
% 2.69/0.74 % (3425311)Instructions burned: 52 (million)
% 2.69/0.74 % (3425318)dis+10_2_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_pi_sigma_gen:si=on:sp=occurrence:plsqr=5,1:bsr=on:plsql=on:random_seed=2782471963:cond=on:i=34:hud=10:nm=10:rtra=on_2995 on theBenchmark for (2995ds/34Mi)
% 2.69/0.74 % (3425319)lrs+1010_1_sil=128000:hsqc=4:si=on:sos=on:random_seed=554034573:hsq=on:i=67:hsqaw=5:rtra=on:fe=abstraction:ntd=on_2995 on theBenchmark for (2995ds/67Mi)
% 2.69/0.74 % (3425315)Instruction limit reached!
% 2.69/0.74 % (3425315)------------------------------
% 2.69/0.74 % (3425315)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.69/0.74 % (3425315)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/0.74 % (3425315)CaDiCaL version: 2.1.3
% 2.69/0.74 % (3425315)Termination reason: Instruction limit
% 2.69/0.74 % (3425315)Termination phase: Saturation
% 2.69/0.74 % (3425315)Time elapsed: 0.030 s
% 2.69/0.74 % (3425315)Peak memory usage: 13 MB
% 2.69/0.74 % (3425315)Instructions burned: 138 (million)
% 2.69/0.74 % (3425304)Instruction limit reached!
% 2.69/0.74 % (3425304)------------------------------
% 2.69/0.74 % (3425304)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.69/0.74 % (3425304)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/0.74 % (3425304)CaDiCaL version: 2.1.3
% 2.69/0.74 % (3425304)Termination reason: Instruction limit
% 2.69/0.74 % (3425304)Termination phase: Saturation
% 2.69/0.74 % (3425304)Time elapsed: 0.087 s
% 2.69/0.74 % (3425304)Peak memory usage: 14 MB
% 2.69/0.74 % (3425304)Instructions burned: 201 (million)
% 2.69/0.74 % (3425318)Instruction limit reached!
% 2.69/0.74 % (3425318)------------------------------
% 2.69/0.74 % (3425318)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.69/0.74 % (3425318)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/0.74 % (3425318)CaDiCaL version: 2.1.3
% 2.69/0.74 % (3425318)Termination reason: Instruction limit
% 2.69/0.74 % (3425318)Termination phase: Property scanning
% 2.69/0.74 % (3425318)Time elapsed: 0.015 s
% 2.69/0.74 % (3425318)Peak memory usage: 10 MB
% 2.69/0.74 % (3425318)Instructions burned: 34 (million)
% 2.69/0.74 % (3425322)WARNING Broken Constraint: if sine_generality_threshold(60) has been set then sine_selection(off) is not equal to off
% 2.69/0.74 % (3425322)dis+21_1_to=lpo:sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:bsr=on:random_seed=530634282:i=180:hud=16:bd=all:fsr=off:rtra=on:sgt=60:ntd=on_2995 on theBenchmark for (2995ds/180Mi)
% 2.69/0.74 % (3425302) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3425148-3425302"...
% 2.69/0.74 % (3425323)lrs+1002_1_sil=128000:si=on:uwa=off:random_seed=1937674135:st=2:i=246:sd=3:rtra=on:ss=axioms_2995 on theBenchmark for (2995ds/246Mi)
% 2.69/0.74 % (3425319)Instruction limit reached!
% 2.69/0.74 % (3425319)------------------------------
% 2.69/0.74 % (3425319)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.69/0.74 % (3425319)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/0.74 % (3425302)...printing done.
% 2.69/0.74 % (3425319)CaDiCaL version: 2.1.3
% 2.69/0.74 % (3425319)Termination reason: Instruction limit
% 2.69/0.74 % (3425319)Termination phase: Property scanning
% 2.69/0.74 % (3425319)Time elapsed: 0.029 s
% 2.69/0.74 % (3425319)Peak memory usage: 11 MB
% 2.69/0.74 % (3425319)Instructions burned: 69 (million)
% 2.69/0.74 % (3425302)Refutation found. Thanks to Tanya!
% 2.69/0.74 % SZS status Theorem for theBenchmark
% 2.69/0.74 % SZS output start Proof for theBenchmark
% 2.69/0.74 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 2.69/0.74 thf(func_def_0, type, in: ($i > $i > $o)).
% 2.69/0.74 thf(func_def_1, type, exu: (($i > $o) > $o)).
% 2.69/0.74 thf(func_def_3, type, setextAx: $o).
% 2.69/0.74 thf(func_def_5, type, emptysetAx: $o).
% 2.69/0.74 thf(func_def_6, type, setadjoin: ($i > $i > $i)).
% 2.69/0.74 thf(func_def_7, type, setadjoinAx: $o).
% 2.69/0.74 thf(func_def_8, type, powerset: ($i > $i)).
% 2.69/0.74 thf(func_def_9, type, powersetAx: $o).
% 2.69/0.74 thf(func_def_10, type, setunion: ($i > $i)).
% 2.69/0.74 thf(func_def_11, type, setunionAx: $o).
% 2.69/0.74 thf(func_def_13, type, omega0Ax: $o).
% 2.69/0.74 thf(func_def_14, type, omegaSAx: $o).
% 2.69/0.74 thf(func_def_15, type, omegaIndAx: $o).
% 2.69/0.74 thf(func_def_16, type, replAx: $o).
% 2.69/0.74 thf(func_def_17, type, foundationAx: $o).
% 2.69/0.74 thf(func_def_18, type, wellorderingAx: $o).
% 2.69/0.74 thf(func_def_19, type, descr: (($i > $o) > $i)).
% 2.69/0.74 thf(func_def_20, type, descrp: $o).
% 2.69/0.74 thf(func_def_21, type, dsetconstr: ($i > ($i > $o) > $i)).
% 2.69/0.74 thf(func_def_22, type, dsetconstrI: $o).
% 2.69/0.74 thf(func_def_23, type, dsetconstrEL: $o).
% 2.69/0.74 thf(func_def_24, type, dsetconstrER: $o).
% 2.69/0.74 thf(func_def_25, type, exuE1: $o).
% 2.69/0.74 thf(func_def_26, type, prop2set: ($o > $i)).
% 2.69/0.74 thf(func_def_27, type, prop2setE: $o).
% 2.69/0.74 thf(func_def_28, type, emptysetE: $o).
% 2.69/0.74 thf(func_def_29, type, emptysetimpfalse: $o).
% 2.69/0.74 thf(func_def_30, type, notinemptyset: $o).
% 2.69/0.74 thf(func_def_31, type, exuE3e: $o).
% 2.69/0.74 thf(func_def_32, type, setext: $o).
% 2.69/0.74 thf(func_def_33, type, emptyI: $o).
% 2.69/0.74 thf(func_def_34, type, noeltsimpempty: $o).
% 2.69/0.74 thf(func_def_35, type, setbeta: $o).
% 2.69/0.74 thf(func_def_36, type, nonempty: ($i > $o)).
% 2.69/0.74 thf(func_def_37, type, nonemptyE1: $o).
% 2.69/0.74 thf(func_def_38, type, nonemptyI: $o).
% 2.69/0.74 thf(func_def_39, type, nonemptyI1: $o).
% 2.69/0.74 thf(func_def_40, type, setadjoinIL: $o).
% 2.69/0.74 thf(func_def_41, type, emptyinunitempty: $o).
% 2.69/0.74 thf(func_def_42, type, setadjoinIR: $o).
% 2.69/0.74 thf(func_def_43, type, setadjoinE: $o).
% 2.69/0.74 thf(func_def_44, type, setadjoinOr: $o).
% 2.69/0.74 thf(func_def_45, type, setoftrueEq: $o).
% 2.69/0.74 thf(func_def_46, type, powersetI: $o).
% 2.69/0.74 thf(func_def_47, type, emptyinPowerset: $o).
% 2.69/0.74 thf(func_def_48, type, emptyInPowerset: $o).
% 2.69/0.74 thf(func_def_49, type, powersetE: $o).
% 2.69/0.74 thf(func_def_50, type, setunionI: $o).
% 2.69/0.74 thf(func_def_51, type, setunionE: $o).
% 2.69/0.74 thf(func_def_52, type, subPowSU: $o).
% 2.69/0.74 thf(func_def_53, type, exuE2: $o).
% 2.69/0.74 thf(func_def_54, type, nonemptyImpWitness: $o).
% 2.69/0.74 thf(func_def_55, type, uniqinunit: $o).
% 2.69/0.74 thf(func_def_56, type, notinsingleton: $o).
% 2.69/0.74 thf(func_def_57, type, eqinunit: $o).
% 2.69/0.74 thf(func_def_58, type, singletonsswitch: $o).
% 2.69/0.74 thf(func_def_59, type, upairsetE: $o).
% 2.69/0.74 thf(func_def_60, type, upairsetIL: $o).
% 2.69/0.74 thf(func_def_61, type, upairsetIR: $o).
% 2.69/0.74 thf(func_def_62, type, emptyE1: $o).
% 2.69/0.74 thf(func_def_63, type, vacuousDall: $o).
% 2.69/0.74 thf(func_def_64, type, quantDeMorgan1: $o).
% 2.69/0.74 thf(func_def_65, type, quantDeMorgan2: $o).
% 2.69/0.74 thf(func_def_66, type, quantDeMorgan3: $o).
% 2.69/0.74 thf(func_def_67, type, quantDeMorgan4: $o).
% 2.69/0.74 thf(func_def_68, type, prop2setI: $o).
% 2.69/0.74 thf(func_def_69, type, set2prop: ($i > $o)).
% 2.69/0.74 thf(func_def_70, type, prop2set2propI: $o).
% 2.69/0.74 thf(func_def_71, type, notdexE: $o).
% 2.69/0.74 thf(func_def_72, type, notdallE: $o).
% 2.69/0.74 thf(func_def_73, type, exuI1: $o).
% 2.69/0.74 thf(func_def_74, type, exuI3: $o).
% 2.69/0.74 thf(func_def_75, type, exuI2: $o).
% 2.69/0.74 thf(func_def_76, type, inCongP: $o).
% 2.69/0.74 thf(func_def_77, type, in__Cong: $o).
% 2.69/0.74 thf(func_def_78, type, exuE3u: $o).
% 2.69/0.74 thf(func_def_79, type, exu__Cong: $o).
% 2.69/0.74 thf(func_def_80, type, emptyset__Cong: $o).
% 2.69/0.74 thf(func_def_81, type, setadjoin__Cong: $o).
% 2.69/0.74 thf(func_def_82, type, powerset__Cong: $o).
% 2.69/0.74 thf(func_def_83, type, setunion__Cong: $o).
% 2.69/0.74 thf(func_def_84, type, omega__Cong: $o).
% 2.69/0.74 thf(func_def_85, type, exuEu: $o).
% 2.69/0.74 thf(func_def_86, type, descr__Cong: $o).
% 2.69/0.74 thf(func_def_87, type, dsetconstr__Cong: $o).
% 2.69/0.74 thf(func_def_88, type, subset: ($i > $i > $o)).
% 2.69/0.74 thf(func_def_89, type, disjoint: ($i > $i > $o)).
% 2.69/0.74 thf(func_def_90, type, setsmeet: ($i > $i > $o)).
% 2.69/0.74 thf(func_def_91, type, subsetI1: $o).
% 2.69/0.74 thf(func_def_92, type, eqimpsubset2: $o).
% 2.69/0.74 thf(func_def_93, type, eqimpsubset1: $o).
% 2.69/0.74 thf(func_def_94, type, subsetI2: $o).
% 2.69/0.74 thf(func_def_95, type, emptysetsubset: $o).
% 2.69/0.74 thf(func_def_96, type, subsetE: $o).
% 2.69/0.74 thf(func_def_97, type, subsetE2: $o).
% 2.69/0.74 thf(func_def_98, type, notsubsetI: $o).
% 2.69/0.74 thf(func_def_99, type, notequalI1: $o).
% 2.69/0.74 thf(func_def_100, type, notequalI2: $o).
% 2.69/0.74 thf(func_def_101, type, subsetRefl: $o).
% 2.69/0.74 thf(func_def_102, type, subsetTrans: $o).
% 2.69/0.74 thf(func_def_103, type, setadjoinSub: $o).
% 2.69/0.74 thf(func_def_104, type, setadjoinSub2: $o).
% 2.69/0.74 thf(func_def_105, type, subset2powerset: $o).
% 2.69/0.74 thf(func_def_106, type, setextsub: $o).
% 2.69/0.74 thf(func_def_107, type, subsetemptysetimpeq: $o).
% 2.69/0.74 thf(func_def_108, type, powersetI1: $o).
% 2.69/0.74 thf(func_def_109, type, powersetE1: $o).
% 2.69/0.74 thf(func_def_110, type, inPowerset: $o).
% 2.69/0.74 thf(func_def_111, type, powersetsubset: $o).
% 2.69/0.74 thf(func_def_112, type, sepInPowerset: $o).
% 2.69/0.74 thf(func_def_113, type, sepSubset: $o).
% 2.69/0.74 thf(func_def_114, type, binunion: ($i > $i > $i)).
% 2.69/0.74 thf(func_def_115, type, binunionIL: $o).
% 2.69/0.74 thf(func_def_116, type, upairset2IR: $o).
% 2.69/0.74 thf(func_def_117, type, binunionIR: $o).
% 2.69/0.74 thf(func_def_118, type, binunionEcases: $o).
% 2.69/0.74 thf(func_def_119, type, binunionE: $o).
% 2.69/0.74 thf(func_def_120, type, binunionLsub: $o).
% 2.69/0.74 thf(func_def_121, type, binunionRsub: $o).
% 2.69/0.74 thf(func_def_122, type, binintersect: ($i > $i > $i)).
% 2.69/0.74 thf(func_def_123, type, binintersectI: $o).
% 2.69/0.74 thf(func_def_124, type, binintersectSubset5: $o).
% 2.69/0.74 thf(func_def_125, type, binintersectEL: $o).
% 2.69/0.74 thf(func_def_126, type, binintersectLsub: $o).
% 2.69/0.74 thf(func_def_127, type, binintersectSubset2: $o).
% 2.69/0.74 thf(func_def_128, type, binintersectSubset3: $o).
% 2.69/0.74 thf(func_def_129, type, binintersectER: $o).
% 2.69/0.74 thf(func_def_130, type, disjointsetsI1: $o).
% 2.69/0.74 thf(func_def_131, type, binintersectRsub: $o).
% 2.69/0.74 thf(func_def_132, type, binintersectSubset4: $o).
% 2.69/0.74 thf(func_def_133, type, binintersectSubset1: $o).
% 2.69/0.74 thf(func_def_134, type, bs114d: $o).
% 2.69/0.74 thf(func_def_135, type, regular: ($i > $o)).
% 2.69/0.74 thf(func_def_136, type, setminus: ($i > $i > $i)).
% 2.69/0.74 thf(func_def_137, type, setminusI: $o).
% 2.69/0.74 thf(func_def_138, type, setminusEL: $o).
% 2.69/0.74 thf(func_def_139, type, setminusER: $o).
% 2.69/0.74 thf(func_def_140, type, setminusSubset2: $o).
% 2.69/0.74 thf(func_def_141, type, setminusERneg: $o).
% 2.69/0.74 thf(func_def_142, type, setminusELneg: $o).
% 2.69/0.74 thf(func_def_143, type, setminusILneg: $o).
% 2.69/0.74 thf(func_def_144, type, setminusIRneg: $o).
% 2.69/0.74 thf(func_def_145, type, setminusLsub: $o).
% 2.69/0.74 thf(func_def_146, type, setminusSubset1: $o).
% 2.69/0.74 thf(func_def_147, type, symdiff: ($i > $i > $i)).
% 2.69/0.74 thf(func_def_148, type, symdiffE: $o).
% 2.69/0.74 thf(func_def_149, type, symdiffI1: $o).
% 2.69/0.74 thf(func_def_150, type, symdiffI2: $o).
% 2.69/0.74 thf(func_def_151, type, symdiffIneg1: $o).
% 2.69/0.74 thf(func_def_152, type, symdiffIneg2: $o).
% 2.69/0.74 thf(func_def_153, type, iskpair: ($i > $o)).
% 2.69/0.74 thf(func_def_154, type, secondinupair: $o).
% 2.69/0.74 thf(func_def_155, type, setukpairIL: $o).
% 2.69/0.74 thf(func_def_156, type, setukpairIR: $o).
% 2.69/0.74 thf(func_def_157, type, kpairiskpair: $o).
% 2.69/0.74 thf(func_def_158, type, kpair: ($i > $i > $i)).
% 2.69/0.74 thf(func_def_159, type, kpairp: $o).
% 2.69/0.74 thf(func_def_160, type, cartprod: ($i > $i > $i)).
% 2.69/0.74 thf(func_def_161, type, singletonsubset: $o).
% 2.69/0.74 thf(func_def_162, type, singletoninpowerset: $o).
% 2.69/0.74 thf(func_def_163, type, singletoninpowunion: $o).
% 2.69/0.74 thf(func_def_164, type, upairset2E: $o).
% 2.69/0.74 thf(func_def_165, type, upairsubunion: $o).
% 2.69/0.74 thf(func_def_166, type, upairinpowunion: $o).
% 2.69/0.74 thf(func_def_167, type, ubforcartprodlem1: $o).
% 2.69/0.74 thf(func_def_168, type, ubforcartprodlem2: $o).
% 2.69/0.74 thf(func_def_169, type, ubforcartprodlem3: $o).
% 2.69/0.74 thf(func_def_170, type, cartprodpairin: $o).
% 2.69/0.74 thf(func_def_171, type, cartprodmempair1: $o).
% 2.69/0.74 thf(func_def_172, type, cartprodmempair: $o).
% 2.69/0.74 thf(func_def_173, type, setunionE2: $o).
% 2.69/0.74 thf(func_def_174, type, setunionsingleton1: $o).
% 2.69/0.74 thf(func_def_175, type, setunionsingleton2: $o).
% 2.69/0.75 thf(func_def_176, type, setunionsingleton: $o).
% 2.69/0.75 thf(func_def_177, type, singleton: ($i > $o)).
% 2.69/0.75 thf(func_def_178, type, singletonprop: $o).
% 2.69/0.75 thf(func_def_179, type, ex1: ($i > ($i > $o) > $o)).
% 2.69/0.75 thf(func_def_180, type, ex1E1: $o).
% 2.69/0.75 thf(func_def_181, type, ex1I: $o).
% 2.69/0.75 thf(func_def_182, type, ex1I2: $o).
% 2.69/0.75 thf(func_def_183, type, singletonsuniq: $o).
% 2.69/0.75 thf(func_def_184, type, atmost1p: ($i > $o)).
% 2.69/0.75 thf(func_def_185, type, atleast2p: ($i > $o)).
% 2.69/0.75 thf(func_def_186, type, atmost2p: ($i > $o)).
% 2.69/0.75 thf(func_def_187, type, upairsetp: ($i > $o)).
% 2.69/0.75 thf(func_def_188, type, setukpairinjL1: $o).
% 2.69/0.75 thf(func_def_189, type, kfstsingleton: $o).
% 2.69/0.75 thf(func_def_190, type, theprop: $o).
% 2.69/0.75 thf(func_def_191, type, kfst: ($i > $i)).
% 2.69/0.75 thf(func_def_192, type, kfstpairEq: $o).
% 2.69/0.75 thf(func_def_193, type, cartprodfstin: $o).
% 2.69/0.75 thf(func_def_194, type, setukpairinjL2: $o).
% 2.69/0.75 thf(func_def_195, type, setukpairinjL: $o).
% 2.69/0.75 thf(func_def_196, type, setukpairinjR11: $o).
% 2.69/0.75 thf(func_def_197, type, setukpairinjR12: $o).
% 2.69/0.75 thf(func_def_198, type, setukpairinjR1: $o).
% 2.69/0.75 thf(func_def_199, type, upairequniteq: $o).
% 2.69/0.75 thf(func_def_200, type, setukpairinjR2: $o).
% 2.69/0.75 thf(func_def_201, type, setukpairinjR: $o).
% 2.69/0.75 thf(func_def_202, type, ksndsingleton: $o).
% 2.69/0.75 thf(func_def_203, type, ksnd: ($i > $i)).
% 2.69/0.75 thf(func_def_204, type, ksndpairEq: $o).
% 2.69/0.75 thf(func_def_205, type, kpairsurjEq: $o).
% 2.69/0.75 thf(func_def_206, type, cartprodsndin: $o).
% 2.69/0.75 thf(func_def_207, type, cartprodpairmemEL: $o).
% 2.69/0.75 thf(func_def_208, type, cartprodpairmemER: $o).
% 2.69/0.75 thf(func_def_209, type, cartprodmempaircEq: $o).
% 2.69/0.75 thf(func_def_210, type, cartprodfstpairEq: $o).
% 2.69/0.75 thf(func_def_211, type, cartprodsndpairEq: $o).
% 2.69/0.75 thf(func_def_212, type, cartprodpairsurjEq: $o).
% 2.69/0.75 thf(func_def_213, type, breln: ($i > $i > $i > $o)).
% 2.69/0.75 thf(func_def_214, type, dpsetconstr: ($i > $i > ($i > $i > $o) > $i)).
% 2.69/0.75 thf(func_def_215, type, dpsetconstrI: $o).
% 2.69/0.75 thf(func_def_216, type, dpsetconstrSub: $o).
% 2.69/0.75 thf(func_def_217, type, setOfPairsIsBReln: $o).
% 2.69/0.75 thf(func_def_218, type, dpsetconstrERa: $o).
% 2.69/0.75 thf(func_def_219, type, dpsetconstrEL1: $o).
% 2.69/0.75 thf(func_def_220, type, dpsetconstrEL2: $o).
% 2.69/0.75 thf(func_def_221, type, dpsetconstrER: $o).
% 2.69/0.75 thf(func_def_222, type, func: ($i > $i > $i > $o)).
% 2.69/0.75 thf(func_def_223, type, funcSet: ($i > $i > $i)).
% 2.69/0.75 thf(func_def_224, type, funcImageSingleton: $o).
% 2.69/0.75 thf(func_def_225, type, apProp: $o).
% 2.69/0.75 thf(func_def_226, type, ap: ($i > $i > $i > $i > $i)).
% 2.69/0.75 thf(func_def_227, type, app: $o).
% 2.69/0.75 thf(func_def_228, type, infuncsetfunc: $o).
% 2.69/0.75 thf(func_def_229, type, ap2p: $o).
% 2.69/0.75 thf(func_def_230, type, funcinfuncset: $o).
% 2.69/0.75 thf(func_def_231, type, lamProp: $o).
% 2.69/0.75 thf(func_def_232, type, lam: ($i > $i > ($i > $i) > $i)).
% 2.69/0.75 thf(func_def_233, type, lamp: $o).
% 2.69/0.75 thf(func_def_234, type, lam2p: $o).
% 2.69/0.75 thf(func_def_235, type, brelnall1: $o).
% 2.69/0.75 thf(func_def_236, type, brelnall2: $o).
% 2.69/0.75 thf(func_def_237, type, ex1E2: $o).
% 2.69/0.75 thf(func_def_238, type, funcGraphProp1: $o).
% 2.69/0.75 thf(func_def_239, type, funcGraphProp3: $o).
% 2.69/0.75 thf(func_def_240, type, funcGraphProp2: $o).
% 2.69/0.75 thf(func_def_241, type, funcextLem: $o).
% 2.69/0.75 thf(func_def_242, type, funcGraphProp4: $o).
% 2.69/0.75 thf(func_def_243, type, subbreln: $o).
% 2.69/0.75 thf(func_def_244, type, eqbreln: $o).
% 2.69/0.75 thf(func_def_245, type, funcext: $o).
% 2.69/0.75 thf(func_def_246, type, funcext2: $o).
% 2.69/0.75 thf(func_def_247, type, ap2apEq1: $o).
% 2.69/0.75 thf(func_def_248, type, ap2apEq2: $o).
% 2.69/0.75 thf(func_def_249, type, beta1: $o).
% 2.69/0.75 thf(func_def_250, type, eta1: $o).
% 2.69/0.75 thf(func_def_251, type, lam2lamEq: $o).
% 2.69/0.75 thf(func_def_254, type, db0: !>[X0: $tType]:(X0)).
% 2.69/0.75 thf(func_def_255, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 2.69/0.75 thf(func_def_256, type, db2: !>[X0: $tType]:(X0)).
% 2.69/0.75 thf(func_def_257, type, db1: !>[X0: $tType]:(X0)).
% 2.69/0.75 thf(func_def_258, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 2.69/0.75 thf(func_def_259, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 2.69/0.75 thf(func_def_260, type, vAND: ($o > $o > $o)).
% 2.69/0.75 thf(func_def_261, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 2.69/0.75 thf(func_def_262, type, vIMP: ($o > $o > $o)).
% 2.69/0.75 thf(func_def_263, type, vNOT: ($o > $o)).
% 2.69/0.75 thf(func_def_264, type, sP0: ($i > $o > $i > $i > $o)).
% 2.69/0.75 thf(func_def_265, type, sP1: $o).
% 2.69/0.75 thf(func_def_266, type, sP2: ($i > $i > $i > $i > $o)).
% 2.69/0.75 thf(func_def_267, type, sP3: $o).
% 2.69/0.75 thf(func_def_268, type, sP4: $o).
% 2.69/0.75 thf(func_def_269, type, sP5: $o).
% 2.69/0.75 thf(func_def_270, type, sP6: ($i > $i > $o)).
% 2.69/0.75 thf(func_def_271, type, sP7: ($i > $o)).
% 2.69/0.75 thf(func_def_272, type, sP8: ($i > $i > $o)).
% 2.69/0.75 thf(func_def_273, type, sP9: ($i > $i > $o)).
% 2.69/0.75 thf(func_def_274, type, sP10: $o).
% 2.69/0.75 thf(func_def_280, type, sK16: ($i > $i > $o)).
% 2.69/0.75 thf(func_def_286, type, sK22: ($i > $o)).
% 2.69/0.75 thf(func_def_288, type, sK24: $o).
% 2.69/0.75 thf(func_def_307, type, sK43: $o).
% 2.69/0.75 thf(func_def_309, type, sK45: ($i > $i > $o)).
% 2.69/0.75 thf(func_def_310, type, sK46: ($i > $i)).
% 2.69/0.75 thf(func_def_311, type, sK47: ($i > $i)).
% 2.69/0.75 thf(func_def_312, type, sK48: (($i > $i > $o) > $i > $i)).
% 2.69/0.75 thf(func_def_313, type, sK49: (($i > $i > $o) > $i > $i)).
% 2.69/0.75 thf(func_def_314, type, sK50: ($i > ($i > $i > $o) > $i > $i)).
% 2.69/0.75 thf(func_def_315, type, sK51: $o).
% 2.69/0.75 thf(func_def_326, type, sK62: ($i > $o)).
% 2.69/0.75 thf(func_def_327, type, sK63: (($i > $o) > $i)).
% 2.69/0.75 thf(func_def_333, type, sK69: ($i > $i)).
% 2.69/0.75 thf(func_def_334, type, sK70: ($i > $o)).
% 2.69/0.75 thf(func_def_337, type, sK73: ($i > $o)).
% 2.69/0.75 thf(func_def_341, type, sK77: ($i > $o)).
% 2.69/0.75 thf(func_def_354, type, sK90: ($i > $i > $o)).
% 2.69/0.75 thf(func_def_375, type, sK111: ($i > $i > $i)).
% 2.69/0.75 thf(func_def_376, type, sK112: ($i > $i > $i)).
% 2.69/0.75 thf(func_def_379, type, sK115: ($i > $i)).
% 2.69/0.75 thf(func_def_397, type, sK133: ($i > $o)).
% 2.69/0.75 thf(func_def_399, type, sK135: (($i > $o) > $i > $i > $i > $i)).
% 2.69/0.75 thf(func_def_400, type, sK136: (($i > $o) > $i > $i > $i > $i)).
% 2.69/0.75 thf(func_def_412, type, sK148: ($i > $i)).
% 2.69/0.75 thf(func_def_415, type, sK151: ($i > $i)).
% 2.69/0.75 thf(func_def_418, type, sK154: ($i > $i > $i)).
% 2.69/0.75 thf(func_def_420, type, sK156: ($i > $i > $o)).
% 2.69/0.75 thf(func_def_425, type, sK161: ($i > $i > $i)).
% 2.69/0.75 thf(func_def_431, type, sK167: ($i > $o)).
% 2.69/0.75 thf(func_def_436, type, sK172: ($i > $o)).
% 2.69/0.75 thf(func_def_439, type, sK175: ($i > ($i > $o) > $i)).
% 2.69/0.75 thf(func_def_445, type, sK181: ($i > $i > $i)).
% 2.69/0.75 thf(func_def_449, type, sK185: (($i > $i) > $i > $i > $i)).
% 2.69/0.75 thf(func_def_452, type, sK188: ($i > $i)).
% 2.69/0.75 thf(func_def_469, type, sK205: ($i > $o)).
% 2.69/0.75 thf(func_def_471, type, sK207: ($i > $i > $i)).
% 2.69/0.75 thf(func_def_474, type, sK210: (($i > $i) > $i > $i > $i)).
% 2.69/0.75 thf(func_def_477, type, sK213: ($i > $i)).
% 2.69/0.75 thf(func_def_495, type, sK231: (($i > $o) > $i > $i > $i)).
% 2.69/0.75 thf(func_def_498, type, sK234: ($i > $o)).
% 2.69/0.75 thf(func_def_500, type, sK236: ($i > $i)).
% 2.69/0.75 thf(func_def_506, type, sK242: ($i > $i)).
% 2.69/0.75 thf(func_def_507, type, sK243: ($i > ($i > $o) > $i)).
% 2.69/0.75 thf(func_def_508, type, sK244: ($i > $o)).
% 2.69/0.75 thf(func_def_521, type, sK257: (($i > $o) > $i > $i)).
% 2.69/0.75 thf(func_def_523, type, sK259: ($i > $o)).
% 2.69/0.75 thf(func_def_525, type, sK261: (($i > $o) > $i)).
% 2.69/0.75 thf(func_def_526, type, sK262: ($i > $o)).
% 2.69/0.75 thf(func_def_527, type, sK263: ($i > $i)).
% 2.69/0.75 thf(func_def_532, type, sK268: (($i > $o) > ($i > $o) > $i)).
% 2.69/0.75 thf(func_def_533, type, sK269: (($i > $o) > ($i > $o) > $i)).
% 2.69/0.75 thf(func_def_534, type, sK270: ($i > $o)).
% 2.69/0.75 thf(func_def_535, type, sK271: ($i > $o)).
% 2.69/0.75 thf(func_def_541, type, sK277: (($i > $o) > $i > $i > $i > $i)).
% 2.69/0.75 thf(func_def_542, type, sK278: (($i > $o) > $i > $i > $i > $i)).
% 2.69/0.75 thf(func_def_546, type, sK282: ($i > $o)).
% 2.69/0.75 thf(func_def_550, type, sK286: $o).
% 2.69/0.75 thf(func_def_558, type, sK294: ($i > $o)).
% 2.69/0.75 thf(func_def_560, type, sK296: (($i > $o) > $i)).
% 2.69/0.75 thf(func_def_561, type, sK297: (($i > $o) > $i)).
% 2.69/0.75 thf(func_def_573, type, sK309: ($i > $o)).
% 2.69/0.75 thf(func_def_587, type, sK323: ($i > $o)).
% 2.69/0.75 thf(func_def_590, type, sK326: ($i > ($i > $o) > $i)).
% 2.69/0.75 thf(func_def_591, type, sK327: ($i > ($i > $o) > $i)).
% 2.69/0.75 thf(func_def_592, type, sK328: ($i > $o)).
% 2.69/0.75 thf(func_def_597, type, sK333: ($i > $i > $i)).
% 2.69/0.75 thf(func_def_601, type, sK337: ($i > $i > $i)).
% 2.69/0.75 thf(func_def_619, type, sK355: ($i > ($i > $i) > $i > $i)).
% 2.69/0.75 thf(func_def_621, type, sK357: ($i > $i)).
% 2.69/0.75 thf(func_def_627, type, sK363: ($i > $i)).
% 2.69/0.75 thf(func_def_628, type, sK364: (($i > $i) > $i > $i > $i)).
% 2.69/0.75 thf(func_def_629, type, sK365: ($i > $o)).
% 2.69/0.75 thf(func_def_644, type, sK380: ($i > $o)).
% 2.69/0.75 thf(func_def_652, type, sK388: ($i > $o)).
% 2.69/0.75 thf(func_def_655, type, sK391: ($i > $i > $o)).
% 2.69/0.75 thf(func_def_682, type, sK418: (($i > $o) > $i > $i)).
% 2.69/0.75 thf(func_def_684, type, sK420: ($i > $o)).
% 2.69/0.75 thf(func_def_703, type, sK439: ($i > $i > $o)).
% 2.69/0.75 thf(func_def_711, type, sK447: ($i > $i > $o)).
% 2.69/0.75 thf(func_def_720, type, sK456: ($i > $i > $i > $i > $i)).
% 2.69/0.75 thf(func_def_721, type, sK457: ($i > $i > $i > $i > $i)).
% 2.69/0.75 thf(func_def_722, type, sK458: ($i > $i > $i > $i > $i)).
% 2.69/0.75 thf(func_def_723, type, sK459: ($i > $i > $i > $i > $i)).
% 2.69/0.75 thf(func_def_725, type, sK461: ($i > $i)).
% 2.69/0.75 thf(func_def_730, type, sK466: ($i > $i > $i > $i > $i)).
% 2.69/0.75 thf(func_def_733, type, sK469: ($i > $o)).
% 2.69/0.75 thf(func_def_735, type, sK471: ($i > ($i > $o) > $i)).
% 2.69/0.75 thf(func_def_736, type, sK472: ($i > $o)).
% 2.69/0.75 thf(func_def_739, type, sK475: ($i > ($i > $o) > $i)).
% 2.69/0.75 thf(func_def_740, type, sK476: ($i > ($i > $o) > $i)).
% 2.69/0.75 thf(func_def_745, type, sK481: $o).
% 2.69/0.75 thf(func_def_751, type, sK487: ($i > $i > $i > $i > $i)).
% 2.69/0.75 thf(func_def_752, type, sK488: ($i > $o)).
% 2.69/0.75 thf(func_def_757, type, sK493: ($i > ($i > $o) > $i)).
% 2.69/0.75 thf(func_def_758, type, sK494: ($i > $o)).
% 2.69/0.75 thf(func_def_783, type, sK519: ($i > $o)).
% 2.69/0.75 thf(func_def_785, type, sK521: (($i > $o) > $i > $i)).
% 2.69/0.75 thf(func_def_786, type, sK522: (($i > $o) > $i > $i)).
% 2.69/0.75 thf(func_def_789, type, sK525: ($i > $i > $i)).
% 2.69/0.75 thf(func_def_795, type, sK531: ($i > $o)).
% 2.69/0.75 thf(func_def_796, type, sK532: ($i > $o)).
% 2.69/0.75 thf(func_def_797, type, sK533: (($i > $o) > ($i > $o) > $i)).
% 2.69/0.75 thf(func_def_798, type, sK534: (($i > $o) > ($i > $o) > $i)).
% 2.69/0.75 thf(func_def_805, type, sK541: ($i > $i)).
% 2.69/0.75 thf(func_def_807, type, sK543: ($i > ($i > $i) > $i > $i)).
% 2.69/0.75 thf(func_def_813, type, sK549: $o).
% 2.69/0.75 thf(func_def_817, type, sK553: ($i > $i > $o)).
% 2.69/0.75 thf(func_def_821, type, sK557: ($i > $i > $i)).
% 2.69/0.75 thf(func_def_822, type, sK558: ($i > $i > $i)).
% 2.69/0.75 thf(func_def_823, type, sK559: ($i > $i > $i)).
% 2.69/0.75 thf(func_def_824, type, sK560: ($i > $i > $i)).
% 2.69/0.75 thf(func_def_825, type, sK561: ($i > $i > $i)).
% 2.69/0.75 thf(func_def_826, type, sK562: ($i > $i > $i > $i)).
% 2.69/0.75 thf(func_def_827, type, sK563: ($i > $i)).
% 2.69/0.75 thf(func_def_828, type, sK564: ($i > $i)).
% 2.69/0.75 thf(func_def_829, type, sK565: ($i > $i)).
% 2.69/0.75 thf(func_def_830, type, sK566: ($i > $i)).
% 2.69/0.75 thf(func_def_831, type, sK567: ($i > $i > $i)).
% 2.69/0.75 thf(func_def_832, type, sK568: ($i > $i > $i > $i)).
% 2.69/0.75 thf(func_def_833, type, sK569: ($i > $i > $i > $i)).
% 2.69/0.75 thf(func_def_834, type, sK570: ($i > $i > $i)).
% 2.69/0.75 thf(func_def_835, type, sK571: ($i > $i > $i)).
% 2.69/0.75 thf(func_def_836, type, sK572: ($i > $i)).
% 2.69/0.75 thf(func_def_838, type, sK574: ($i > $i)).
% 2.69/0.75 thf(func_def_839, type, sK575: ($i > $i)).
% 2.69/0.75 thf(func_def_841, type, sK577: ($i > $o)).
% 2.69/0.75 thf(func_def_852, type, sK588: $o).
% 2.69/0.75 thf(func_def_859, type, sK595: ($i > $i)).
% 2.69/0.75 thf(func_def_866, type, sK602: ($i > $i > $i > $i)).
% 2.69/0.75 thf(func_def_867, type, sK603: ($i > $i > $i > $i)).
% 2.69/0.75 thf(func_def_876, type, sK612: $o).
% 2.69/0.75 thf(func_def_877, type, sK613: ($o > $i > $i > $i)).
% 2.69/0.75 thf(func_def_878, type, sK614: (($i > $o) > $i)).
% 2.69/0.75 thf(func_def_879, type, sK615: ($i > $o)).
% 2.69/0.75 thf(func_def_880, type, sK616: ($i > $i)).
% 2.69/0.75 thf(func_def_894, type, sK630: ($i > $i > $i > $i > $i)).
% 2.69/0.75 thf(func_def_895, type, sK631: ($i > ($i > $o) > $i)).
% 2.69/0.75 thf(func_def_896, type, sK632: ($i > $o)).
% 2.69/0.75 thf(func_def_905, type, sK641: (($i > $o) > ($i > $o) > $i > $i > $i)).
% 2.69/0.75 thf(func_def_906, type, sK642: (($i > $o) > ($i > $o) > $i > $i > $i)).
% 2.69/0.75 thf(func_def_909, type, sK645: ($i > $o)).
% 2.69/0.75 thf(func_def_910, type, sK646: ($i > $o)).
% 2.69/0.75 thf(func_def_916, type, sK652: ($i > $i > $i)).
% 2.69/0.75 thf(func_def_923, type, sK659: ($i > $i > $i > $i > $i)).
% 2.69/0.75 thf(func_def_924, type, sK660: ($i > $i > $i > $i > $i)).
% 2.69/0.75 thf(func_def_927, type, sK663: ($i > $o)).
% 2.69/0.75 thf(f218,axiom,(
% 2.69/0.75 (! [X2 : ($i > $i),X1 : $i,X0 : $i] : (! [X3 : $i] : ((in @ X3 @ X0) => (in @ (X2 @ X3) @ X1)) => ! [X3 : $i] : ((in @ X3 @ X0) => (((X2 @ X3)) = ((ap @ X0 @ X1 @ (lam @ X0 @ X1 @ (^[X4 : $i] : ((X2 @ X4)))) @ X3))))) = beta1)),
% 2.69/0.75 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',beta1)).
% 2.69/0.75 thf(f221,conjecture,(
% 2.69/0.75 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => ! [X0 : $i,X1 : $i,X2 : ($i > $i)] : (! [X3 : $i] : ((in @ X3 @ X0) => (in @ (X2 @ X3) @ X1)) => ! [X3 : $i] : ((in @ X3 @ X0) => (((ap @ X0 @ X1 @ (lam @ X0 @ X1 @ (^[X4 : $i] : ((X2 @ X4)))) @ X3)) = ((X2 @ X3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.69/0.75 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',beta2)).
% 2.69/0.75 thf(f222,negated_conjecture,(
% 2.69/0.75 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => ! [X0 : $i,X1 : $i,X2 : ($i > $i)] : (! [X3 : $i] : ((in @ X3 @ X0) => (in @ (X2 @ X3) @ X1)) => ! [X3 : $i] : ((in @ X3 @ X0) => (((ap @ X0 @ X1 @ (lam @ X0 @ X1 @ (^[X4 : $i] : ((X2 @ X4)))) @ X3)) = ((X2 @ X3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.69/0.75 inference(negated_conjecture,[status(cth)],[f221])).
% 2.69/0.75 thf(f469,plain,(
% 2.69/0.75 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => ! [X0 : $i,X1 : $i,X2 : ($i > $i)] : (! [X3 : $i] : ((in @ X3 @ X0) => (in @ (X2 @ X3) @ X1)) => ! [X4 : $i] : ((in @ X4 @ X0) => (((ap @ X0 @ X1 @ (lam @ X0 @ X1 @ (^[X5 : $i] : ((X2 @ X5)))) @ X4)) = ((X2 @ X4)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.69/0.75 inference(rectify,[],[f222])).
% 2.69/0.75 thf(f470,plain,(
% 2.69/0.75 ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ((emptyI = $true) => ((noeltsimpempty = $true) => ((setbeta = $true) => ((nonemptyE1 = $true) => ((nonemptyI = $true) => ((nonemptyI1 = $true) => ((setadjoinIL = $true) => ((emptyinunitempty = $true) => ((setadjoinIR = $true) => ((setadjoinE = $true) => ((setadjoinOr = $true) => ((setoftrueEq = $true) => ((powersetI = $true) => ((emptyinPowerset = $true) => ((emptyInPowerset = $true) => ((powersetE = $true) => ((setunionI = $true) => ((setunionE = $true) => ((subPowSU = $true) => ((exuE2 = $true) => ((nonemptyImpWitness = $true) => ((uniqinunit = $true) => ((notinsingleton = $true) => ((eqinunit = $true) => ((singletonsswitch = $true) => ((upairsetE = $true) => ((upairsetIL = $true) => ((upairsetIR = $true) => ((emptyE1 = $true) => ((vacuousDall = $true) => ((quantDeMorgan1 = $true) => ((quantDeMorgan2 = $true) => ((quantDeMorgan3 = $true) => ((quantDeMorgan4 = $true) => ((prop2setI = $true) => ((prop2set2propI = $true) => ((notdexE = $true) => ((notdallE = $true) => ((exuI1 = $true) => ((exuI3 = $true) => ((exuI2 = $true) => ((inCongP = $true) => ((in__Cong = $true) => ((exuE3u = $true) => ((exu__Cong = $true) => ((emptyset__Cong = $true) => ((setadjoin__Cong = $true) => ((powerset__Cong = $true) => ((setunion__Cong = $true) => ((omega__Cong = $true) => ((exuEu = $true) => ((descr__Cong = $true) => ((dsetconstr__Cong = $true) => ((subsetI1 = $true) => ((eqimpsubset2 = $true) => ((eqimpsubset1 = $true) => ((subsetI2 = $true) => ((emptysetsubset = $true) => ((subsetE = $true) => ((subsetE2 = $true) => ((notsubsetI = $true) => ((notequalI1 = $true) => ((notequalI2 = $true) => ((subsetRefl = $true) => ((subsetTrans = $true) => ((setadjoinSub = $true) => ((setadjoinSub2 = $true) => ((subset2powerset = $true) => ((setextsub = $true) => ((subsetemptysetimpeq = $true) => ((powersetI1 = $true) => ((powersetE1 = $true) => ((inPowerset = $true) => ((powersetsubset = $true) => ((sepInPowerset = $true) => ((sepSubset = $true) => ((binunionIL = $true) => ((upairset2IR = $true) => ((binunionIR = $true) => ((binunionEcases = $true) => ((binunionE = $true) => ((binunionLsub = $true) => ((binunionRsub = $true) => ((binintersectI = $true) => ((binintersectSubset5 = $true) => ((binintersectEL = $true) => ((binintersectLsub = $true) => ((binintersectSubset2 = $true) => ((binintersectSubset3 = $true) => ((binintersectER = $true) => ((disjointsetsI1 = $true) => ((binintersectRsub = $true) => ((binintersectSubset4 = $true) => ((binintersectSubset1 = $true) => ((bs114d = $true) => ((setminusI = $true) => ((setminusEL = $true) => ((setminusER = $true) => ((setminusSubset2 = $true) => ((setminusERneg = $true) => ((setminusELneg = $true) => ((setminusILneg = $true) => ((setminusIRneg = $true) => ((setminusLsub = $true) => ((setminusSubset1 = $true) => ((symdiffE = $true) => ((symdiffI1 = $true) => ((symdiffI2 = $true) => ((symdiffIneg1 = $true) => ((symdiffIneg2 = $true) => ((secondinupair = $true) => ((setukpairIL = $true) => ((setukpairIR = $true) => ((kpairiskpair = $true) => ((kpairp = $true) => ((singletonsubset = $true) => ((singletoninpowerset = $true) => ((singletoninpowunion = $true) => ((upairset2E = $true) => ((upairsubunion = $true) => ((upairinpowunion = $true) => ((ubforcartprodlem1 = $true) => ((ubforcartprodlem2 = $true) => ((ubforcartprodlem3 = $true) => ((cartprodpairin = $true) => ((cartprodmempair1 = $true) => ((cartprodmempair = $true) => ((setunionE2 = $true) => ((setunionsingleton1 = $true) => ((setunionsingleton2 = $true) => ((setunionsingleton = $true) => ((singletonprop = $true) => ((ex1E1 = $true) => ((ex1I = $true) => ((ex1I2 = $true) => ((singletonsuniq = $true) => ((setukpairinjL1 = $true) => ((kfstsingleton = $true) => ((theprop = $true) => ((kfstpairEq = $true) => ((cartprodfstin = $true) => ((setukpairinjL2 = $true) => ((setukpairinjL = $true) => ((setukpairinjR11 = $true) => ((setukpairinjR12 = $true) => ((setukpairinjR1 = $true) => ((upairequniteq = $true) => ((setukpairinjR2 = $true) => ((setukpairinjR = $true) => ((ksndsingleton = $true) => ((ksndpairEq = $true) => ((kpairsurjEq = $true) => ((cartprodsndin = $true) => ((cartprodpairmemEL = $true) => ((cartprodpairmemER = $true) => ((cartprodmempaircEq = $true) => ((cartprodfstpairEq = $true) => ((cartprodsndpairEq = $true) => ((cartprodpairsurjEq = $true) => ((dpsetconstrI = $true) => ((dpsetconstrSub = $true) => ((setOfPairsIsBReln = $true) => ((dpsetconstrERa = $true) => ((dpsetconstrEL1 = $true) => ((dpsetconstrEL2 = $true) => ((dpsetconstrER = $true) => ((funcImageSingleton = $true) => ((apProp = $true) => ((app = $true) => ((infuncsetfunc = $true) => ((ap2p = $true) => ((funcinfuncset = $true) => ((lamProp = $true) => ((lamp = $true) => ((lam2p = $true) => ((brelnall1 = $true) => ((brelnall2 = $true) => ((ex1E2 = $true) => ((funcGraphProp1 = $true) => ((funcGraphProp3 = $true) => ((funcGraphProp2 = $true) => ((funcextLem = $true) => ((funcGraphProp4 = $true) => ((subbreln = $true) => ((eqbreln = $true) => ((funcext = $true) => ((funcext2 = $true) => ((ap2apEq1 = $true) => ((ap2apEq2 = $true) => ((beta1 = $true) => ((eta1 = $true) => ((lam2lamEq = $true) => ! [X1 : $i,X0 : $i,X2 : ($i > $i)] : (! [X3 : $i] : ((((in @ X3 @ X0)) = $true) => (((in @ (X2 @ X3) @ X1)) = $true)) => ! [X4 : $i] : ((((in @ X4 @ X0)) = $true) => (((X2 @ X4)) = ((ap @ X0 @ X1 @ (lam @ X0 @ X1 @ (^[Y0 : $i]: (X2 @ Y0))) @ X4)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.69/0.75 inference(fool_elimination,[],[f469])).
% 2.69/0.75 thf(f514,plain,(
% 2.69/0.75 (! [X0 : ($i > $i),X1 : $i,X2 : $i] : (! [X3 : $i] : ((in @ X3 @ X2) => (in @ (X0 @ X3) @ X1)) => ! [X4 : $i] : ((in @ X4 @ X2) => (((X0 @ X4)) = ((ap @ X2 @ X1 @ (lam @ X2 @ X1 @ (^[X5 : $i] : ((X0 @ X5)))) @ X4))))) = beta1)),
% 2.69/0.75 inference(rectify,[],[f218])).
% 2.69/0.75 thf(f515,plain,(
% 2.69/0.75 ! [X1 : $i,X0 : ($i > $i),X2 : $i] : (! [X3 : $i] : ((((in @ X3 @ X2)) = $true) => ($true = ((in @ (X0 @ X3) @ X1)))) => ! [X4 : $i] : ((((in @ X4 @ X2)) = $true) => (((X0 @ X4)) = ((ap @ X2 @ X1 @ (lam @ X2 @ X1 @ (^[Y0 : $i]: (X0 @ Y0))) @ X4))))) <=> (beta1 = $true)),
% 2.69/0.75 inference(fool_elimination,[],[f514])).
% 2.69/0.75 thf(f728,plain,(
% 2.69/0.75 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X2 : ($i > $i),X1 : $i,X0 : $i] : (! [X3 : $i] : ((((in @ (X2 @ X3) @ X1)) = $true) | (((in @ X3 @ X0)) != $true)) & ? [X4 : $i] : ((((X2 @ X4)) != ((ap @ X0 @ X1 @ (lam @ X0 @ X1 @ (^[Y0 : $i]: (X2 @ Y0))) @ X4))) & (((in @ X4 @ X0)) = $true))) & (lam2lamEq = $true)) & (eta1 = $true)) & (beta1 = $true)) & (ap2apEq2 = $true)) & (ap2apEq1 = $true)) & (funcext2 = $true)) & (funcext = $true)) & (eqbreln = $true)) & (subbreln = $true)) & (funcGraphProp4 = $true)) & (funcextLem = $true)) & (funcGraphProp2 = $true)) & (funcGraphProp3 = $true)) & (funcGraphProp1 = $true)) & (ex1E2 = $true)) & (brelnall2 = $true)) & (brelnall1 = $true)) & (lam2p = $true)) & (lamp = $true)) & (lamProp = $true)) & (funcinfuncset = $true)) & (ap2p = $true)) & (infuncsetfunc = $true)) & (app = $true)) & (apProp = $true)) & (funcImageSingleton = $true)) & (dpsetconstrER = $true)) & (dpsetconstrEL2 = $true)) & (dpsetconstrEL1 = $true)) & (dpsetconstrERa = $true)) & (setOfPairsIsBReln = $true)) & (dpsetconstrSub = $true)) & (dpsetconstrI = $true)) & (cartprodpairsurjEq = $true)) & (cartprodsndpairEq = $true)) & (cartprodfstpairEq = $true)) & (cartprodmempaircEq = $true)) & (cartprodpairmemER = $true)) & (cartprodpairmemEL = $true)) & (cartprodsndin = $true)) & (kpairsurjEq = $true)) & (ksndpairEq = $true)) & (ksndsingleton = $true)) & (setukpairinjR = $true)) & (setukpairinjR2 = $true)) & (upairequniteq = $true)) & (setukpairinjR1 = $true)) & (setukpairinjR12 = $true)) & (setukpairinjR11 = $true)) & (setukpairinjL = $true)) & (setukpairinjL2 = $true)) & (cartprodfstin = $true)) & (kfstpairEq = $true)) & (theprop = $true)) & (kfstsingleton = $true)) & (setukpairinjL1 = $true)) & (singletonsuniq = $true)) & (ex1I2 = $true)) & (ex1I = $true)) & (ex1E1 = $true)) & (singletonprop = $true)) & (setunionsingleton = $true)) & (setunionsingleton2 = $true)) & (setunionsingleton1 = $true)) & (setunionE2 = $true)) & (cartprodmempair = $true)) & (cartprodmempair1 = $true)) & (cartprodpairin = $true)) & (ubforcartprodlem3 = $true)) & (ubforcartprodlem2 = $true)) & (ubforcartprodlem1 = $true)) & (upairinpowunion = $true)) & (upairsubunion = $true)) & (upairset2E = $true)) & (singletoninpowunion = $true)) & (singletoninpowerset = $true)) & (singletonsubset = $true)) & (kpairp = $true)) & (kpairiskpair = $true)) & (setukpairIR = $true)) & (setukpairIL = $true)) & (secondinupair = $true)) & (symdiffIneg2 = $true)) & (symdiffIneg1 = $true)) & (symdiffI2 = $true)) & (symdiffI1 = $true)) & (symdiffE = $true)) & (setminusSubset1 = $true)) & (setminusLsub = $true)) & (setminusIRneg = $true)) & (setminusILneg = $true)) & (setminusELneg = $true)) & (setminusERneg = $true)) & (setminusSubset2 = $true)) & (setminusER = $true)) & (setminusEL = $true)) & (setminusI = $true)) & (bs114d = $true)) & (binintersectSubset1 = $true)) & (binintersectSubset4 = $true)) & (binintersectRsub = $true)) & (disjointsetsI1 = $true)) & (binintersectER = $true)) & (binintersectSubset3 = $true)) & (binintersectSubset2 = $true)) & (binintersectLsub = $true)) & (binintersectEL = $true)) & (binintersectSubset5 = $true)) & (binintersectI = $true)) & (binunionRsub = $true)) & (binunionLsub = $true)) & (binunionE = $true)) & (binunionEcases = $true)) & (binunionIR = $true)) & (upairset2IR = $true)) & (binunionIL = $true)) & (sepSubset = $true)) & (sepInPowerset = $true)) & (powersetsubset = $true)) & (inPowerset = $true)) & (powersetE1 = $true)) & (powersetI1 = $true)) & (subsetemptysetimpeq = $true)) & (setextsub = $true)) & (subset2powerset = $true)) & (setadjoinSub2 = $true)) & (setadjoinSub = $true)) & (subsetTrans = $true)) & (subsetRefl = $true)) & (notequalI2 = $true)) & (notequalI1 = $true)) & (notsubsetI = $true)) & (subsetE2 = $true)) & (subsetE = $true)) & (emptysetsubset = $true)) & (subsetI2 = $true)) & (eqimpsubset1 = $true)) & (eqimpsubset2 = $true)) & (subsetI1 = $true)) & (dsetconstr__Cong = $true)) & (descr__Cong = $true)) & (exuEu = $true)) & (omega__Cong = $true)) & (setunion__Cong = $true)) & (powerset__Cong = $true)) & (setadjoin__Cong = $true)) & (emptyset__Cong = $true)) & (exu__Cong = $true)) & (exuE3u = $true)) & (in__Cong = $true)) & (inCongP = $true)) & (exuI2 = $true)) & (exuI3 = $true)) & (exuI1 = $true)) & (notdallE = $true)) & (notdexE = $true)) & (prop2set2propI = $true)) & (prop2setI = $true)) & (quantDeMorgan4 = $true)) & (quantDeMorgan3 = $true)) & (quantDeMorgan2 = $true)) & (quantDeMorgan1 = $true)) & (vacuousDall = $true)) & (emptyE1 = $true)) & (upairsetIR = $true)) & (upairsetIL = $true)) & (upairsetE = $true)) & (singletonsswitch = $true)) & (eqinunit = $true)) & (notinsingleton = $true)) & (uniqinunit = $true)) & (nonemptyImpWitness = $true)) & (exuE2 = $true)) & (subPowSU = $true)) & (setunionE = $true)) & (setunionI = $true)) & (powersetE = $true)) & (emptyInPowerset = $true)) & (emptyinPowerset = $true)) & (powersetI = $true)) & (setoftrueEq = $true)) & (setadjoinOr = $true)) & (setadjoinE = $true)) & (setadjoinIR = $true)) & (emptyinunitempty = $true)) & (setadjoinIL = $true)) & (nonemptyI1 = $true)) & (nonemptyI = $true)) & (nonemptyE1 = $true)) & (setbeta = $true)) & (noeltsimpempty = $true)) & (emptyI = $true)) & (setext = $true)) & (exuE3e = $true)) & (notinemptyset = $true)) & (emptysetimpfalse = $true)) & (emptysetE = $true)) & (prop2setE = $true)) & (exuE1 = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)) & (descrp = $true)) & (wellorderingAx = $true)) & (foundationAx = $true)) & (replAx = $true)) & (omegaIndAx = $true)) & (omegaSAx = $true)) & (omega0Ax = $true)) & (setunionAx = $true)) & (powersetAx = $true)) & (setadjoinAx = $true)) & (emptysetAx = $true)) & (setextAx = $true)),
% 2.69/0.75 inference(ennf_transformation,[],[f470])).
% 2.69/0.75 thf(f729,plain,(
% 2.69/0.75 (cartprodpairmemER = $true) & (omega0Ax = $true) & (eqbreln = $true) & (funcGraphProp1 = $true) & (binintersectER = $true) & (bs114d = $true) & (setukpairIL = $true) & (emptysetE = $true) & (kpairp = $true) & (notinemptyset = $true) & (eqinunit = $true) & (upairset2IR = $true) & (cartprodfstpairEq = $true) & (setoftrueEq = $true) & (ex1E1 = $true) & (setextsub = $true) & (foundationAx = $true) & (emptysetimpfalse = $true) & (funcext2 = $true) & (binintersectLsub = $true) & (setminusSubset2 = $true) & (upairsetIR = $true) & (setminusLsub = $true) & (kfstpairEq = $true) & (setminusSubset1 = $true) & (in__Cong = $true) & (funcGraphProp3 = $true) & (subsetE2 = $true) & (cartprodpairin = $true) & (binunionE = $true) & (nonemptyE1 = $true) & (ex1I2 = $true) & (binintersectSubset4 = $true) & (quantDeMorgan3 = $true) & (vacuousDall = $true) & (notdallE = $true) & (setadjoinIR = $true) & (cartprodsndin = $true) & (binintersectSubset3 = $true) & (dpsetconstrSub = $true) & (funcImageSingleton = $true) & (sepSubset = $true) & (subsetRefl = $true) & (cartprodmempaircEq = $true) & (upairsubunion = $true) & (symdiffI2 = $true) & (exuI3 = $true) & (setunionsingleton = $true) & (ap2p = $true) & (emptysetsubset = $true) & (cartprodpairsurjEq = $true) & (subbreln = $true) & (setukpairinjL1 = $true) & (setukpairinjR11 = $true) & (powersetAx = $true) & (funcextLem = $true) & (emptyE1 = $true) & (binunionEcases = $true) & (symdiffIneg2 = $true) & (setunionE = $true) & (eqimpsubset2 = $true) & (symdiffI1 = $true) & (setukpairinjL2 = $true) & (dsetconstrEL = $true) & (funcext = $true) & (singletoninpowunion = $true) & (dsetconstrI = $true) & (dpsetconstrER = $true) & (quantDeMorgan1 = $true) & (nonemptyI1 = $true) & (subsetemptysetimpeq = $true) & (setminusELneg = $true) & (lam2p = $true) & (notequalI1 = $true) & (upairinpowunion = $true) & (ex1E2 = $true) & (binunionIL = $true) & (powersetI = $true) & (setbeta = $true) & (setukpairIR = $true) & (kpairsurjEq = $true) & (beta1 = $true) & (noeltsimpempty = $true) & (ubforcartprodlem1 = $true) & (exuE3e = $true) & (notsubsetI = $true) & (powersetI1 = $true) & (setukpairinjR2 = $true) & (brelnall2 = $true) & (setukpairinjL = $true) & (binunionIR = $true) & (binintersectI = $true) & (theprop = $true) & (inPowerset = $true) & (lamProp = $true) & (lamp = $true) & (exuI1 = $true) & (singletonsubset = $true) & (eqimpsubset1 = $true) & (setminusEL = $true) & (upairsetE = $true) & (singletonprop = $true) & (sepInPowerset = $true) & (setOfPairsIsBReln = $true) & (apProp = $true) & (setextAx = $true) & (binunionLsub = $true) & (singletoninpowerset = $true) & (uniqinunit = $true) & (notdexE = $true) & (subsetTrans = $true) & (emptyI = $true) & (prop2set2propI = $true) & (setadjoinAx = $true) & (setadjoinE = $true) & (setukpairinjR = $true) & (dpsetconstrERa = $true) & (setunionsingleton1 = $true) & (setminusI = $true) & (ap2apEq2 = $true) & (dpsetconstrEL2 = $true) & (emptyinunitempty = $true) & (cartprodmempair1 = $true) & (setminusIRneg = $true) & (funcGraphProp2 = $true) & (descr__Cong = $true) & (binintersectRsub = $true) & (prop2setE = $true) & (ksndsingleton = $true) & (exuE3u = $true) & (notinsingleton = $true) & (dsetconstrER = $true) & (dpsetconstrEL1 = $true) & (setadjoinSub = $true) & (symdiffE = $true) & (subPowSU = $true) & (setunionsingleton2 = $true) & (prop2setI = $true) & (exuE1 = $true) & (upairset2E = $true) & (setunionE2 = $true) & (setunionI = $true) & (exu__Cong = $true) & (omega__Cong = $true) & (omegaIndAx = $true) & (secondinupair = $true) & (subsetI2 = $true) & (binintersectSubset5 = $true) & (cartprodmempair = $true) & (emptyInPowerset = $true) & (setminusILneg = $true) & (setext = $true) & (subsetE = $true) & (omegaSAx = $true) & (kfstsingleton = $true) & (binintersectSubset2 = $true) & (lam2lamEq = $true) & (ksndpairEq = $true) & (ap2apEq1 = $true) & (setunion__Cong = $true) & (emptyset__Cong = $true) & (disjointsetsI1 = $true) & (eta1 = $true) & (emptyinPowerset = $true) & (cartprodfstin = $true) & (setadjoinIL = $true) & (subsetI1 = $true) & (wellorderingAx = $true) & (nonemptyI = $true) & (setukpairinjR12 = $true) & (setadjoinOr = $true) & (funcinfuncset = $true) & (ubforcartprodlem3 = $true) & (funcGraphProp4 = $true) & (binintersectEL = $true) & (cartprodsndpairEq = $true) & (setukpairinjR1 = $true) & (powersetE1 = $true) & (quantDeMorgan2 = $true) & (exuEu = $true) & (upairsetIL = $true) & (setadjoin__Cong = $true) & (quantDeMorgan4 = $true) & (inCongP = $true) & ? [X2 : ($i > $i),X1 : $i,X0 : $i] : (! [X3 : $i] : ((((in @ (X2 @ X3) @ X1)) = $true) | (((in @ X3 @ X0)) != $true)) & ? [X4 : $i] : ((((X2 @ X4)) != ((ap @ X0 @ X1 @ (lam @ X0 @ X1 @ (^[Y0 : $i]: (X2 @ Y0))) @ X4))) & (((in @ X4 @ X0)) = $true))) & (singletonsswitch = $true) & (upairequniteq = $true) & (symdiffIneg1 = $true) & (ubforcartprodlem2 = $true) & (singletonsuniq = $true) & (exuE2 = $true) & (setunionAx = $true) & (powersetsubset = $true) & (infuncsetfunc = $true) & (notequalI2 = $true) & (brelnall1 = $true) & (descrp = $true) & (binunionRsub = $true) & (ex1I = $true) & (exuI2 = $true) & (nonemptyImpWitness = $true) & (replAx = $true) & (subset2powerset = $true) & (setadjoinSub2 = $true) & (app = $true) & (dsetconstr__Cong = $true) & (dpsetconstrI = $true) & (cartprodpairmemEL = $true) & (powerset__Cong = $true) & (powersetE = $true) & (setminusER = $true) & (emptysetAx = $true) & (setminusERneg = $true) & (kpairiskpair = $true) & (binintersectSubset1 = $true)),
% 2.69/0.75 inference(flattening,[],[f728])).
% 2.69/0.75 thf(f876,plain,(
% 2.69/0.75 ! [X1 : $i,X2 : $i,X0 : ($i > $i)] : (? [X3 : $i] : (($true != ((in @ (X0 @ X3) @ X1))) & (((in @ X3 @ X2)) = $true)) | ! [X4 : $i] : ((((in @ X4 @ X2)) != $true) | (((X0 @ X4)) = ((ap @ X2 @ X1 @ (lam @ X2 @ X1 @ (^[Y0 : $i]: (X0 @ Y0))) @ X4))))) <=> (beta1 = $true)),
% 2.69/0.75 inference(ennf_transformation,[],[f515])).
% 2.69/0.75 thf(f1123,plain,(
% 2.69/0.75 (! [X1 : $i,X2 : $i,X0 : ($i > $i)] : (? [X3 : $i] : (($true != ((in @ (X0 @ X3) @ X1))) & (((in @ X3 @ X2)) = $true)) | ! [X4 : $i] : ((((in @ X4 @ X2)) != $true) | (((X0 @ X4)) = ((ap @ X2 @ X1 @ (lam @ X2 @ X1 @ (^[Y0 : $i]: (X0 @ Y0))) @ X4))))) | (beta1 != $true)) & ((beta1 = $true) | ? [X1 : $i,X2 : $i,X0 : ($i > $i)] : (! [X3 : $i] : (($true = ((in @ (X0 @ X3) @ X1))) | (((in @ X3 @ X2)) != $true)) & ? [X4 : $i] : ((((in @ X4 @ X2)) = $true) & (((X0 @ X4)) != ((ap @ X2 @ X1 @ (lam @ X2 @ X1 @ (^[Y0 : $i]: (X0 @ Y0))) @ X4))))))),
% 2.69/0.75 inference(nnf_transformation,[],[f876])).
% 2.69/0.75 thf(f1124,plain,(
% 2.69/0.75 (! [X0 : $i,X1 : $i,X2 : ($i > $i)] : (? [X3 : $i] : ((((in @ (X2 @ X3) @ X0)) != $true) & (((in @ X3 @ X1)) = $true)) | ! [X4 : $i] : ((((in @ X4 @ X1)) != $true) | (((X2 @ X4)) = ((ap @ X1 @ X0 @ (lam @ X1 @ X0 @ (^[Y0 : $i]: (X2 @ Y0))) @ X4))))) | (beta1 != $true)) & ((beta1 = $true) | ? [X5 : $i,X6 : $i,X7 : ($i > $i)] : (! [X8 : $i] : ((((in @ (X7 @ X8) @ X5)) = $true) | (((in @ X8 @ X6)) != $true)) & ? [X9 : $i] : ((((in @ X9 @ X6)) = $true) & (((ap @ X6 @ X5 @ (lam @ X6 @ X5 @ (^[Y0 : $i]: (X7 @ Y0))) @ X9)) != ((X7 @ X9))))))),
% 2.69/0.75 inference(rectify,[],[f1123])).
% 2.69/0.75 thf(f1125,plain,(
% 2.69/0.75 (! [X0 : $i,X1 : $i,X2 : ($i > $i)] : ((($true != ((in @ (X2 @ (sK185 @ X2 @ X1 @ X0)) @ X0))) & ($true = ((in @ (sK185 @ X2 @ X1 @ X0) @ X1)))) | ! [X4 : $i] : ((((in @ X4 @ X1)) != $true) | (((X2 @ X4)) = ((ap @ X1 @ X0 @ (lam @ X1 @ X0 @ (^[Y0 : $i]: (X2 @ Y0))) @ X4))))) | (beta1 != $true)) & ((beta1 = $true) | (! [X8 : $i] : (($true = ((in @ (sK188 @ X8) @ sK186))) | (((in @ X8 @ sK187)) != $true)) & ((((in @ sK189 @ sK187)) = $true) & (((ap @ sK187 @ sK186 @ (lam @ sK187 @ sK186 @ (^[Y0 : $i]: (sK188 @ Y0))) @ sK189)) != ((sK188 @ sK189))))))),
% 2.69/0.75 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK186,sK187,sK188,sK189]),skolemize(X13,sK50 @ X11 @ X8 @ X7),skolemize(X5,sK186),skolemize(X6,sK187),skolemize(X7,sK188),skolemize(X9,sK189)],[f1124])).
% 2.69/0.75 thf(f1527,plain,(
% 2.69/0.75 (cartprodpairmemER = $true) & (omega0Ax = $true) & (eqbreln = $true) & (funcGraphProp1 = $true) & (binintersectER = $true) & (bs114d = $true) & (setukpairIL = $true) & (emptysetE = $true) & (kpairp = $true) & (notinemptyset = $true) & (eqinunit = $true) & (upairset2IR = $true) & (cartprodfstpairEq = $true) & (setoftrueEq = $true) & (ex1E1 = $true) & (setextsub = $true) & (foundationAx = $true) & (emptysetimpfalse = $true) & (funcext2 = $true) & (binintersectLsub = $true) & (setminusSubset2 = $true) & (upairsetIR = $true) & (setminusLsub = $true) & (kfstpairEq = $true) & (setminusSubset1 = $true) & (in__Cong = $true) & (funcGraphProp3 = $true) & (subsetE2 = $true) & (cartprodpairin = $true) & (binunionE = $true) & (nonemptyE1 = $true) & (ex1I2 = $true) & (binintersectSubset4 = $true) & (quantDeMorgan3 = $true) & (vacuousDall = $true) & (notdallE = $true) & (setadjoinIR = $true) & (cartprodsndin = $true) & (binintersectSubset3 = $true) & (dpsetconstrSub = $true) & (funcImageSingleton = $true) & (sepSubset = $true) & (subsetRefl = $true) & (cartprodmempaircEq = $true) & (upairsubunion = $true) & (symdiffI2 = $true) & (exuI3 = $true) & (setunionsingleton = $true) & (ap2p = $true) & (emptysetsubset = $true) & (cartprodpairsurjEq = $true) & (subbreln = $true) & (setukpairinjL1 = $true) & (setukpairinjR11 = $true) & (powersetAx = $true) & (funcextLem = $true) & (emptyE1 = $true) & (binunionEcases = $true) & (symdiffIneg2 = $true) & (setunionE = $true) & (eqimpsubset2 = $true) & (symdiffI1 = $true) & (setukpairinjL2 = $true) & (dsetconstrEL = $true) & (funcext = $true) & (singletoninpowunion = $true) & (dsetconstrI = $true) & (dpsetconstrER = $true) & (quantDeMorgan1 = $true) & (nonemptyI1 = $true) & (subsetemptysetimpeq = $true) & (setminusELneg = $true) & (lam2p = $true) & (notequalI1 = $true) & (upairinpowunion = $true) & (ex1E2 = $true) & (binunionIL = $true) & (powersetI = $true) & (setbeta = $true) & (setukpairIR = $true) & (kpairsurjEq = $true) & (beta1 = $true) & (noeltsimpempty = $true) & (ubforcartprodlem1 = $true) & (exuE3e = $true) & (notsubsetI = $true) & (powersetI1 = $true) & (setukpairinjR2 = $true) & (brelnall2 = $true) & (setukpairinjL = $true) & (binunionIR = $true) & (binintersectI = $true) & (theprop = $true) & (inPowerset = $true) & (lamProp = $true) & (lamp = $true) & (exuI1 = $true) & (singletonsubset = $true) & (eqimpsubset1 = $true) & (setminusEL = $true) & (upairsetE = $true) & (singletonprop = $true) & (sepInPowerset = $true) & (setOfPairsIsBReln = $true) & (apProp = $true) & (setextAx = $true) & (binunionLsub = $true) & (singletoninpowerset = $true) & (uniqinunit = $true) & (notdexE = $true) & (subsetTrans = $true) & (emptyI = $true) & (prop2set2propI = $true) & (setadjoinAx = $true) & (setadjoinE = $true) & (setukpairinjR = $true) & (dpsetconstrERa = $true) & (setunionsingleton1 = $true) & (setminusI = $true) & (ap2apEq2 = $true) & (dpsetconstrEL2 = $true) & (emptyinunitempty = $true) & (cartprodmempair1 = $true) & (setminusIRneg = $true) & (funcGraphProp2 = $true) & (descr__Cong = $true) & (binintersectRsub = $true) & (prop2setE = $true) & (ksndsingleton = $true) & (exuE3u = $true) & (notinsingleton = $true) & (dsetconstrER = $true) & (dpsetconstrEL1 = $true) & (setadjoinSub = $true) & (symdiffE = $true) & (subPowSU = $true) & (setunionsingleton2 = $true) & (prop2setI = $true) & (exuE1 = $true) & (upairset2E = $true) & (setunionE2 = $true) & (setunionI = $true) & (exu__Cong = $true) & (omega__Cong = $true) & (omegaIndAx = $true) & (secondinupair = $true) & (subsetI2 = $true) & (binintersectSubset5 = $true) & (cartprodmempair = $true) & (emptyInPowerset = $true) & (setminusILneg = $true) & (setext = $true) & (subsetE = $true) & (omegaSAx = $true) & (kfstsingleton = $true) & (binintersectSubset2 = $true) & (lam2lamEq = $true) & (ksndpairEq = $true) & (ap2apEq1 = $true) & (setunion__Cong = $true) & (emptyset__Cong = $true) & (disjointsetsI1 = $true) & (eta1 = $true) & (emptyinPowerset = $true) & (cartprodfstin = $true) & (setadjoinIL = $true) & (subsetI1 = $true) & (wellorderingAx = $true) & (nonemptyI = $true) & (setukpairinjR12 = $true) & (setadjoinOr = $true) & (funcinfuncset = $true) & (ubforcartprodlem3 = $true) & (funcGraphProp4 = $true) & (binintersectEL = $true) & (cartprodsndpairEq = $true) & (setukpairinjR1 = $true) & (powersetE1 = $true) & (quantDeMorgan2 = $true) & (exuEu = $true) & (upairsetIL = $true) & (setadjoin__Cong = $true) & (quantDeMorgan4 = $true) & (inCongP = $true) & ? [X0 : ($i > $i),X1 : $i,X2 : $i] : (! [X3 : $i] : (($true = ((in @ (X0 @ X3) @ X1))) | (((in @ X3 @ X2)) != $true)) & ? [X4 : $i] : ((((X0 @ X4)) != ((ap @ X2 @ X1 @ (lam @ X2 @ X1 @ (^[Y0 : $i]: (X0 @ Y0))) @ X4))) & (((in @ X4 @ X2)) = $true))) & (singletonsswitch = $true) & (upairequniteq = $true) & (symdiffIneg1 = $true) & (ubforcartprodlem2 = $true) & (singletonsuniq = $true) & (exuE2 = $true) & (setunionAx = $true) & (powersetsubset = $true) & (infuncsetfunc = $true) & (notequalI2 = $true) & (brelnall1 = $true) & (descrp = $true) & (binunionRsub = $true) & (ex1I = $true) & (exuI2 = $true) & (nonemptyImpWitness = $true) & (replAx = $true) & (subset2powerset = $true) & (setadjoinSub2 = $true) & (app = $true) & (dsetconstr__Cong = $true) & (dpsetconstrI = $true) & (cartprodpairmemEL = $true) & (powerset__Cong = $true) & (powersetE = $true) & (setminusER = $true) & (emptysetAx = $true) & (setminusERneg = $true) & (kpairiskpair = $true) & (binintersectSubset1 = $true)),
% 2.69/0.75 inference(rectify,[],[f729])).
% 2.69/0.75 thf(f1528,plain,(
% 2.69/0.75 (cartprodpairmemER = $true) & (omega0Ax = $true) & (eqbreln = $true) & (funcGraphProp1 = $true) & (binintersectER = $true) & (bs114d = $true) & (setukpairIL = $true) & (emptysetE = $true) & (kpairp = $true) & (notinemptyset = $true) & (eqinunit = $true) & (upairset2IR = $true) & (cartprodfstpairEq = $true) & (setoftrueEq = $true) & (ex1E1 = $true) & (setextsub = $true) & (foundationAx = $true) & (emptysetimpfalse = $true) & (funcext2 = $true) & (binintersectLsub = $true) & (setminusSubset2 = $true) & (upairsetIR = $true) & (setminusLsub = $true) & (kfstpairEq = $true) & (setminusSubset1 = $true) & (in__Cong = $true) & (funcGraphProp3 = $true) & (subsetE2 = $true) & (cartprodpairin = $true) & (binunionE = $true) & (nonemptyE1 = $true) & (ex1I2 = $true) & (binintersectSubset4 = $true) & (quantDeMorgan3 = $true) & (vacuousDall = $true) & (notdallE = $true) & (setadjoinIR = $true) & (cartprodsndin = $true) & (binintersectSubset3 = $true) & (dpsetconstrSub = $true) & (funcImageSingleton = $true) & (sepSubset = $true) & (subsetRefl = $true) & (cartprodmempaircEq = $true) & (upairsubunion = $true) & (symdiffI2 = $true) & (exuI3 = $true) & (setunionsingleton = $true) & (ap2p = $true) & (emptysetsubset = $true) & (cartprodpairsurjEq = $true) & (subbreln = $true) & (setukpairinjL1 = $true) & (setukpairinjR11 = $true) & (powersetAx = $true) & (funcextLem = $true) & (emptyE1 = $true) & (binunionEcases = $true) & (symdiffIneg2 = $true) & (setunionE = $true) & (eqimpsubset2 = $true) & (symdiffI1 = $true) & (setukpairinjL2 = $true) & (dsetconstrEL = $true) & (funcext = $true) & (singletoninpowunion = $true) & (dsetconstrI = $true) & (dpsetconstrER = $true) & (quantDeMorgan1 = $true) & (nonemptyI1 = $true) & (subsetemptysetimpeq = $true) & (setminusELneg = $true) & (lam2p = $true) & (notequalI1 = $true) & (upairinpowunion = $true) & (ex1E2 = $true) & (binunionIL = $true) & (powersetI = $true) & (setbeta = $true) & (setukpairIR = $true) & (kpairsurjEq = $true) & (beta1 = $true) & (noeltsimpempty = $true) & (ubforcartprodlem1 = $true) & (exuE3e = $true) & (notsubsetI = $true) & (powersetI1 = $true) & (setukpairinjR2 = $true) & (brelnall2 = $true) & (setukpairinjL = $true) & (binunionIR = $true) & (binintersectI = $true) & (theprop = $true) & (inPowerset = $true) & (lamProp = $true) & (lamp = $true) & (exuI1 = $true) & (singletonsubset = $true) & (eqimpsubset1 = $true) & (setminusEL = $true) & (upairsetE = $true) & (singletonprop = $true) & (sepInPowerset = $true) & (setOfPairsIsBReln = $true) & (apProp = $true) & (setextAx = $true) & (binunionLsub = $true) & (singletoninpowerset = $true) & (uniqinunit = $true) & (notdexE = $true) & (subsetTrans = $true) & (emptyI = $true) & (prop2set2propI = $true) & (setadjoinAx = $true) & (setadjoinE = $true) & (setukpairinjR = $true) & (dpsetconstrERa = $true) & (setunionsingleton1 = $true) & (setminusI = $true) & (ap2apEq2 = $true) & (dpsetconstrEL2 = $true) & (emptyinunitempty = $true) & (cartprodmempair1 = $true) & (setminusIRneg = $true) & (funcGraphProp2 = $true) & (descr__Cong = $true) & (binintersectRsub = $true) & (prop2setE = $true) & (ksndsingleton = $true) & (exuE3u = $true) & (notinsingleton = $true) & (dsetconstrER = $true) & (dpsetconstrEL1 = $true) & (setadjoinSub = $true) & (symdiffE = $true) & (subPowSU = $true) & (setunionsingleton2 = $true) & (prop2setI = $true) & (exuE1 = $true) & (upairset2E = $true) & (setunionE2 = $true) & (setunionI = $true) & (exu__Cong = $true) & (omega__Cong = $true) & (omegaIndAx = $true) & (secondinupair = $true) & (subsetI2 = $true) & (binintersectSubset5 = $true) & (cartprodmempair = $true) & (emptyInPowerset = $true) & (setminusILneg = $true) & (setext = $true) & (subsetE = $true) & (omegaSAx = $true) & (kfstsingleton = $true) & (binintersectSubset2 = $true) & (lam2lamEq = $true) & (ksndpairEq = $true) & (ap2apEq1 = $true) & (setunion__Cong = $true) & (emptyset__Cong = $true) & (disjointsetsI1 = $true) & (eta1 = $true) & (emptyinPowerset = $true) & (cartprodfstin = $true) & (setadjoinIL = $true) & (subsetI1 = $true) & (wellorderingAx = $true) & (nonemptyI = $true) & (setukpairinjR12 = $true) & (setadjoinOr = $true) & (funcinfuncset = $true) & (ubforcartprodlem3 = $true) & (funcGraphProp4 = $true) & (binintersectEL = $true) & (cartprodsndpairEq = $true) & (setukpairinjR1 = $true) & (powersetE1 = $true) & (quantDeMorgan2 = $true) & (exuEu = $true) & (upairsetIL = $true) & (setadjoin__Cong = $true) & (quantDeMorgan4 = $true) & (inCongP = $true) & (! [X3 : $i] : (($true = ((in @ (sK595 @ X3) @ sK596))) | (((in @ X3 @ sK597)) != $true)) & ((((ap @ sK597 @ sK596 @ (lam @ sK597 @ sK596 @ (^[Y0 : $i]: (sK595 @ Y0))) @ sK598)) != ((sK595 @ sK598))) & ($true = ((in @ sK598 @ sK597))))) & (singletonsswitch = $true) & (upairequniteq = $true) & (symdiffIneg1 = $true) & (ubforcartprodlem2 = $true) & (singletonsuniq = $true) & (exuE2 = $true) & (setunionAx = $true) & (powersetsubset = $true) & (infuncsetfunc = $true) & (notequalI2 = $true) & (brelnall1 = $true) & (descrp = $true) & (binunionRsub = $true) & (ex1I = $true) & (exuI2 = $true) & (nonemptyImpWitness = $true) & (replAx = $true) & (subset2powerset = $true) & (setadjoinSub2 = $true) & (app = $true) & (dsetconstr__Cong = $true) & (dpsetconstrI = $true) & (cartprodpairmemEL = $true) & (powerset__Cong = $true) & (powersetE = $true) & (setminusER = $true) & (emptysetAx = $true) & (setminusERneg = $true) & (kpairiskpair = $true) & (binintersectSubset1 = $true)),
% 2.69/0.75 inference(skolemize,[status(esa),new_symbols(skolem,[sK595,sK596,sK597,sK598]),skolemize(X0,sK595),skolemize(X1,sK596),skolemize(X2,sK597),skolemize(X4,sK598)],[f1527])).
% 2.69/0.75 thf(f1827,plain,(
% 2.69/0.75 ( ! [X2 : ($i > $i),X0 : $i,X1 : $i,X4 : $i] : ((((in @ X4 @ X1)) != $true) | (((X2 @ X4)) = ((ap @ X1 @ X0 @ (lam @ X1 @ X0 @ (^[Y0 : $i]: (X2 @ Y0))) @ X4))) | (beta1 != $true) | ($true = ((in @ (sK185 @ X2 @ X1 @ X0) @ X1)))) )),
% 2.69/0.75 inference(cnf_transformation,[],[f1125])).
% 2.69/0.75 thf(f1828,plain,(
% 2.69/0.75 ( ! [X2 : ($i > $i),X0 : $i,X1 : $i,X4 : $i] : (($true != ((in @ (X2 @ (sK185 @ X2 @ X1 @ X0)) @ X0))) | (beta1 != $true) | (((X2 @ X4)) = ((ap @ X1 @ X0 @ (lam @ X1 @ X0 @ (^[Y0 : $i]: (X2 @ Y0))) @ X4))) | (((in @ X4 @ X1)) != $true)) )),
% 2.69/0.75 inference(cnf_transformation,[],[f1125])).
% 2.69/0.75 thf(f2394,plain,(
% 2.69/0.75 ($true = ((in @ sK598 @ sK597)))),
% 2.69/0.75 inference(cnf_transformation,[],[f1528])).
% 2.69/0.75 thf(f2395,plain,(
% 2.69/0.75 (((ap @ sK597 @ sK596 @ (lam @ sK597 @ sK596 @ (^[Y0 : $i]: (sK595 @ Y0))) @ sK598)) != ((sK595 @ sK598)))),
% 2.69/0.75 inference(cnf_transformation,[],[f1528])).
% 2.69/0.75 thf(f2396,plain,(
% 2.69/0.75 ( ! [X3 : $i] : (($true = ((in @ (sK595 @ X3) @ sK596))) | (((in @ X3 @ sK597)) != $true)) )),
% 2.69/0.75 inference(cnf_transformation,[],[f1528])).
% 2.69/0.75 thf(f2499,plain,(
% 2.69/0.75 (beta1 = $true)),
% 2.69/0.75 inference(cnf_transformation,[],[f1528])).
% 2.69/0.75 thf(f2715,plain,(
% 2.69/0.75 ( ! [X2 : ($i > $i),X0 : $i,X1 : $i,X4 : $i] : ((((X2 @ X4)) = ((ap @ X1 @ X0 @ (lam @ X1 @ X0 @ X2) @ X4))) | (beta1 != $true) | ($true != ((in @ (X2 @ (sK185 @ X2 @ X1 @ X0)) @ X0))) | (((in @ X4 @ X1)) != $true)) )),
% 2.69/0.75 inference(beta-eta_normalization,[],[f1828])).
% 2.69/0.75 thf(f2736,plain,(
% 2.69/0.75 ( ! [X2 : ($i > $i),X0 : $i,X1 : $i,X4 : $i] : ((((X2 @ X4)) = ((ap @ X1 @ X0 @ (lam @ X1 @ X0 @ X2) @ X4))) | (((in @ X4 @ X1)) != $true) | (beta1 != $true) | ($true = ((in @ (sK185 @ X2 @ X1 @ X0) @ X1)))) )),
% 2.69/0.75 inference(beta-eta_normalization,[],[f1827])).
% 2.69/0.75 thf(f2826,plain,(
% 2.69/0.75 (((ap @ sK597 @ sK596 @ (lam @ sK597 @ sK596 @ sK595) @ sK598)) != ((sK595 @ sK598)))),
% 2.69/0.75 inference(beta-eta_normalization,[],[f2395])).
% 2.69/0.75 thf(f2841,plain,(
% 2.69/0.75 (((sK595 @ sK598)) != ((sK595 @ sK598))) | (beta1 != $true) | (((in @ (sK185 @ sK595 @ sK597 @ sK596) @ sK597)) = $true) | ($true != ((in @ sK598 @ sK597)))),
% 2.69/0.75 inference(constrained_superposition,[],[f2826,f2736])).
% 2.69/0.75 thf(f2842,plain,(
% 2.69/0.75 (((sK595 @ sK598)) != ((sK595 @ sK598))) | (beta1 != $true) | ($true != ((in @ sK598 @ sK597))) | ($true != ((in @ (sK595 @ (sK185 @ sK595 @ sK597 @ sK596)) @ sK596)))),
% 2.69/0.75 inference(constrained_superposition,[],[f2826,f2715])).
% 2.69/0.75 thf(f2845,plain,(
% 2.69/0.75 ($true != ((in @ sK598 @ sK597))) | (beta1 != $true) | (((in @ (sK185 @ sK595 @ sK597 @ sK596) @ sK597)) = $true)),
% 2.69/0.75 inference(trivial_inequality_removal,[],[f2841])).
% 2.69/0.75 thf(f2846,plain,(
% 2.69/0.75 ($true != ((in @ sK598 @ sK597))) | ($true != ((in @ (sK595 @ (sK185 @ sK595 @ sK597 @ sK596)) @ sK596))) | (beta1 != $true)),
% 2.69/0.75 inference(trivial_inequality_removal,[],[f2842])).
% 2.69/0.75 thf(f3123,plain,(
% 2.69/0.75 (beta1 != $true) | (((in @ (sK185 @ sK595 @ sK597 @ sK596) @ sK597)) = $true)),
% 2.69/0.75 inference(forward_subsumption_resolution,[],[f2845,f2394])).
% 2.69/0.75 thf(f3125,plain,(
% 2.69/0.75 (beta1 != $true) | ($true != ((in @ (sK595 @ (sK185 @ sK595 @ sK597 @ sK596)) @ sK596)))),
% 2.69/0.75 inference(forward_subsumption_resolution,[],[f2846,f2394])).
% 2.69/0.75 thf(f3127,plain,(
% 2.69/0.75 (((in @ (sK185 @ sK595 @ sK597 @ sK596) @ sK597)) = $true)),
% 2.69/0.75 inference(forward_subsumption_resolution,[],[f3123,f2499])).
% 2.69/0.75 thf(f3129,plain,(
% 2.69/0.75 ($true != ((in @ (sK595 @ (sK185 @ sK595 @ sK597 @ sK596)) @ sK596)))),
% 2.69/0.75 inference(forward_subsumption_resolution,[],[f3125,f2499])).
% 2.69/0.75 thf(f3146,plain,(
% 2.69/0.75 ($true != $true) | (((in @ (sK185 @ sK595 @ sK597 @ sK596) @ sK597)) != $true)),
% 2.69/0.75 inference(constrained_superposition,[],[f3129,f2396])).
% 2.69/0.75 thf(f3152,plain,(
% 2.69/0.75 (((in @ (sK185 @ sK595 @ sK597 @ sK596) @ sK597)) != $true)),
% 2.69/0.75 inference(trivial_inequality_removal,[],[f3146])).
% 2.69/0.75 thf(f3158,plain,(
% 2.69/0.75 $false),
% 2.69/0.75 inference(forward_subsumption_resolution,[],[f3152,f3127])).
% 2.69/0.75 % SZS output end Proof for theBenchmark
% 2.69/0.75 % (3425302)------------------------------
% 2.69/0.75 % (3425302)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.69/0.75 % (3425302)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/0.75 % (3425302)CaDiCaL version: 2.1.3
% 2.69/0.75 % (3425302)Termination reason: Refutation
% 2.69/0.75 % (3425302)Time elapsed: 0.120 s
% 2.69/0.75 % (3425302)Peak memory usage: 16 MB
% 2.69/0.75 % (3425302)Instructions burned: 246 (million)
% 2.69/0.75 % (3425148)Success in time 0.475 s
% 2.69/0.75 % Vampire exiting
%------------------------------------------------------------------------------