%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT152^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 07:48:26 AM UTC 2026
% Result : Theorem 0.48s 0.40s
% Output : Refutation 0.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : DAT152^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n005.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 18:02:01 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running higher-order theorem proving
% 0.22/0.27 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.48/0.40 % (2005904)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.48/0.40 % (2005909)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=382150795:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.48/0.40 % (2005915)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.48/0.40 % (2005915)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
% 0.48/0.40 % (2005910)lrs+10_16_si=on:nwc=1.5:random_seed=3456826047:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.48/0.40 % (2005911)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1344887576:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.48/0.40 % (2005913)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3929111993:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.48/0.40 % (2005912)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=3336185219: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)
% 0.48/0.40 % (2005914)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1946211767:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.48/0.40 % (2005915)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=2338024617:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.48/0.40 % (2005911)Instruction limit reached!
% 0.48/0.40 % (2005911)------------------------------
% 0.48/0.40 % (2005911)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.40 % (2005911)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.40 % (2005911)CaDiCaL version: 2.1.3
% 0.48/0.40 % (2005911)Termination reason: Instruction limit
% 0.48/0.40 % (2005911)Termination phase: shuffling
% 0.48/0.40 % (2005911)Time elapsed: 0.004 s
% 0.48/0.40 % (2005911)Peak memory usage: 10 MB
% 0.48/0.40 % (2005911)Instructions burned: 6 (million)
% 0.48/0.40 % (2005910)Instruction limit reached!
% 0.48/0.40 % (2005910)------------------------------
% 0.48/0.40 % (2005910)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.40 % (2005910)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.40 % (2005910)CaDiCaL version: 2.1.3
% 0.48/0.40 % (2005910)Termination reason: Instruction limit
% 0.48/0.40 % (2005910)Termination phase: Property scanning
% 0.48/0.40 % (2005910)Time elapsed: 0.009 s
% 0.48/0.40 % (2005910)Peak memory usage: 10 MB
% 0.48/0.40 % (2005910)Instructions burned: 19 (million)
% 0.48/0.40 % (2005913)Instruction limit reached!
% 0.48/0.40 % (2005913)------------------------------
% 0.48/0.40 % (2005913)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.40 % (2005913)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.40 % (2005913)CaDiCaL version: 2.1.3
% 0.48/0.40 % (2005913)Termination reason: Instruction limit
% 0.48/0.40 % (2005913)Termination phase: Property scanning
% 0.48/0.40 % (2005913)Time elapsed: 0.012 s
% 0.48/0.40 % (2005913)Peak memory usage: 10 MB
% 0.48/0.40 % (2005913)Instructions burned: 26 (million)
% 0.48/0.40 % (2005909)Instruction limit reached!
% 0.48/0.40 % (2005909)------------------------------
% 0.48/0.40 % (2005909)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.40 % (2005909)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.40 % (2005909)CaDiCaL version: 2.1.3
% 0.48/0.40 % (2005909)Termination reason: Instruction limit
% 0.48/0.40 % (2005909)Termination phase: Saturation
% 0.48/0.40 % (2005909)Time elapsed: 0.026 s
% 0.48/0.40 % (2005909)Peak memory usage: 13 MB
% 0.48/0.40 % (2005909)Instructions burned: 102 (million)
% 0.48/0.40 % (2005923)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2764672855:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.48/0.40 % (2005923)Instruction limit reached!
% 0.48/0.40 % (2005923)------------------------------
% 0.48/0.40 % (2005923)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.40 % (2005923)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.40 % (2005923)CaDiCaL version: 2.1.3
% 0.48/0.40 % (2005923)Termination reason: Instruction limit
% 0.48/0.40 % (2005923)Termination phase: shuffling
% 0.48/0.40 % (2005923)Time elapsed: 0.003 s
% 0.48/0.40 % (2005923)Peak memory usage: 10 MB
% 0.48/0.40 % (2005923)Instructions burned: 6 (million)
% 0.48/0.40 % (2005924)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2550397999:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.48/0.40 % (2005926)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=618268622:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.48/0.40 % (2005925)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.48/0.40 % (2005924)Instruction limit reached!
% 0.48/0.40 % (2005924)------------------------------
% 0.48/0.40 % (2005924)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.40 % (2005924)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.40 % (2005924)CaDiCaL version: 2.1.3
% 0.48/0.40 % (2005924)Termination reason: Instruction limit
% 0.48/0.40 % (2005924)Termination phase: shuffling
% 0.48/0.40 % (2005924)Time elapsed: 0.003 s
% 0.48/0.40 % (2005924)Peak memory usage: 10 MB
% 0.48/0.40 % (2005924)Instructions burned: 5 (million)
% 0.48/0.40 % (2005925)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1037939762:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.48/0.40 % (2005926)Instruction limit reached!
% 0.48/0.40 % (2005926)------------------------------
% 0.48/0.40 % (2005926)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.40 % (2005926)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.40 % (2005926)CaDiCaL version: 2.1.3
% 0.48/0.40 % (2005926)Termination reason: Instruction limit
% 0.48/0.40 % (2005926)Termination phase: shuffling
% 0.48/0.40 % (2005926)Time elapsed: 0.004 s
% 0.48/0.40 % (2005926)Peak memory usage: 10 MB
% 0.48/0.40 % (2005926)Instructions burned: 15 (million)
% 0.48/0.40 % (2005925)Instruction limit reached!
% 0.48/0.40 % (2005925)------------------------------
% 0.48/0.40 % (2005925)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.40 % (2005925)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.40 % (2005925)CaDiCaL version: 2.1.3
% 0.48/0.40 % (2005925)Termination reason: Instruction limit
% 0.48/0.40 % (2005925)Termination phase: shuffling
% 0.48/0.40 % (2005925)Time elapsed: 0.004 s
% 0.48/0.40 % (2005925)Peak memory usage: 10 MB
% 0.48/0.40 % (2005925)Instructions burned: 7 (million)
% 0.48/0.40 % (2005914)Instruction limit reached!
% 0.48/0.40 % (2005914)------------------------------
% 0.48/0.40 % (2005914)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.40 % (2005914)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.40 % (2005914)CaDiCaL version: 2.1.3
% 0.48/0.40 % (2005914)Termination reason: Instruction limit
% 0.48/0.40 % (2005914)Termination phase: Property scanning
% 0.48/0.40 % (2005914)Time elapsed: 0.036 s
% 0.48/0.40 % (2005914)Peak memory usage: 12 MB
% 0.48/0.40 % (2005914)Instructions burned: 76 (million)
% 0.48/0.40 % (2005929)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
% 0.48/0.40 % (2005929)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.48/0.40 % (2005933)lrs+10_1_si=on:cs=on:random_seed=3691674273:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.48/0.40 % (2005933)Instruction limit reached!
% 0.48/0.40 % (2005933)------------------------------
% 0.48/0.40 % (2005933)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.40 % (2005933)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.40 % (2005933)CaDiCaL version: 2.1.3
% 0.48/0.40 % (2005933)Termination reason: Instruction limit
% 0.48/0.40 % (2005933)Termination phase: shuffling
% 0.48/0.40 % (2005933)Time elapsed: 0.003 s
% 0.48/0.40 % (2005933)Peak memory usage: 10 MB
% 0.48/0.40 % (2005933)Instructions burned: 10 (million)
% 0.48/0.40 % (2005929)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=4198294802:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.48/0.40 % (2005931)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=1110923723:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.48/0.40 % (2005934)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.48/0.40 % (2005934)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=1654979048:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.48/0.40 % (2005935)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1202021605:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.48/0.40 % (2005938)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=47168296:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.48/0.40 % (2005934)Instruction limit reached!
% 0.48/0.40 % (2005934)------------------------------
% 0.48/0.40 % (2005934)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.40 % (2005934)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.40 % (2005934)CaDiCaL version: 2.1.3
% 0.48/0.40 % (2005934)Termination reason: Instruction limit
% 0.48/0.40 % (2005934)Termination phase: shuffling
% 0.48/0.40 % (2005934)Time elapsed: 0.002 s
% 0.48/0.40 % (2005934)Peak memory usage: 10 MB
% 0.48/0.40 % (2005934)Instructions burned: 3 (million)
% 0.48/0.40 % (2005929)Instruction limit reached!
% 0.48/0.40 % (2005929)------------------------------
% 0.48/0.40 % (2005929)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.40 % (2005929)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.40 % (2005929)CaDiCaL version: 2.1.3
% 0.48/0.40 % (2005929)Termination reason: Instruction limit
% 0.48/0.40 % (2005929)Termination phase: Property scanning
% 0.48/0.40 % (2005929)Time elapsed: 0.014 s
% 0.48/0.40 % (2005929)Peak memory usage: 11 MB
% 0.48/0.40 % (2005929)Instructions burned: 30 (million)
% 0.48/0.40 % (2005938) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2005904-2005938"...
% 0.48/0.40 % (2005938)...printing done.
% 0.48/0.40 % (2005935)Instruction limit reached!
% 0.48/0.40 % (2005935)------------------------------
% 0.48/0.40 % (2005935)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.40 % (2005935)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.40 % (2005935)CaDiCaL version: 2.1.3
% 0.48/0.40 % (2005935)Termination reason: Instruction limit
% 0.48/0.40 % (2005935)Termination phase: Preprocessing 3
% 0.48/0.40 % (2005935)Time elapsed: 0.019 s
% 0.48/0.40 % (2005935)Peak memory usage: 11 MB
% 0.48/0.40 % (2005935)Instructions burned: 39 (million)
% 0.48/0.40 % (2005938)Refutation found. Thanks to Tanya!
% 0.48/0.40 % SZS status Theorem for theBenchmark
% 0.48/0.40 % SZS output start Proof for theBenchmark
% 0.48/0.40 thf(type_def_5, type, extended_enat: $tType).
% 0.48/0.40 thf(type_def_6, type, stream: $tType > $tType).
% 0.48/0.40 thf(type_def_7, type, set: $tType > $tType).
% 0.48/0.40 thf(type_def_8, type, nat: $tType).
% 0.48/0.40 thf(type_def_9, type, itself: $tType > $tType).
% 0.48/0.40 thf(type_def_10, type, a: $tType).
% 0.48/0.40 thf(type_def_11, type, sTfun: ($tType * $tType) > $tType).
% 0.48/0.40 thf(func_def_0, type, type: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.48/0.40 thf(func_def_1, type, ord: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.48/0.40 thf(func_def_2, type, order: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.48/0.40 thf(func_def_3, type, no_bot: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.48/0.40 thf(func_def_4, type, no_top: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.48/0.40 thf(func_def_5, type, finite_finite: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.48/0.40 thf(func_def_6, type, linorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.48/0.40 thf(func_def_7, type, preorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.48/0.40 thf(func_def_8, type, wellorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.48/0.40 thf(func_def_9, type, dense_order: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.48/0.40 thf(func_def_10, type, linordered_idom: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.48/0.40 thf(func_def_11, type, dense_linorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.48/0.40 thf(func_def_12, type, condit1656338222tinuum: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.48/0.40 thf(func_def_13, type, condit1037483654norder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.48/0.40 thf(func_def_14, type, coindu1365464361scount: !>[X0: $tType]:(((stream @ X0 > $o) > stream @ X0 > extended_enat))).
% 0.48/0.40 thf(func_def_15, type, extended_enat2: (nat > extended_enat)).
% 0.48/0.40 thf(func_def_16, type, extended_case_enat: !>[X0: $tType]:(((nat > X0) > X0 > extended_enat > X0))).
% 0.48/0.40 thf(func_def_17, type, extended_rec_enat: !>[X0: $tType]:(((nat > X0) > X0 > extended_enat > X0))).
% 0.48/0.40 thf(func_def_18, type, extend1396239628finity: !>[X0: $tType]:(X0)).
% 0.48/0.40 thf(func_def_19, type, finite_card: !>[X0: $tType]:((set @ X0 > nat))).
% 0.48/0.40 thf(func_def_20, type, finite_finite2: !>[X0: $tType]:((set @ X0 > $o))).
% 0.48/0.40 thf(func_def_21, type, linear1386806755on_alw: !>[X0: $tType]:(((stream @ X0 > $o) > stream @ X0 > $o))).
% 0.48/0.40 thf(func_def_22, type, linear505997466_on_ev: !>[X0: $tType]:(((stream @ X0 > $o) > stream @ X0 > $o))).
% 0.48/0.40 thf(func_def_23, type, linear1494993505on_nxt: !>[X0: $tType, X1: $tType]:(((stream @ X0 > X1) > stream @ X0 > X1))).
% 0.48/0.40 thf(func_def_24, type, linear1335279038n_wait: !>[X0: $tType]:(((stream @ X0 > $o) > stream @ X0 > nat))).
% 0.48/0.40 thf(func_def_25, type, ord_less: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.48/0.40 thf(func_def_26, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.48/0.40 thf(func_def_27, type, type2: !>[X0: $tType]:(itself @ X0)).
% 0.48/0.40 thf(func_def_28, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.48/0.40 thf(func_def_29, type, sdrop: !>[X0: $tType]:((nat > stream @ X0 > stream @ X0))).
% 0.48/0.40 thf(func_def_30, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.48/0.40 thf(func_def_31, type, p: (stream @ a > $o)).
% 0.48/0.40 thf(func_def_32, type, omega: stream @ a).
% 0.48/0.40 thf(func_def_36, type, vAND: ($o > $o > $o)).
% 0.48/0.40 thf(func_def_37, type, vNOT: ($o > $o)).
% 0.48/0.40 thf(func_def_38, type, db0: !>[X0: $tType]:(X0)).
% 0.48/0.40 thf(func_def_39, type, db1: !>[X0: $tType]:(X0)).
% 0.48/0.40 thf(func_def_40, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.48/0.40 thf(func_def_41, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.48/0.40 thf(func_def_42, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.48/0.40 thf(func_def_43, type, db2: !>[X0: $tType]:(X0)).
% 0.48/0.40 thf(func_def_44, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.48/0.40 thf(func_def_45, type, vIMP: ($o > $o > $o)).
% 0.48/0.40 thf(func_def_46, type, vOR: ($o > $o > $o)).
% 0.48/0.40 thf(func_def_47, type, sP0: (extended_enat > extended_enat > $o)).
% 0.48/0.40 thf(func_def_48, type, sP1: (extended_enat > extended_enat > extended_enat > $o)).
% 0.48/0.40 thf(func_def_49, type, sP2: (extended_enat > extended_enat > extended_enat > $o)).
% 0.48/0.40 thf(func_def_50, type, sP3: (extended_enat > extended_enat > extended_enat > $o)).
% 0.48/0.40 thf(func_def_51, type, sP4: (extended_enat > extended_enat > extended_enat > $o)).
% 0.48/0.40 thf(func_def_52, type, sP5: (extended_enat > extended_enat > extended_enat > $o)).
% 0.48/0.40 thf(func_def_53, type, sP6: (extended_enat > extended_enat > extended_enat > $o)).
% 0.48/0.40 thf(func_def_54, type, sP7: (extended_enat > extended_enat > extended_enat > $o)).
% 0.48/0.40 thf(func_def_55, type, sK8: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > X0))).
% 0.48/0.40 thf(func_def_56, type, sK9: (extended_enat > nat)).
% 0.48/0.40 thf(func_def_57, type, sK10: (extended_enat > nat)).
% 0.48/0.40 thf(func_def_58, type, sK11: (extended_enat > nat)).
% 0.48/0.40 thf(func_def_59, type, sK12: (extended_enat > nat)).
% 0.48/0.40 thf(func_def_60, type, sK13: (extended_enat > nat)).
% 0.48/0.40 thf(func_def_61, type, sK14: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > X0))).
% 0.48/0.40 thf(func_def_62, type, sK15: ((extended_enat > $o) > nat)).
% 0.48/0.40 thf(func_def_63, type, sK16: ((nat > $o) > nat)).
% 0.48/0.40 thf(func_def_64, type, sK17: !>[X0: $tType]:(((stream @ X0 > $o) > (stream @ X0 > $o) > (stream @ X0 > $o) > stream @ X0))).
% 0.48/0.40 thf(func_def_65, type, sK18: (nat > set @ extended_enat > extended_enat)).
% 0.48/0.40 thf(func_def_66, type, sK19: !>[X0: $tType]:(((stream @ X0 > $o) > stream @ X0))).
% 0.48/0.40 thf(func_def_67, type, sK20: ((nat > $o) > nat)).
% 0.48/0.40 thf(func_def_68, type, sK21: ((extended_enat > $o) > extended_enat)).
% 0.48/0.40 thf(func_def_69, type, sK22: !>[X0: $tType]:(((X0 > $o) > (X0 > nat) > X0))).
% 0.48/0.40 thf(func_def_70, type, sK23: !>[X0: $tType]:(((stream @ X0 > $o) > (stream @ X0 > $o) > stream @ X0))).
% 0.48/0.40 thf(func_def_71, type, sK24: (extended_enat > nat)).
% 0.48/0.40 thf(func_def_72, type, sK25: (extended_enat > nat)).
% 0.48/0.40 thf(func_def_73, type, sK26: (extended_enat > nat)).
% 0.48/0.40 thf(func_def_74, type, sK27: (extended_enat > nat)).
% 0.48/0.40 thf(func_def_75, type, sK28: (extended_enat > nat)).
% 0.48/0.40 thf(func_def_76, type, sK29: (extended_enat > nat)).
% 0.48/0.40 thf(func_def_77, type, sK30: (extended_enat > nat)).
% 0.48/0.40 thf(func_def_78, type, sK31: (extended_enat > nat)).
% 0.48/0.40 thf(func_def_79, type, sK32: (extended_enat > nat)).
% 0.48/0.40 thf(func_def_80, type, sK33: (extended_enat > nat)).
% 0.48/0.40 thf(func_def_81, type, sK34: (extended_enat > nat)).
% 0.48/0.40 thf(func_def_82, type, sK35: (extended_enat > nat)).
% 0.48/0.40 thf(func_def_83, type, sK36: (extended_enat > nat)).
% 0.48/0.40 thf(func_def_84, type, sK37: !>[X0: $tType]:(((stream @ X0 > $o) > (stream @ X0 > $o) > stream @ X0))).
% 0.48/0.40 thf(func_def_85, type, sK38: (extended_enat > nat)).
% 0.48/0.40 thf(func_def_86, type, sK39: !>[X0: $tType]:(((X0 > $o) > (X0 > nat) > X0))).
% 0.48/0.40 thf(func_def_87, type, sK40: !>[X0: $tType]:(((stream @ X0 > $o) > (stream @ X0 > $o) > (stream @ X0 > $o) > stream @ X0))).
% 0.48/0.40 thf(func_def_88, type, sK41: (extended_enat > nat > nat)).
% 0.48/0.40 thf(func_def_89, type, sK42: !>[X0: $tType]:(((X0 > $o) > (X0 > nat) > nat > X0))).
% 0.48/0.40 thf(func_def_90, type, sK43: !>[X0: $tType]:(((X0 > $o) > (X0 > nat) > X0))).
% 0.48/0.40 thf(func_def_91, type, sK44: !>[X0: $tType]:(((X0 > extended_enat) > X0))).
% 0.48/0.40 thf(func_def_92, type, sK45: !>[X0: $tType]:((nat > (X0 > extended_enat) > X0))).
% 0.48/0.40 thf(func_def_93, type, sK46: ((nat > nat) > nat)).
% 0.48/0.40 thf(func_def_94, type, sK47: ((nat > nat) > nat)).
% 0.48/0.40 thf(func_def_95, type, sK48: (extended_enat > nat)).
% 0.48/0.40 thf(f1,axiom,(
% 0.48/0.40 (linear505997466_on_ev @ a @ (linear1386806755on_alw @ a @ (^[X4 : stream @ a] : (~(p @ X4)))) @ omega) => (((extended_enat2 @ (finite_card @ nat @ (collect @ nat @ (^[X5 : nat] : ((p @ (sdrop @ a @ X5 @ omega)))))))) = ((coindu1365464361scount @ a @ p @ omega)))),
% 0.48/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__092_060open_062ev_A_Ialw_A_I_092_060lambda_062xs_O_A_092_060not_062_AP_Axs_J_J_A_092_060omega_062_A_092_060Longrightarrow_062_Ascount_AP_A_092_060omega_062_A_061_Aenat_A_Icard_A_123i_O_AP_A_Isdrop_Ai_A_092_060omega_062_J_125_J_092_060close_062)).
% 0.48/0.40 thf(f39,axiom,(
% 0.48/0.40 ! [X0 : nat] : (ord_less @ extended_enat @ (extended_enat2 @ X0) @ extend1396239628finity @ extended_enat)),
% 0.48/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_enat__ord__code_I4_J)).
% 0.48/0.40 thf(f283,axiom,(
% 0.48/0.40 (linear505997466_on_ev @ a @ (linear1386806755on_alw @ a @ (^[X0 : stream @ a] : (~(p @ X0)))) @ omega)),
% 0.48/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 0.48/0.40 thf(f284,conjecture,(
% 0.48/0.40 (ord_less @ extended_enat @ (coindu1365464361scount @ a @ p @ omega) @ extend1396239628finity @ extended_enat)),
% 0.48/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1)).
% 0.48/0.40 thf(f285,negated_conjecture,(
% 0.48/0.40 ~(ord_less @ extended_enat @ (coindu1365464361scount @ a @ p @ omega) @ extend1396239628finity @ extended_enat)),
% 0.48/0.40 inference(negated_conjecture,[status(cth)],[f284])).
% 0.48/0.40 thf(f386,plain,(
% 0.48/0.40 ! [X0 : nat] : (ord_less @ extended_enat @ (extended_enat2 @ X0) @ extend1396239628finity @ extended_enat)),
% 0.48/0.40 inference(rectify,[],[f39])).
% 0.48/0.40 thf(f387,plain,(
% 0.48/0.40 ! [X0 : nat] : (((ord_less @ extended_enat @ (extended_enat2 @ X0) @ extend1396239628finity @ extended_enat)) = $true)),
% 0.48/0.40 inference(fool_elimination,[],[f386])).
% 0.48/0.40 thf(f492,plain,(
% 0.48/0.40 (linear505997466_on_ev @ a @ (linear1386806755on_alw @ a @ (^[X0 : stream @ a] : (~(p @ X0)))) @ omega)),
% 0.48/0.40 inference(rectify,[],[f283])).
% 0.48/0.40 thf(f493,plain,(
% 0.48/0.40 ($true = ((linear505997466_on_ev @ a @ (linear1386806755on_alw @ a @ (^[Y0 : stream @ a]: (~ (p @ Y0)))) @ omega)))),
% 0.48/0.40 inference(fool_elimination,[],[f492])).
% 0.48/0.40 thf(f638,plain,(
% 0.48/0.40 ~(ord_less @ extended_enat @ (coindu1365464361scount @ a @ p @ omega) @ extend1396239628finity @ extended_enat)),
% 0.48/0.40 inference(rectify,[],[f285])).
% 0.48/0.40 thf(f639,plain,(
% 0.48/0.40 ~ (((ord_less @ extended_enat @ (coindu1365464361scount @ a @ p @ omega) @ extend1396239628finity @ extended_enat)) = $true)),
% 0.48/0.40 inference(fool_elimination,[],[f638])).
% 0.48/0.40 thf(f694,plain,(
% 0.48/0.40 (linear505997466_on_ev @ a @ (linear1386806755on_alw @ a @ (^[X0 : stream @ a] : (~(p @ X0)))) @ omega) => (((extended_enat2 @ (finite_card @ nat @ (collect @ nat @ (^[X1 : nat] : ((p @ (sdrop @ a @ X1 @ omega)))))))) = ((coindu1365464361scount @ a @ p @ omega)))),
% 0.48/0.40 inference(rectify,[],[f1])).
% 0.48/0.40 thf(f695,plain,(
% 0.48/0.40 ($true = ((linear505997466_on_ev @ a @ (linear1386806755on_alw @ a @ (^[Y0 : stream @ a]: (~ (p @ Y0)))) @ omega))) => (((coindu1365464361scount @ a @ p @ omega)) = ((extended_enat2 @ (finite_card @ nat @ (collect @ nat @ (^[Y0 : nat]: (p @ (sdrop @ a @ Y0 @ omega))))))))),
% 0.48/0.40 inference(fool_elimination,[],[f694])).
% 0.48/0.40 thf(f815,plain,(
% 0.48/0.40 (((ord_less @ extended_enat @ (coindu1365464361scount @ a @ p @ omega) @ extend1396239628finity @ extended_enat)) != $true)),
% 0.48/0.40 inference(flattening,[],[f639])).
% 0.48/0.40 thf(f895,plain,(
% 0.48/0.40 ($true != ((linear505997466_on_ev @ a @ (linear1386806755on_alw @ a @ (^[Y0 : stream @ a]: (~ (p @ Y0)))) @ omega))) | (((coindu1365464361scount @ a @ p @ omega)) = ((extended_enat2 @ (finite_card @ nat @ (collect @ nat @ (^[Y0 : nat]: (p @ (sdrop @ a @ Y0 @ omega))))))))),
% 0.48/0.40 inference(ennf_transformation,[],[f695])).
% 0.48/0.40 thf(f1021,plain,(
% 0.48/0.40 (((coindu1365464361scount @ a @ p @ omega)) = ((extended_enat2 @ (finite_card @ nat @ (collect @ nat @ (^[Y0 : nat]: (p @ (sdrop @ a @ Y0 @ omega)))))))) | ($true != ((linear505997466_on_ev @ a @ (linear1386806755on_alw @ a @ (^[Y0 : stream @ a]: (~ (p @ Y0)))) @ omega)))),
% 0.48/0.40 inference(cnf_transformation,[],[f895])).
% 0.48/0.40 thf(f1077,plain,(
% 0.48/0.40 (((ord_less @ extended_enat @ (coindu1365464361scount @ a @ p @ omega) @ extend1396239628finity @ extended_enat)) != $true)),
% 0.48/0.40 inference(cnf_transformation,[],[f815])).
% 0.48/0.40 thf(f1088,plain,(
% 0.48/0.40 ($true = ((linear505997466_on_ev @ a @ (linear1386806755on_alw @ a @ (^[Y0 : stream @ a]: (~ (p @ Y0)))) @ omega)))),
% 0.48/0.40 inference(cnf_transformation,[],[f493])).
% 0.48/0.40 thf(f1106,plain,(
% 0.48/0.40 ( ! [X0 : nat] : ((((ord_less @ extended_enat @ (extended_enat2 @ X0) @ extend1396239628finity @ extended_enat)) = $true)) )),
% 0.48/0.40 inference(cnf_transformation,[],[f387])).
% 0.48/0.40 thf(f1120,plain,(
% 0.48/0.40 (((ord_less @ extended_enat @ (extended_enat2 @ (finite_card @ nat @ (collect @ nat @ (^[Y0 : nat]: (p @ (sdrop @ a @ Y0 @ omega)))))) @ extend1396239628finity @ extended_enat)) != $true) | ($true != ((linear505997466_on_ev @ a @ (linear1386806755on_alw @ a @ (^[Y0 : stream @ a]: (~ (p @ Y0)))) @ omega)))),
% 0.48/0.40 inference(superposition,[],[f1077,f1021])).
% 0.48/0.40 thf(f1124,plain,(
% 0.48/0.40 ($true != ((linear505997466_on_ev @ a @ (linear1386806755on_alw @ a @ (^[Y0 : stream @ a]: (~ (p @ Y0)))) @ omega)))),
% 0.48/0.40 inference(forward_subsumption_resolution,[],[f1120,f1106])).
% 0.48/0.40 thf(f1126,plain,(
% 0.48/0.40 $false),
% 0.48/0.40 inference(forward_subsumption_resolution,[],[f1124,f1088])).
% 0.48/0.40 % SZS output end Proof for theBenchmark
% 0.48/0.40 % (2005938)------------------------------
% 0.48/0.40 % (2005938)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.40 % (2005938)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.40 % (2005938)CaDiCaL version: 2.1.3
% 0.48/0.40 % (2005938)Termination reason: Refutation
% 0.48/0.40 % (2005938)Time elapsed: 0.016 s
% 0.48/0.40 % (2005938)Peak memory usage: 13 MB
% 0.48/0.40 % (2005938)Instructions burned: 60 (million)
% 0.48/0.40 % (2005904)Success in time 0.127 s
% 0.48/0.40 % Vampire exiting
%------------------------------------------------------------------------------