%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT162^1 : 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 : n011.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 07:48:27 AM UTC 2026
% Result : Theorem 0.54s 0.39s
% Output : Refutation 0.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT162^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n011.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
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 18:03:31 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.21/0.27 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
% 0.54/0.39 % (451915)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.54/0.39 % (451925)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2753424274:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.54/0.39 % (451926)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.54/0.39 % (451926)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
% 0.54/0.39 % (451920)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=67372853:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.54/0.39 % (451921)lrs+10_16_si=on:nwc=1.5:random_seed=1728548212:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.54/0.39 % (451922)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2617183359:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.54/0.39 % (451924)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=372395567:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.54/0.39 % (451923)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=3931833133: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)
% 0.54/0.39 % (451926)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=1614307549:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.54/0.39 % (451922)Instruction limit reached!
% 0.54/0.39 % (451922)------------------------------
% 0.54/0.39 % (451922)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.39 % (451922)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.39 % (451922)CaDiCaL version: 2.1.3
% 0.54/0.39 % (451922)Termination reason: Instruction limit
% 0.54/0.39 % (451922)Termination phase: shuffling
% 0.54/0.39 % (451922)Time elapsed: 0.002 s
% 0.54/0.39 % (451922)Peak memory usage: 10 MB
% 0.54/0.39 % (451922)Instructions burned: 3 (million)
% 0.54/0.39 % (451921)Instruction limit reached!
% 0.54/0.39 % (451921)------------------------------
% 0.54/0.39 % (451921)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.39 % (451921)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.39 % (451921)CaDiCaL version: 2.1.3
% 0.54/0.39 % (451921)Termination reason: Instruction limit
% 0.54/0.39 % (451921)Termination phase: Property scanning
% 0.54/0.39 % (451921)Time elapsed: 0.010 s
% 0.54/0.39 % (451921)Peak memory usage: 10 MB
% 0.54/0.39 % (451921)Instructions burned: 19 (million)
% 0.54/0.39 % (451924)Instruction limit reached!
% 0.54/0.39 % (451924)------------------------------
% 0.54/0.39 % (451924)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.39 % (451924)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.39 % (451924)CaDiCaL version: 2.1.3
% 0.54/0.39 % (451924)Termination reason: Instruction limit
% 0.54/0.39 % (451924)Termination phase: Preprocessing 1
% 0.54/0.39 % (451924)Time elapsed: 0.012 s
% 0.54/0.39 % (451924)Peak memory usage: 10 MB
% 0.54/0.39 % (451924)Instructions burned: 26 (million)
% 0.54/0.39 % (451925)Instruction limit reached!
% 0.54/0.39 % (451925)------------------------------
% 0.54/0.39 % (451925)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.39 % (451925)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.39 % (451925)CaDiCaL version: 2.1.3
% 0.54/0.39 % (451925)Termination reason: Instruction limit
% 0.54/0.39 % (451925)Termination phase: Property scanning
% 0.54/0.39 % (451925)Time elapsed: 0.020 s
% 0.54/0.39 % (451925)Peak memory usage: 12 MB
% 0.54/0.39 % (451925)Instructions burned: 80 (million)
% 0.54/0.39 % (451936)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.54/0.39 % (451934)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2507626468:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.54/0.39 % (451936)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2549213012:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.54/0.39 % (451934)Instruction limit reached!
% 0.54/0.39 % (451934)------------------------------
% 0.54/0.39 % (451934)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.39 % (451934)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.39 % (451936)Instruction limit reached!
% 0.54/0.39 % (451936)------------------------------
% 0.54/0.39 % (451936)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.39 % (451934)CaDiCaL version: 2.1.3
% 0.54/0.39 % (451936)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.39 % (451934)Termination reason: Instruction limit
% 0.54/0.39 % (451934)Termination phase: shuffling
% 0.54/0.39 % (451934)Time elapsed: 0.004 s
% 0.54/0.39 % (451936)CaDiCaL version: 2.1.3
% 0.54/0.39 % (451934)Peak memory usage: 10 MB
% 0.54/0.39 % (451936)Termination reason: Instruction limit
% 0.54/0.39 % (451936)Termination phase: shuffling
% 0.54/0.39 % (451936)Time elapsed: 0.002 s
% 0.54/0.39 % (451934)Instructions burned: 7 (million)
% 0.54/0.39 % (451936)Peak memory usage: 10 MB
% 0.54/0.39 % (451936)Instructions burned: 10 (million)
% 0.54/0.39 % (451935)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1106081460:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.54/0.39 % (451937)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2251634547:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.54/0.39 % (451935)Instruction limit reached!
% 0.54/0.39 % (451935)------------------------------
% 0.54/0.39 % (451935)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.39 % (451940)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
% 0.54/0.39 % (451940)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.54/0.39 % (451940)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=257768354:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.54/0.39 % (451935)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.39 % (451935)CaDiCaL version: 2.1.3
% 0.54/0.39 % (451935)Termination reason: Instruction limit
% 0.54/0.39 % (451935)Termination phase: shuffling
% 0.54/0.39 % (451935)Time elapsed: 0.006 s
% 0.54/0.39 % (451935)Peak memory usage: 10 MB
% 0.54/0.39 % (451935)Instructions burned: 11 (million)
% 0.54/0.39 % (451937)Instruction limit reached!
% 0.54/0.39 % (451937)------------------------------
% 0.54/0.39 % (451937)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.39 % (451937)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.39 % (451937)CaDiCaL version: 2.1.3
% 0.54/0.39 % (451937)Termination reason: Instruction limit
% 0.54/0.39 % (451937)Termination phase: shuffling
% 0.54/0.39 % (451937)Time elapsed: 0.006 s
% 0.54/0.39 % (451937)Peak memory usage: 10 MB
% 0.54/0.39 % (451937)Instructions burned: 12 (million)
% 0.54/0.39 % (451920)Instruction limit reached!
% 0.54/0.39 % (451920)------------------------------
% 0.54/0.39 % (451920)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.39 % (451920)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.39 % (451920)CaDiCaL version: 2.1.3
% 0.54/0.39 % (451920)Termination reason: Instruction limit
% 0.54/0.39 % (451920)Termination phase: Saturation
% 0.54/0.39 % (451920)Time elapsed: 0.041 s
% 0.54/0.39 % (451920)Peak memory usage: 13 MB
% 0.54/0.39 % (451920)Instructions burned: 88 (million)
% 0.54/0.39 % (451940)Instruction limit reached!
% 0.54/0.39 % (451940)------------------------------
% 0.54/0.39 % (451940)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.39 % (451940)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.39 % (451940)CaDiCaL version: 2.1.3
% 0.54/0.39 % (451940)Termination reason: Instruction limit
% 0.54/0.39 % (451940)Termination phase: Property scanning
% 0.54/0.39 % (451940)Time elapsed: 0.007 s
% 0.54/0.39 % (451940)Peak memory usage: 11 MB
% 0.54/0.39 % (451940)Instructions burned: 31 (million)
% 0.54/0.39 % (451941)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=2937972599:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.54/0.39 % (451946)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.54/0.39 % (451948)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=1061782368:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.54/0.39 % (451945)lrs+10_1_si=on:cs=on:random_seed=1691292943:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.54/0.39 % (451946)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=3980382816:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.54/0.39 % (451946)Instruction limit reached!
% 0.54/0.39 % (451946)------------------------------
% 0.54/0.39 % (451946)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.39 % (451946)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.39 % (451946)CaDiCaL version: 2.1.3
% 0.54/0.39 % (451946)Termination reason: Instruction limit
% 0.54/0.39 % (451946)Termination phase: shuffling
% 0.54/0.39 % (451946)Time elapsed: 0.002 s
% 0.54/0.39 % (451946)Peak memory usage: 10 MB
% 0.54/0.39 % (451946)Instructions burned: 3 (million)
% 0.54/0.39 % (451947)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=4100859140:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.54/0.39 % (451945)Instruction limit reached!
% 0.54/0.39 % (451945)------------------------------
% 0.54/0.39 % (451945)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.39 % (451945)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.39 % (451945)CaDiCaL version: 2.1.3
% 0.54/0.39 % (451945)Termination reason: Instruction limit
% 0.54/0.39 % (451945)Termination phase: shuffling
% 0.54/0.39 % (451945)Time elapsed: 0.004 s
% 0.54/0.39 % (451945)Peak memory usage: 10 MB
% 0.54/0.39 % (451945)Instructions burned: 8 (million)
% 0.54/0.39 % (451923) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-451915-451923"...
% 0.54/0.39 % (451948) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-451915-451948"...
% 0.54/0.39 % (451948)...printing done.
% 0.54/0.39 % (451948)Refutation found. Thanks to Tanya!
% 0.54/0.39 % SZS status Theorem for theBenchmark
% 0.54/0.39 % SZS output start Proof for theBenchmark
% 0.54/0.39 thf(type_def_5, type, coinductive_llist: $tType > $tType).
% 0.54/0.39 thf(type_def_6, type, set: $tType > $tType).
% 0.54/0.39 thf(type_def_7, type, nat: $tType).
% 0.54/0.39 thf(type_def_8, type, itself: $tType > $tType).
% 0.54/0.39 thf(type_def_9, type, sTfun: ($tType * $tType) > $tType).
% 0.54/0.39 thf(func_def_0, type, type: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.54/0.39 thf(func_def_1, type, dvd: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.54/0.39 thf(func_def_2, type, one: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.54/0.39 thf(func_def_3, type, ord: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.54/0.39 thf(func_def_4, type, order: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.54/0.39 thf(func_def_5, type, semiring_gcd: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.54/0.39 thf(func_def_6, type, no_bot: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.54/0.39 thf(func_def_7, type, no_top: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.54/0.39 thf(func_def_8, type, monoid_mult: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.54/0.39 thf(func_def_9, type, linorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.54/0.39 thf(func_def_10, type, preorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.54/0.39 thf(func_def_11, type, wellorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.54/0.39 thf(func_def_12, type, semigroup_mult: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.54/0.39 thf(func_def_13, type, dense_order: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.54/0.39 thf(func_def_14, type, comm_semiring_1: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.54/0.39 thf(func_def_15, type, linordered_idom: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.54/0.39 thf(func_def_16, type, comm_monoid_mult: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.54/0.39 thf(func_def_17, type, algebraic_semidom: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.54/0.39 thf(func_def_18, type, ab_semigroup_mult: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.54/0.39 thf(func_def_19, type, dense_linorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.54/0.39 thf(func_def_20, type, linordered_semidom: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.54/0.39 thf(func_def_21, type, coindu351974385stinct: !>[X0: $tType]:((coinductive_llist @ X0 > $o))).
% 0.54/0.39 thf(func_def_22, type, coinductive_lfinite: !>[X0: $tType]:((coinductive_llist @ X0 > $o))).
% 0.54/0.39 thf(func_def_23, type, coinductive_LNil: !>[X0: $tType]:(coinductive_llist @ X0)).
% 0.54/0.39 thf(func_def_24, type, coinductive_lnull: !>[X0: $tType]:((coinductive_llist @ X0 > $o))).
% 0.54/0.39 thf(func_def_25, type, coinductive_lset: !>[X0: $tType]:((coinductive_llist @ X0 > set @ X0))).
% 0.54/0.39 thf(func_def_26, type, coinductive_lmember: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > $o))).
% 0.54/0.39 thf(func_def_27, type, coinductive_lsetp: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > $o))).
% 0.54/0.39 thf(func_def_28, type, coindu63249387sorted: !>[X0: $tType]:((coinductive_llist @ X0 > $o))).
% 0.54/0.39 thf(func_def_29, type, one_one: !>[X0: $tType]:(X0)).
% 0.54/0.39 thf(func_def_30, type, times_times: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.54/0.39 thf(func_def_31, type, hammin2015774020amming: coinductive_llist @ nat).
% 0.54/0.39 thf(func_def_32, type, hammin1328233080lmerge: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.54/0.39 thf(func_def_33, type, hammin1138290136lmerge: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.54/0.39 thf(func_def_34, type, hammin1195055315smooth: (nat > $o)).
% 0.54/0.39 thf(func_def_35, type, ord_less: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.54/0.39 thf(func_def_36, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.54/0.39 thf(func_def_37, type, prime: (nat > $o)).
% 0.54/0.39 thf(func_def_38, type, type2: !>[X0: $tType]:(itself @ X0)).
% 0.54/0.39 thf(func_def_39, type, dvd_dvd: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.54/0.39 thf(func_def_40, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.54/0.39 thf(func_def_41, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.54/0.39 thf(func_def_42, type, n: nat).
% 0.54/0.39 thf(func_def_43, type, n2: nat).
% 0.54/0.39 thf(func_def_44, type, na: nat).
% 0.54/0.39 thf(func_def_45, type, p: nat).
% 0.54/0.39 thf(func_def_49, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.54/0.39 thf(func_def_50, type, vOR: ($o > $o > $o)).
% 0.54/0.39 thf(func_def_51, type, db1: !>[X0: $tType]:(X0)).
% 0.54/0.39 thf(func_def_52, type, db0: !>[X0: $tType]:(X0)).
% 0.54/0.39 thf(func_def_53, type, vAND: ($o > $o > $o)).
% 0.54/0.39 thf(func_def_54, type, vNOT: ($o > $o)).
% 0.54/0.39 thf(func_def_55, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.54/0.39 thf(func_def_56, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.54/0.39 thf(func_def_57, type, db2: !>[X0: $tType]:(X0)).
% 0.54/0.39 thf(func_def_58, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.54/0.39 thf(func_def_59, type, vIMP: ($o > $o > $o)).
% 0.54/0.39 thf(func_def_60, type, sK0: ((nat > $o) > nat)).
% 0.54/0.39 thf(func_def_61, type, sK1: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > X0))).
% 0.54/0.39 thf(func_def_62, type, sK2: ((nat > nat) > nat)).
% 0.54/0.39 thf(func_def_63, type, sK3: ((nat > nat) > nat)).
% 0.54/0.39 thf(func_def_64, type, sK4: ((nat > $o) > nat)).
% 0.54/0.39 thf(func_def_65, type, sK5: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > X0))).
% 0.54/0.39 thf(func_def_66, type, sK6: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > X0))).
% 0.54/0.39 thf(f1,axiom,(
% 0.54/0.39 (hammin1195055315smooth @ n2)),
% 0.54/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__092_060open_062smooth_An_H_092_060close_062)).
% 0.54/0.39 thf(f2,axiom,(
% 0.54/0.39 (ord_less @ nat @ n2 @ na)),
% 0.54/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__092_060open_062n_H_A_060_An_092_060close_062)).
% 0.54/0.39 thf(f3,axiom,(
% 0.54/0.39 ! [X0 : nat] : ((ord_less @ nat @ X0 @ na) => ((hammin1195055315smooth @ X0) => (member @ nat @ X0 @ (coinductive_lset @ nat @ hammin2015774020amming))))),
% 0.54/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_less_OIH)).
% 0.54/0.39 thf(f280,conjecture,(
% 0.54/0.39 (member @ nat @ n2 @ (coinductive_lset @ nat @ hammin2015774020amming))),
% 0.54/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 0.54/0.39 thf(f281,negated_conjecture,(
% 0.54/0.39 ~(member @ nat @ n2 @ (coinductive_lset @ nat @ hammin2015774020amming))),
% 0.54/0.39 inference(negated_conjecture,[status(cth)],[f280])).
% 0.54/0.39 thf(f296,plain,(
% 0.54/0.39 (hammin1195055315smooth @ n2)),
% 0.54/0.39 inference(rectify,[],[f1])).
% 0.54/0.39 thf(f297,plain,(
% 0.54/0.39 (((hammin1195055315smooth @ n2)) = $true)),
% 0.54/0.39 inference(fool_elimination,[],[f296])).
% 0.54/0.39 thf(f604,plain,(
% 0.54/0.39 ! [X0 : nat] : ((ord_less @ nat @ X0 @ na) => ((hammin1195055315smooth @ X0) => (member @ nat @ X0 @ (coinductive_lset @ nat @ hammin2015774020amming))))),
% 0.54/0.39 inference(rectify,[],[f3])).
% 0.54/0.39 thf(f605,plain,(
% 0.54/0.39 ! [X0 : nat] : ((((ord_less @ nat @ X0 @ na)) = $true) => ((((hammin1195055315smooth @ X0)) = $true) => (((member @ nat @ X0 @ (coinductive_lset @ nat @ hammin2015774020amming))) = $true)))),
% 0.54/0.39 inference(fool_elimination,[],[f604])).
% 0.54/0.39 thf(f652,plain,(
% 0.54/0.39 (ord_less @ nat @ n2 @ na)),
% 0.54/0.39 inference(rectify,[],[f2])).
% 0.54/0.39 thf(f653,plain,(
% 0.54/0.39 (((ord_less @ nat @ n2 @ na)) = $true)),
% 0.54/0.39 inference(fool_elimination,[],[f652])).
% 0.54/0.39 thf(f800,plain,(
% 0.54/0.39 ~(member @ nat @ n2 @ (coinductive_lset @ nat @ hammin2015774020amming))),
% 0.54/0.39 inference(rectify,[],[f281])).
% 0.54/0.39 thf(f801,plain,(
% 0.54/0.39 ~ (((member @ nat @ n2 @ (coinductive_lset @ nat @ hammin2015774020amming))) = $true)),
% 0.54/0.39 inference(fool_elimination,[],[f800])).
% 0.54/0.39 thf(f820,plain,(
% 0.54/0.39 (((member @ nat @ n2 @ (coinductive_lset @ nat @ hammin2015774020amming))) != $true)),
% 0.54/0.39 inference(flattening,[],[f801])).
% 0.54/0.39 thf(f854,plain,(
% 0.54/0.39 ! [X0 : nat] : (((((member @ nat @ X0 @ (coinductive_lset @ nat @ hammin2015774020amming))) = $true) | (((hammin1195055315smooth @ X0)) != $true)) | (((ord_less @ nat @ X0 @ na)) != $true))),
% 0.54/0.39 inference(ennf_transformation,[],[f605])).
% 0.54/0.39 thf(f855,plain,(
% 0.54/0.39 ! [X0 : nat] : ((((hammin1195055315smooth @ X0)) != $true) | (((ord_less @ nat @ X0 @ na)) != $true) | (((member @ nat @ X0 @ (coinductive_lset @ nat @ hammin2015774020amming))) = $true))),
% 0.54/0.39 inference(flattening,[],[f854])).
% 0.54/0.39 thf(f901,plain,(
% 0.54/0.39 ( ! [X0 : nat] : ((((member @ nat @ X0 @ (coinductive_lset @ nat @ hammin2015774020amming))) = $true) | (((ord_less @ nat @ X0 @ na)) != $true) | (((hammin1195055315smooth @ X0)) != $true)) )),
% 0.54/0.39 inference(cnf_transformation,[],[f855])).
% 0.54/0.39 thf(f911,plain,(
% 0.54/0.39 (((hammin1195055315smooth @ n2)) = $true)),
% 0.54/0.39 inference(cnf_transformation,[],[f297])).
% 0.54/0.39 thf(f923,plain,(
% 0.54/0.39 (((member @ nat @ n2 @ (coinductive_lset @ nat @ hammin2015774020amming))) != $true)),
% 0.54/0.39 inference(cnf_transformation,[],[f820])).
% 0.54/0.39 thf(f929,plain,(
% 0.54/0.39 (((ord_less @ nat @ n2 @ na)) = $true)),
% 0.54/0.39 inference(cnf_transformation,[],[f653])).
% 0.54/0.39 thf(f942,plain,(
% 0.54/0.39 (((ord_less @ nat @ n2 @ na)) != $true) | (((hammin1195055315smooth @ n2)) != $true) | ($true != $true)),
% 0.54/0.39 inference(superposition,[],[f923,f901])).
% 0.54/0.39 thf(f944,plain,(
% 0.54/0.39 (((ord_less @ nat @ n2 @ na)) != $true) | (((hammin1195055315smooth @ n2)) != $true)),
% 0.54/0.39 inference(trivial_inequality_removal,[],[f942])).
% 0.54/0.39 thf(f946,plain,(
% 0.54/0.39 (((hammin1195055315smooth @ n2)) != $true)),
% 0.54/0.39 inference(forward_subsumption_resolution,[],[f944,f929])).
% 0.54/0.39 thf(f947,plain,(
% 0.54/0.39 $false),
% 0.54/0.39 inference(forward_subsumption_resolution,[],[f946,f911])).
% 0.54/0.39 % SZS output end Proof for theBenchmark
% 0.54/0.39 % (451948)------------------------------
% 0.54/0.39 % (451948)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.39 % (451948)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.39 % (451948)CaDiCaL version: 2.1.3
% 0.54/0.39 % (451948)Termination reason: Refutation
% 0.54/0.39 % (451948)Time elapsed: 0.010 s
% 0.54/0.39 % (451948)Peak memory usage: 13 MB
% 0.54/0.39 % (451948)Instructions burned: 39 (million)
% 0.54/0.39 % (451915)Success in time 0.115 s
% 0.54/0.39 % Vampire exiting
%------------------------------------------------------------------------------