%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT140^1 : 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 : 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 07:48:24 AM UTC 2026
% Result : Theorem 0.48s 0.39s
% Output : Refutation 0.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : DAT140^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n007.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 17:59:11 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.21/0.28 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
% 0.48/0.39 % (3727075)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.48/0.39 % (3727080)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=794224484:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.48/0.39 % (3727086)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.48/0.39 % (3727086)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
% 0.48/0.39 % (3727082)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2532374090:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.48/0.39 % (3727084)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3998006868:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.48/0.39 % (3727083)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=2519922548: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)
% 0.48/0.39 % (3727085)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=581949737:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.48/0.39 % (3727086)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=112583508:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.48/0.39 % (3727081)lrs+10_16_si=on:nwc=1.5:random_seed=521899149:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.48/0.39 % (3727082)Instruction limit reached!
% 0.48/0.39 % (3727082)------------------------------
% 0.48/0.39 % (3727082)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.39 % (3727082)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.39 % (3727082)CaDiCaL version: 2.1.3
% 0.48/0.39 % (3727082)Termination reason: Instruction limit
% 0.48/0.39 % (3727082)Termination phase: shuffling
% 0.48/0.39 % (3727082)Time elapsed: 0.003 s
% 0.48/0.39 % (3727082)Peak memory usage: 10 MB
% 0.48/0.39 % (3727082)Instructions burned: 4 (million)
% 0.48/0.39 % (3727081)Instruction limit reached!
% 0.48/0.39 % (3727081)------------------------------
% 0.48/0.39 % (3727081)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.39 % (3727081)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.39 % (3727081)CaDiCaL version: 2.1.3
% 0.48/0.39 % (3727081)Termination reason: Instruction limit
% 0.48/0.39 % (3727081)Termination phase: Property scanning
% 0.48/0.39 % (3727081)Time elapsed: 0.010 s
% 0.48/0.39 % (3727081)Peak memory usage: 10 MB
% 0.48/0.39 % (3727081)Instructions burned: 19 (million)
% 0.48/0.39 % (3727084)Instruction limit reached!
% 0.48/0.39 % (3727084)------------------------------
% 0.48/0.39 % (3727084)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.39 % (3727084)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.39 % (3727084)CaDiCaL version: 2.1.3
% 0.48/0.39 % (3727084)Termination reason: Instruction limit
% 0.48/0.39 % (3727084)Termination phase: Property scanning
% 0.48/0.39 % (3727084)Time elapsed: 0.011 s
% 0.48/0.39 % (3727084)Peak memory usage: 10 MB
% 0.48/0.39 % (3727084)Instructions burned: 24 (million)
% 0.48/0.39 % (3727080)Instruction limit reached!
% 0.48/0.39 % (3727080)------------------------------
% 0.48/0.39 % (3727080)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.39 % (3727080)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.39 % (3727080)CaDiCaL version: 2.1.3
% 0.48/0.39 % (3727080)Termination reason: Instruction limit
% 0.48/0.39 % (3727080)Termination phase: Property scanning
% 0.48/0.39 % (3727080)Time elapsed: 0.023 s
% 0.48/0.39 % (3727080)Peak memory usage: 12 MB
% 0.48/0.39 % (3727080)Instructions burned: 92 (million)
% 0.48/0.39 % (3727094)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3565582950:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.48/0.39 % (3727097)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3730082242:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.48/0.39 % (3727094)Instruction limit reached!
% 0.48/0.39 % (3727094)------------------------------
% 0.48/0.39 % (3727094)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.39 % (3727094)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.39 % (3727094)CaDiCaL version: 2.1.3
% 0.48/0.39 % (3727094)Termination reason: Instruction limit
% 0.48/0.39 % (3727094)Termination phase: shuffling
% 0.48/0.39 % (3727094)Time elapsed: 0.002 s
% 0.48/0.39 % (3727094)Peak memory usage: 10 MB
% 0.48/0.39 % (3727094)Instructions burned: 3 (million)
% 0.48/0.39 % (3727096)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.48/0.39 % (3727097)Instruction limit reached!
% 0.48/0.39 % (3727097)------------------------------
% 0.48/0.39 % (3727097)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.39 % (3727097)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.39 % (3727097)CaDiCaL version: 2.1.3
% 0.48/0.39 % (3727097)Termination reason: Instruction limit
% 0.48/0.39 % (3727097)Termination phase: shuffling
% 0.48/0.39 % (3727097)Time elapsed: 0.004 s
% 0.48/0.39 % (3727097)Peak memory usage: 10 MB
% 0.48/0.39 % (3727097)Instructions burned: 16 (million)
% 0.48/0.39 % (3727095)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3183595211:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.48/0.39 % (3727096)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2628581230:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.48/0.39 % (3727095)Instruction limit reached!
% 0.48/0.39 % (3727095)------------------------------
% 0.48/0.39 % (3727095)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.39 % (3727095)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.39 % (3727095)CaDiCaL version: 2.1.3
% 0.48/0.39 % (3727095)Termination reason: Instruction limit
% 0.48/0.39 % (3727095)Termination phase: shuffling
% 0.48/0.39 % (3727095)Time elapsed: 0.003 s
% 0.48/0.39 % (3727095)Peak memory usage: 10 MB
% 0.48/0.39 % (3727095)Instructions burned: 6 (million)
% 0.48/0.39 % (3727096)Instruction limit reached!
% 0.48/0.39 % (3727096)------------------------------
% 0.48/0.39 % (3727096)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.39 % (3727096)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.39 % (3727096)CaDiCaL version: 2.1.3
% 0.48/0.39 % (3727096)Termination reason: Instruction limit
% 0.48/0.39 % (3727096)Termination phase: shuffling
% 0.48/0.39 % (3727096)Time elapsed: 0.004 s
% 0.48/0.39 % (3727096)Peak memory usage: 10 MB
% 0.48/0.39 % (3727096)Instructions burned: 8 (million)
% 0.48/0.39 % (3727085)Instruction limit reached!
% 0.48/0.39 % (3727085)------------------------------
% 0.48/0.39 % (3727085)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.39 % (3727085)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.39 % (3727085)CaDiCaL version: 2.1.3
% 0.48/0.39 % (3727085)Termination reason: Instruction limit
% 0.48/0.39 % (3727085)Termination phase: Property scanning
% 0.48/0.39 % (3727085)Time elapsed: 0.036 s
% 0.48/0.39 % (3727085)Peak memory usage: 12 MB
% 0.48/0.39 % (3727085)Instructions burned: 75 (million)
% 0.48/0.39 % (3727101)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=2712941337:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.48/0.39 % (3727100)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
% 0.48/0.39 % (3727100)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.48/0.39 % (3727100)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3441409724:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.48/0.39 % (3727086) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3727075-3727086"...
% 0.48/0.39 % (3727086)...printing done.
% 0.48/0.39 % (3727105)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.48/0.39 % (3727086)Refutation found. Thanks to Tanya!
% 0.48/0.39 % SZS status Theorem for theBenchmark
% 0.48/0.39 % SZS output start Proof for theBenchmark
% 0.48/0.39 thf(type_def_5, type, coinductive_llist: $tType > $tType).
% 0.48/0.39 thf(type_def_6, type, nat: $tType).
% 0.48/0.39 thf(type_def_7, type, itself: $tType > $tType).
% 0.48/0.39 thf(type_def_8, type, a: $tType).
% 0.48/0.39 thf(type_def_9, type, sTfun: ($tType * $tType) > $tType).
% 0.48/0.39 thf(func_def_0, type, type: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.48/0.39 thf(func_def_1, type, ord: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.48/0.39 thf(func_def_2, type, order: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.48/0.39 thf(func_def_3, type, no_bot: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.48/0.39 thf(func_def_4, type, no_top: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.48/0.39 thf(func_def_5, type, linorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.48/0.39 thf(func_def_6, type, preorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.48/0.39 thf(func_def_7, type, wellorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.48/0.39 thf(func_def_8, type, dense_order: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.48/0.39 thf(func_def_9, type, dense_linorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.48/0.39 thf(func_def_10, type, comple187826305attice: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.48/0.39 thf(func_def_11, type, condit1656338222tinuum: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.48/0.39 thf(func_def_12, type, condit1037483654norder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.48/0.39 thf(func_def_13, type, coindu328551480prefix: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > $o))).
% 0.48/0.39 thf(func_def_14, type, coinductive_lappend: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.48/0.39 thf(func_def_15, type, coinductive_lfinite: !>[X0: $tType]:((coinductive_llist @ X0 > $o))).
% 0.48/0.39 thf(func_def_16, type, coinductive_llast: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 0.48/0.39 thf(func_def_17, type, coinductive_LCons: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.48/0.39 thf(func_def_18, type, coinductive_LNil: !>[X0: $tType]:(coinductive_llist @ X0)).
% 0.48/0.39 thf(func_def_19, type, coinductive_lnull: !>[X0: $tType]:((coinductive_llist @ X0 > $o))).
% 0.48/0.39 thf(func_def_20, type, coinductive_lmember: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > $o))).
% 0.48/0.39 thf(func_def_21, type, coinductive_lprefix: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > $o))).
% 0.48/0.39 thf(func_def_22, type, coindu1478340336prefix: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > $o))).
% 0.48/0.39 thf(func_def_23, type, coindu63249387sorted: !>[X0: $tType]:((coinductive_llist @ X0 > $o))).
% 0.48/0.39 thf(func_def_24, type, hilbert_GreatestM: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > $o) > X0))).
% 0.48/0.39 thf(func_def_25, type, hilbert_LeastM: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > $o) > X0))).
% 0.48/0.39 thf(func_def_26, type, ord_less: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.48/0.39 thf(func_def_27, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.48/0.39 thf(func_def_28, type, order_antimono: !>[X0: $tType, X1: $tType]:(((X0 > X1) > $o))).
% 0.48/0.39 thf(func_def_29, type, order_strict_mono: !>[X0: $tType, X1: $tType]:(((X0 > X1) > $o))).
% 0.48/0.39 thf(func_def_30, type, type2: !>[X0: $tType]:(itself @ X0)).
% 0.48/0.39 thf(func_def_34, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.48/0.39 thf(func_def_35, type, vIMP: ($o > $o > $o)).
% 0.48/0.39 thf(func_def_36, type, db1: !>[X0: $tType]:(X0)).
% 0.48/0.39 thf(func_def_37, type, db0: !>[X0: $tType]:(X0)).
% 0.48/0.39 thf(func_def_38, type, db2: !>[X0: $tType]:(X0)).
% 0.48/0.39 thf(func_def_39, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.48/0.39 thf(func_def_40, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.48/0.39 thf(func_def_41, type, vAND: ($o > $o > $o)).
% 0.48/0.39 thf(func_def_42, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.48/0.39 thf(func_def_43, type, vNOT: ($o > $o)).
% 0.48/0.39 thf(func_def_44, type, vOR: ($o > $o > $o)).
% 0.48/0.39 thf(func_def_45, type, db3: !>[X0: $tType]:(X0)).
% 0.48/0.39 thf(func_def_46, type, db4: !>[X0: $tType]:(X0)).
% 0.48/0.39 thf(func_def_47, type, sP0: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > $o) > (X0 > $o) > $o))).
% 0.48/0.39 thf(func_def_48, type, sP1: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > $o))).
% 0.48/0.39 thf(func_def_49, type, sP2: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.48/0.39 thf(func_def_50, type, sP3: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.48/0.39 thf(func_def_51, type, sP4: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.48/0.39 thf(func_def_52, type, sP5: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.48/0.39 thf(func_def_53, type, sP6: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.48/0.39 thf(func_def_54, type, sP7: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > $o))).
% 0.48/0.39 thf(func_def_55, type, sP8: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > $o))).
% 0.48/0.39 thf(func_def_56, type, sP9: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > $o))).
% 0.48/0.39 thf(func_def_57, type, sP10: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.48/0.39 thf(func_def_58, type, sP11: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > $o))).
% 0.48/0.39 thf(func_def_59, type, sP12: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (coinductive_llist @ X0 > coinductive_llist @ X0 > $o) > $o))).
% 0.48/0.39 thf(func_def_60, type, sP13: !>[X0: $tType]:(((coinductive_llist @ X0 > coinductive_llist @ X0 > $o) > $o))).
% 0.48/0.39 thf(func_def_61, type, sP14: !>[X0: $tType]:(((X0 > X0 > $o) > $o))).
% 0.48/0.39 thf(func_def_62, type, sP15: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > $o))).
% 0.48/0.39 thf(func_def_63, type, sP16: !>[X0: $tType]:((X0 > (X0 > $o) > X0 > $o))).
% 0.48/0.39 thf(func_def_64, type, sP17: !>[X0: $tType]:((X0 > X0 > (X0 > $o) > $o))).
% 0.48/0.39 thf(func_def_65, type, sP18: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > $o))).
% 0.48/0.39 thf(func_def_66, type, sP19: !>[X0: $tType]:(((X0 > X0 > $o) > $o))).
% 0.48/0.39 thf(func_def_67, type, sP20: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > $o))).
% 0.48/0.39 thf(func_def_68, type, sP21: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > coinductive_llist @ X0 > $o))).
% 0.48/0.39 thf(func_def_69, type, sP22: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > $o))).
% 0.48/0.39 thf(func_def_70, type, sP23: !>[X0: $tType, X1: $tType]:(((X0 > $o) > (X0 > X1) > (X0 > $o) > $o))).
% 0.48/0.39 thf(func_def_71, type, sP24: !>[X0: $tType]:((coinductive_llist @ X0 > $o))).
% 0.48/0.39 thf(func_def_72, type, sP25: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > $o))).
% 0.48/0.39 thf(func_def_73, type, sP26: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.48/0.39 thf(func_def_74, type, sP27: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > $o))).
% 0.48/0.39 thf(func_def_75, type, sK28: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.48/0.39 thf(func_def_76, type, sK29: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.48/0.39 thf(func_def_77, type, sK30: !>[X0: $tType]:((X0 > X0))).
% 0.48/0.39 thf(func_def_78, type, sK31: !>[X0: $tType]:((X0 > X0))).
% 0.48/0.39 thf(func_def_79, type, sK32: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > $o) > (X0 > $o) > X0))).
% 0.48/0.39 thf(func_def_80, type, sK33: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > $o) > X0 > X0))).
% 0.48/0.39 thf(func_def_81, type, sK34: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.48/0.39 thf(func_def_82, type, sK35: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > X0))).
% 0.48/0.39 thf(func_def_83, type, sK36: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.48/0.39 thf(func_def_84, type, sK37: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.48/0.39 thf(func_def_85, type, sK38: !>[X0: $tType]:((X0 > X0))).
% 0.48/0.39 thf(func_def_86, type, sK39: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > X0))).
% 0.48/0.39 thf(func_def_87, type, sK40: !>[X0: $tType]:(((X0 > $o) > nat > (X0 > nat) > X0))).
% 0.48/0.39 thf(func_def_88, type, sK41: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.48/0.39 thf(func_def_89, type, sK42: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.48/0.39 thf(func_def_90, type, sK43: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 0.48/0.39 thf(func_def_91, type, sK44: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.48/0.39 thf(func_def_92, type, sK45: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.48/0.39 thf(func_def_93, type, sK46: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 0.48/0.39 thf(func_def_94, type, sK47: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.48/0.39 thf(func_def_95, type, sK48: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.48/0.39 thf(func_def_96, type, sK49: !>[X0: $tType]:((X0 > X0 > X0 > X0))).
% 0.48/0.39 thf(func_def_97, type, sK50: !>[X0: $tType]:(((X0 > $o) > (X0 > nat) > X0))).
% 0.48/0.39 thf(func_def_98, type, sK51: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > X0))).
% 0.48/0.39 thf(func_def_99, type, sK52: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.48/0.39 thf(func_def_100, type, sK53: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.48/0.39 thf(func_def_101, type, sK54: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.48/0.39 thf(func_def_102, type, sK55: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.48/0.39 thf(func_def_103, type, sK56: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.48/0.39 thf(func_def_104, type, sK57: !>[X0: $tType]:(((coinductive_llist @ X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.48/0.39 thf(func_def_105, type, sK58: !>[X0: $tType]:(((coinductive_llist @ X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.48/0.39 thf(func_def_106, type, sK59: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.48/0.39 thf(func_def_107, type, sK60: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.48/0.39 thf(func_def_108, type, sK61: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.48/0.39 thf(func_def_109, type, sK62: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.48/0.39 thf(func_def_110, type, sK63: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.48/0.39 thf(func_def_111, type, sK64: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.48/0.39 thf(func_def_112, type, sK65: !>[X0: $tType]:((X0 > X0))).
% 0.48/0.39 thf(func_def_113, type, sK66: !>[X0: $tType]:((X0 > X0))).
% 0.48/0.39 thf(func_def_114, type, sK67: !>[X0: $tType, X1: $tType]:((X1 > X0))).
% 0.48/0.39 thf(func_def_115, type, sK68: !>[X0: $tType, X1: $tType]:((X0 > X1))).
% 0.48/0.39 thf(func_def_116, type, sK69: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.48/0.39 thf(func_def_117, type, sK70: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.48/0.39 thf(func_def_118, type, sK71: !>[X0: $tType]:(((X0 > $o) > (X0 > nat) > nat > X0))).
% 0.48/0.39 thf(func_def_119, type, sK72: !>[X0: $tType]:((X0 > X0 > (X0 > $o) > X0))).
% 0.48/0.39 thf(func_def_120, type, sK73: !>[X0: $tType]:((X0 > (X0 > $o) > X0 > X0))).
% 0.48/0.39 thf(func_def_121, type, sK74: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.48/0.39 thf(func_def_122, type, sK75: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.48/0.39 thf(func_def_123, type, sK76: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 0.48/0.39 thf(func_def_124, type, sK77: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.48/0.39 thf(func_def_125, type, sK78: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 0.48/0.39 thf(func_def_126, type, sK79: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.48/0.39 thf(func_def_127, type, sK80: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.48/0.39 thf(func_def_128, type, sK81: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.48/0.39 thf(func_def_129, type, sK82: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.48/0.39 thf(func_def_130, type, sK83: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > nat > X0))).
% 0.48/0.39 thf(func_def_131, type, sK84: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.48/0.39 thf(func_def_132, type, sK85: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.48/0.39 thf(func_def_133, type, sK86: !>[X0: $tType]:((X0 > X0))).
% 0.48/0.39 thf(func_def_134, type, sK87: !>[X0: $tType]:((X0 > X0))).
% 0.48/0.39 thf(func_def_135, type, sK88: !>[X0: $tType]:((X0 > X0))).
% 0.48/0.39 thf(func_def_136, type, sK89: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.48/0.39 thf(func_def_137, type, sK90: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.48/0.39 thf(func_def_138, type, sK91: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > X0))).
% 0.48/0.39 thf(func_def_139, type, sK92: !>[X0: $tType]:((X0 > X0))).
% 0.48/0.39 thf(func_def_140, type, sK93: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.48/0.39 thf(func_def_141, type, sK94: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.48/0.39 thf(func_def_142, type, sK95: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.48/0.39 thf(func_def_143, type, sK96: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.48/0.39 thf(func_def_144, type, sK97: !>[X0: $tType, X1: $tType]:(((X0 > $o) > (X0 > X1) > (X0 > $o) > X0))).
% 0.48/0.39 thf(func_def_145, type, sK98: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1 > (X1 > $o) > X1))).
% 0.48/0.39 thf(func_def_146, type, sK99: !>[X0: $tType]:((X0 > X0))).
% 0.48/0.39 thf(func_def_147, type, sK100: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.48/0.39 thf(func_def_148, type, sK101: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.48/0.39 thf(func_def_149, type, sK102: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 0.48/0.39 thf(func_def_150, type, sK103: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 0.48/0.39 thf(func_def_151, type, sK104: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.48/0.39 thf(func_def_152, type, sK105: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 0.48/0.39 thf(func_def_153, type, sK106: ((nat > nat) > nat)).
% 0.48/0.39 thf(func_def_154, type, sK107: ((nat > nat) > nat)).
% 0.48/0.39 thf(func_def_155, type, sK108: !>[X0: $tType]:((X0 > X0))).
% 0.48/0.39 thf(func_def_156, type, sK109: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 0.48/0.39 thf(func_def_157, type, sK110: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.48/0.39 thf(func_def_158, type, sK111: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.48/0.39 thf(func_def_159, type, sK112: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.48/0.39 thf(func_def_160, type, sK113: !>[X0: $tType]:((X0 > X0))).
% 0.48/0.39 thf(func_def_161, type, sK114: !>[X0: $tType]:((X0 > X0))).
% 0.48/0.39 thf(func_def_162, type, sK115: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > X0))).
% 0.48/0.39 thf(func_def_163, type, sK116: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.48/0.39 thf(func_def_164, type, sK117: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.48/0.39 thf(func_def_165, type, sK118: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.48/0.39 thf(func_def_166, type, sK119: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.48/0.39 thf(func_def_167, type, sK120: !>[X0: $tType]:((X0 > X0 > X0 > X0))).
% 0.48/0.39 thf(func_def_168, type, sK121: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.48/0.39 thf(func_def_169, type, sK122: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.48/0.39 thf(func_def_170, type, sK123: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.48/0.39 thf(func_def_171, type, sK124: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.48/0.39 thf(func_def_172, type, sK125: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > X0))).
% 0.48/0.39 thf(func_def_173, type, sK126: !>[X0: $tType]:((X0 > X0))).
% 0.48/0.39 thf(func_def_174, type, sK127: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.48/0.39 thf(func_def_175, type, sK128: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.48/0.39 thf(func_def_176, type, sK129: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 0.48/0.39 thf(func_def_177, type, sK130: !>[X0: $tType]:((X0 > X0))).
% 0.48/0.39 thf(func_def_178, type, sK131: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.48/0.39 thf(func_def_179, type, sK132: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.48/0.39 thf(func_def_180, type, sK133: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.48/0.39 thf(func_def_181, type, sK134: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.48/0.39 thf(func_def_182, type, sK135: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > X0 > coinductive_llist @ X0))).
% 0.48/0.39 thf(func_def_183, type, sK136: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.48/0.39 thf(func_def_184, type, sK137: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 0.48/0.39 thf(f1,axiom,(
% 0.48/0.39 ! [X0 : $tType] : (ord_less_eq @ coinductive_llist @ X0 = coinductive_lprefix @ X0)),
% 0.48/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_less__eq__llist__def)).
% 0.48/0.39 thf(f274,conjecture,(
% 0.48/0.39 (ord_less_eq @ coinductive_llist @ a = coinductive_lprefix @ a)),
% 0.48/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 0.48/0.39 thf(f275,negated_conjecture,(
% 0.48/0.39 ~ (ord_less_eq @ coinductive_llist @ a = coinductive_lprefix @ a)),
% 0.48/0.39 inference(negated_conjecture,[status(cth)],[f274])).
% 0.48/0.39 thf(f819,plain,(
% 0.48/0.39 (ord_less_eq @ coinductive_llist @ a != coinductive_lprefix @ a)),
% 0.48/0.39 inference(flattening,[],[f275])).
% 0.48/0.39 thf(f1463,plain,(
% 0.48/0.39 ( ! [X0 : $tType] : ((ord_less_eq @ coinductive_llist @ X0 = coinductive_lprefix @ X0)) )),
% 0.48/0.39 inference(cnf_transformation,[],[f1])).
% 0.48/0.39 thf(f1719,plain,(
% 0.48/0.39 (ord_less_eq @ coinductive_llist @ a != coinductive_lprefix @ a)),
% 0.48/0.39 inference(cnf_transformation,[],[f819])).
% 0.48/0.39 thf(f1882,plain,(
% 0.48/0.39 (ord_less_eq @ coinductive_llist @ a != ord_less_eq @ coinductive_llist @ a)),
% 0.48/0.39 inference(definition_unfolding,[],[f1719,f1463])).
% 0.48/0.39 thf(f2262,plain,(
% 0.48/0.39 $false),
% 0.48/0.39 inference(trivial_inequality_removal,[],[f1882])).
% 0.48/0.39 % SZS output end Proof for theBenchmark
% 0.48/0.39 % (3727086)------------------------------
% 0.48/0.39 % (3727086)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.39 % (3727086)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.39 % (3727086)CaDiCaL version: 2.1.3
% 0.48/0.39 % (3727086)Termination reason: Refutation
% 0.48/0.39 % (3727086)Time elapsed: 0.048 s
% 0.48/0.39 % (3727086)Peak memory usage: 13 MB
% 0.48/0.39 % (3727086)Instructions burned: 101 (million)
% 0.48/0.39 % (3727075)Success in time 0.104 s
% 0.48/0.39 % Vampire exiting
%------------------------------------------------------------------------------