%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT189^1 : 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 : n013.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 07:48:30 AM UTC 2026
% Result : Theorem 0.45s 0.38s
% Output : Refutation 0.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT189^1 : 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 : n013.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 18:06:21 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.22/0.28 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
% 0.45/0.38 % (2457645)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.45/0.38 % (2457665)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=1436067649: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)
% 0.45/0.38 % (2457668)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.45/0.38 % (2457668)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
% 0.45/0.38 % (2457662)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4131663460:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.45/0.38 % (2457663)lrs+10_16_si=on:nwc=1.5:random_seed=2933192652:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.45/0.38 % (2457664)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1866832023:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.45/0.38 % (2457668)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=2425724920:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.45/0.38 % (2457666)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=13998577:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.45/0.38 % (2457664)Instruction limit reached!
% 0.45/0.38 % (2457664)------------------------------
% 0.45/0.38 % (2457664)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.45/0.38 % (2457664)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.45/0.38 % (2457664)CaDiCaL version: 2.1.3
% 0.45/0.38 % (2457664)Termination reason: Instruction limit
% 0.45/0.38 % (2457664)Termination phase: shuffling
% 0.45/0.38 % (2457664)Time elapsed: 0.002 s
% 0.45/0.38 % (2457664)Peak memory usage: 10 MB
% 0.45/0.38 % (2457664)Instructions burned: 4 (million)
% 0.45/0.38 % (2457667)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3078806911:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.45/0.38 % (2457663)Instruction limit reached!
% 0.45/0.38 % (2457663)------------------------------
% 0.45/0.38 % (2457663)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.45/0.38 % (2457663)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.45/0.38 % (2457663)CaDiCaL version: 2.1.3
% 0.45/0.38 % (2457663)Termination reason: Instruction limit
% 0.45/0.38 % (2457663)Termination phase: shuffling
% 0.45/0.38 % (2457663)Time elapsed: 0.010 s
% 0.45/0.38 % (2457663)Peak memory usage: 10 MB
% 0.45/0.38 % (2457663)Instructions burned: 19 (million)
% 0.45/0.38 % (2457666)Instruction limit reached!
% 0.45/0.38 % (2457666)------------------------------
% 0.45/0.38 % (2457666)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.45/0.38 % (2457666)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.45/0.38 % (2457666)CaDiCaL version: 2.1.3
% 0.45/0.38 % (2457666)Termination reason: Instruction limit
% 0.45/0.38 % (2457666)Termination phase: Property scanning
% 0.45/0.38 % (2457666)Time elapsed: 0.013 s
% 0.45/0.38 % (2457666)Peak memory usage: 10 MB
% 0.45/0.38 % (2457666)Instructions burned: 24 (million)
% 0.45/0.38 % (2457682)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=371301564:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.45/0.38 % (2457682)Instruction limit reached!
% 0.45/0.38 % (2457682)------------------------------
% 0.45/0.38 % (2457682)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.45/0.38 % (2457682)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.45/0.38 % (2457682)CaDiCaL version: 2.1.3
% 0.45/0.38 % (2457682)Termination reason: Instruction limit
% 0.45/0.38 % (2457682)Termination phase: shuffling
% 0.45/0.38 % (2457682)Time elapsed: 0.002 s
% 0.45/0.38 % (2457682)Peak memory usage: 10 MB
% 0.45/0.38 % (2457682)Instructions burned: 3 (million)
% 0.45/0.38 % (2457665) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2457645-2457665"...
% 0.45/0.38 % (2457665)...printing done.
% 0.45/0.38 % (2457665)Refutation found. Thanks to Tanya!
% 0.45/0.38 % SZS status Theorem for theBenchmark
% 0.45/0.38 % SZS output start Proof for theBenchmark
% 0.45/0.38 thf(type_def_5, type, coinductive_llist: $tType > $tType).
% 0.45/0.38 thf(type_def_6, type, set: $tType > $tType).
% 0.45/0.38 thf(type_def_7, type, itself: $tType > $tType).
% 0.45/0.38 thf(type_def_8, type, a: $tType).
% 0.45/0.38 thf(type_def_9, type, sTfun: ($tType * $tType) > $tType).
% 0.45/0.38 thf(func_def_0, type, type: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.45/0.38 thf(func_def_1, type, ord: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.45/0.38 thf(func_def_2, type, order: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.45/0.38 thf(func_def_3, type, linorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.45/0.38 thf(func_def_4, type, preorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.45/0.38 thf(func_def_5, type, coindu328551480prefix: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > $o))).
% 0.45/0.38 thf(func_def_6, type, coinductive_gen_lset: !>[X0: $tType]:((set @ X0 > coinductive_llist @ X0 > set @ X0))).
% 0.45/0.38 thf(func_def_7, type, coinductive_lappend: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.45/0.38 thf(func_def_8, type, coinductive_lfinite: !>[X0: $tType]:((coinductive_llist @ X0 > $o))).
% 0.45/0.38 thf(func_def_9, type, coinductive_llast: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 0.45/0.38 thf(func_def_10, type, coinductive_llexord: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > $o))).
% 0.45/0.38 thf(func_def_11, type, coinductive_LCons: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.45/0.38 thf(func_def_12, type, coinductive_LNil: !>[X0: $tType]:(coinductive_llist @ X0)).
% 0.45/0.38 thf(func_def_13, type, coindu1259883913_llist: !>[X0: $tType, X1: $tType]:(((X0 > $o) > (X0 > X1) > (X0 > $o) > (X0 > coinductive_llist @ X1) > (X0 > X0) > X0 > coinductive_llist @ X1))).
% 0.45/0.38 thf(func_def_14, type, coinductive_lhd: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 0.45/0.38 thf(func_def_15, type, coinductive_lnull: !>[X0: $tType]:((coinductive_llist @ X0 > $o))).
% 0.45/0.38 thf(func_def_16, type, coinductive_ltl: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.45/0.38 thf(func_def_17, type, coinductive_lmember: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > $o))).
% 0.45/0.38 thf(func_def_18, type, coinductive_lprefix: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > $o))).
% 0.45/0.38 thf(func_def_19, type, coindu1478340336prefix: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > $o))).
% 0.45/0.38 thf(func_def_20, type, coindu501562517eWhile: !>[X0: $tType]:(((X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.45/0.38 thf(func_def_21, type, coindu63249387sorted: !>[X0: $tType]:((coinductive_llist @ X0 > $o))).
% 0.45/0.38 thf(func_def_22, type, coindu1441602521_llist: !>[X0: $tType, X1: $tType]:(((X0 > $o) > (X0 > X1) > (X0 > X0) > X0 > coinductive_llist @ X1))).
% 0.45/0.38 thf(func_def_23, type, undefined: !>[X0: $tType]:(X0)).
% 0.45/0.38 thf(func_def_24, type, if: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 0.45/0.38 thf(func_def_25, type, lMirro427583474mirror: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.45/0.38 thf(func_def_26, type, lMirro999291890or_aux: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.45/0.38 thf(func_def_27, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.45/0.38 thf(func_def_28, type, type2: !>[X0: $tType]:(itself @ X0)).
% 0.45/0.38 thf(func_def_29, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.45/0.38 thf(func_def_30, type, insert: !>[X0: $tType]:((X0 > set @ X0 > set @ X0))).
% 0.45/0.38 thf(func_def_31, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.45/0.38 thf(func_def_32, type, acc: coinductive_llist @ a).
% 0.45/0.38 thf(func_def_33, type, xs: coinductive_llist @ a).
% 0.45/0.38 thf(func_def_37, type, vOR: ($o > $o > $o)).
% 0.45/0.38 thf(func_def_38, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.45/0.38 thf(func_def_39, type, vAND: ($o > $o > $o)).
% 0.45/0.38 thf(func_def_40, type, db2: !>[X0: $tType]:(X0)).
% 0.45/0.38 thf(func_def_41, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.45/0.38 thf(func_def_42, type, db1: !>[X0: $tType]:(X0)).
% 0.45/0.38 thf(func_def_43, type, db0: !>[X0: $tType]:(X0)).
% 0.45/0.38 thf(func_def_44, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.45/0.38 thf(func_def_45, type, db4: !>[X0: $tType]:(X0)).
% 0.45/0.38 thf(func_def_46, type, db3: !>[X0: $tType]:(X0)).
% 0.45/0.38 thf(func_def_47, type, vIMP: ($o > $o > $o)).
% 0.45/0.38 thf(func_def_48, type, vNOT: ($o > $o)).
% 0.45/0.38 thf(func_def_49, type, db5: !>[X0: $tType]:(X0)).
% 0.45/0.38 thf(func_def_50, type, db6: !>[X0: $tType]:(X0)).
% 0.45/0.38 thf(func_def_51, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.45/0.38 thf(func_def_52, type, sP0: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > $o))).
% 0.45/0.38 thf(func_def_53, type, sP1: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.45/0.38 thf(func_def_54, type, sP2: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.45/0.38 thf(func_def_55, type, sK3: !>[X0: $tType]:(((coinductive_llist @ X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.45/0.38 thf(func_def_56, type, sK4: !>[X0: $tType]:(((coinductive_llist @ X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.45/0.38 thf(func_def_57, type, sK5: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.45/0.38 thf(func_def_58, type, sK6: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 0.45/0.38 thf(func_def_59, type, sK7: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > X0))).
% 0.45/0.38 thf(func_def_60, type, sK8: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.45/0.38 thf(func_def_61, type, sK9: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.45/0.38 thf(func_def_62, type, sK10: !>[X0: $tType]:(((coinductive_llist @ X0 > coinductive_llist @ X0 > $o) > (X0 > X0 > $o) > coinductive_llist @ X0))).
% 0.45/0.38 thf(func_def_63, type, sK11: !>[X0: $tType]:(((coinductive_llist @ X0 > coinductive_llist @ X0 > $o) > (X0 > X0 > $o) > coinductive_llist @ X0))).
% 0.45/0.38 thf(func_def_64, type, sK12: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.45/0.38 thf(func_def_65, type, sK13: !>[X0: $tType]:((X0 > set @ X0 > set @ X0 > X0 > set @ X0))).
% 0.45/0.38 thf(func_def_66, type, sK14: !>[X0: $tType]:((X0 > set @ X0 > set @ X0))).
% 0.45/0.38 thf(func_def_67, type, sK15: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.45/0.38 thf(func_def_68, type, sK16: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.45/0.38 thf(func_def_69, type, sK17: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.45/0.38 thf(func_def_70, type, sK18: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.45/0.38 thf(func_def_71, type, sK19: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.45/0.38 thf(func_def_72, type, sK20: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 0.45/0.38 thf(func_def_73, type, sK21: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.45/0.38 thf(func_def_74, type, sK22: !>[X0: $tType]:(((coinductive_llist @ X0 > coinductive_llist @ X0 > $o) > (X0 > X0 > $o) > coinductive_llist @ X0))).
% 0.45/0.38 thf(func_def_75, type, sK23: !>[X0: $tType]:(((coinductive_llist @ X0 > coinductive_llist @ X0 > $o) > (X0 > X0 > $o) > coinductive_llist @ X0))).
% 0.45/0.38 thf(func_def_76, type, sK24: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.45/0.38 thf(func_def_77, type, sK25: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.45/0.38 thf(func_def_78, type, sK26: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 0.45/0.38 thf(func_def_79, type, sK27: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.45/0.38 thf(func_def_80, type, sK28: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.45/0.38 thf(func_def_81, type, sK29: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > X0 > coinductive_llist @ X0 > X0))).
% 0.45/0.38 thf(func_def_82, type, sK30: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > X0 > coinductive_llist @ X0))).
% 0.45/0.38 thf(func_def_83, type, sK31: !>[X0: $tType]:(((coinductive_llist @ X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.45/0.38 thf(func_def_84, type, sK32: !>[X0: $tType]:(((coinductive_llist @ X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.45/0.38 thf(func_def_85, type, sK33: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.45/0.38 thf(func_def_86, type, sK34: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.45/0.38 thf(func_def_87, type, sK35: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.45/0.38 thf(func_def_88, type, sK36: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.45/0.38 thf(func_def_89, type, sK37: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.45/0.38 thf(func_def_90, type, sK38: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.45/0.38 thf(func_def_91, type, sK39: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.45/0.38 thf(func_def_92, type, sK40: !>[X0: $tType]:(((coinductive_llist @ X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.45/0.38 thf(func_def_93, type, sK41: !>[X0: $tType]:(((coinductive_llist @ X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.45/0.38 thf(func_def_94, type, sK42: !>[X0: $tType]:((X0 > set @ X0 > set @ X0))).
% 0.45/0.38 thf(func_def_95, type, sK43: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.45/0.38 thf(func_def_96, type, sK44: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 0.45/0.38 thf(func_def_97, type, sK45: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.45/0.38 thf(func_def_98, type, sK46: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.45/0.38 thf(func_def_99, type, sK47: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 0.45/0.38 thf(func_def_100, type, sK48: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 0.45/0.38 thf(func_def_101, type, sK49: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.45/0.38 thf(func_def_102, type, sK50: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 0.45/0.38 thf(func_def_103, type, sK51: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.45/0.38 thf(func_def_104, type, sK52: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > X0))).
% 0.45/0.38 thf(func_def_105, type, sK53: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.45/0.38 thf(func_def_106, type, sK54: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.45/0.38 thf(func_def_107, type, sK55: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.45/0.38 thf(func_def_108, type, sK56: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > X0))).
% 0.45/0.38 thf(func_def_109, type, sK57: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.45/0.38 thf(func_def_110, type, sK58: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.45/0.38 thf(func_def_111, type, sK59: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.45/0.38 thf(func_def_112, type, sK60: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.45/0.38 thf(func_def_113, type, sK61: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.45/0.38 thf(func_def_114, type, sK62: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.45/0.38 thf(func_def_115, type, sK63: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > X0 > coinductive_llist @ X0))).
% 0.45/0.38 thf(func_def_116, type, sK64: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.45/0.38 thf(func_def_117, type, sK65: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.45/0.38 thf(func_def_118, type, sK66: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.45/0.38 thf(func_def_119, type, sK67: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > X0))).
% 0.45/0.38 thf(func_def_120, type, sK68: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.45/0.38 thf(func_def_121, type, sK69: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > X0))).
% 0.45/0.38 thf(func_def_122, type, sK70: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0))).
% 0.45/0.38 thf(func_def_123, type, sK71: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > X0))).
% 0.45/0.38 thf(func_def_124, type, sK72: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0))).
% 0.45/0.38 thf(func_def_125, type, sK73: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.45/0.38 thf(func_def_126, type, sK74: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.45/0.38 thf(func_def_127, type, sK75: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > X0))).
% 0.45/0.38 thf(func_def_128, type, sK76: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.45/0.38 thf(func_def_129, type, sK77: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.45/0.38 thf(func_def_130, type, sK78: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.45/0.38 thf(func_def_131, type, sK79: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.45/0.38 thf(func_def_132, type, sK80: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.45/0.38 thf(func_def_133, type, sK81: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > X0))).
% 0.45/0.38 thf(func_def_134, type, sK82: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.45/0.38 thf(f1,axiom,(
% 0.45/0.38 ! [X0 : $tType,X3 : coinductive_llist @ X0,X4 : coinductive_llist @ X0] : (~(coinductive_lnull @ X0 @ X3) | ~(coinductive_lnull @ X0 @ X4) = ~(coinductive_lnull @ X0 @ (lMirro999291890or_aux @ X0 @ X3 @ X4)))),
% 0.45/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_lmirror__aux_Odisc__iff_I2_J)).
% 0.45/0.38 thf(f9,axiom,(
% 0.45/0.38 ! [X0 : $tType,X1 : coinductive_llist @ X0] : (((lMirro999291890or_aux @ X0 @ X1 @ coinductive_LNil @ X0)) = X1)),
% 0.45/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_lmirror__aux__simps_I1_J)).
% 0.45/0.38 thf(f31,axiom,(
% 0.45/0.38 ! [X0 : $tType,X1 : coinductive_llist @ X0] : ((coinductive_lnull @ X0 @ X1) => (X1 = coinductive_LNil @ X0))),
% 0.45/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_llist_Ocollapse_I1_J)).
% 0.45/0.38 thf(f33,axiom,(
% 0.45/0.38 ! [X0 : $tType] : (coinductive_lnull @ X0 @ coinductive_LNil @ X0)),
% 0.45/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_llist_Odisc_I1_J)).
% 0.45/0.38 thf(f268,conjecture,(
% 0.45/0.38 (((coinductive_lnull @ a @ (lMirro999291890or_aux @ a @ acc @ xs))) = (coinductive_lnull @ a @ xs) & (coinductive_lnull @ a @ acc))),
% 0.45/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 0.45/0.38 thf(f269,negated_conjecture,(
% 0.45/0.38 ~ (((coinductive_lnull @ a @ (lMirro999291890or_aux @ a @ acc @ xs))) = (coinductive_lnull @ a @ xs) & (coinductive_lnull @ a @ acc))),
% 0.45/0.38 inference(negated_conjecture,[status(cth)],[f268])).
% 0.45/0.38 thf(f328,plain,(
% 0.45/0.38 ! [X0 : $tType,X1 : coinductive_llist @ X0,X2 : coinductive_llist @ X0] : (~(coinductive_lnull @ X0 @ X1) | ~(coinductive_lnull @ X0 @ X2) = ~(coinductive_lnull @ X0 @ (lMirro999291890or_aux @ X0 @ X1 @ X2)))),
% 0.45/0.38 inference(rectify,[],[f1])).
% 0.45/0.38 thf(f329,plain,(
% 0.45/0.38 ! [X0 : $tType,X1 : coinductive_llist @ X0,X2 : coinductive_llist @ X0] : ((~ (((coinductive_lnull @ X0 @ X1)) = $true) | ~ (((coinductive_lnull @ X0 @ X2)) = $true)) <=> ~ (((coinductive_lnull @ X0 @ (lMirro999291890or_aux @ X0 @ X1 @ X2))) = $true))),
% 0.45/0.38 inference(fool_elimination,[],[f328])).
% 0.45/0.38 thf(f406,plain,(
% 0.45/0.38 ~ (((coinductive_lnull @ a @ (lMirro999291890or_aux @ a @ acc @ xs))) = (coinductive_lnull @ a @ xs) & (coinductive_lnull @ a @ acc))),
% 0.45/0.38 inference(rectify,[],[f269])).
% 0.45/0.38 thf(f407,plain,(
% 0.45/0.38 ~(((((coinductive_lnull @ a @ acc)) = $true) & (((coinductive_lnull @ a @ xs)) = $true)) <=> (((coinductive_lnull @ a @ (lMirro999291890or_aux @ a @ acc @ xs))) = $true))),
% 0.45/0.38 inference(fool_elimination,[],[f406])).
% 0.45/0.38 thf(f447,plain,(
% 0.45/0.38 ! [X0 : $tType,X1 : coinductive_llist @ X0] : ((coinductive_lnull @ X0 @ X1) => (X1 = coinductive_LNil @ X0))),
% 0.45/0.38 inference(rectify,[],[f31])).
% 0.45/0.38 thf(f448,plain,(
% 0.45/0.38 ! [X0 : $tType,X1 : coinductive_llist @ X0] : ((((coinductive_lnull @ X0 @ X1)) = $true) => (coinductive_LNil @ X0 = X1))),
% 0.45/0.38 inference(fool_elimination,[],[f447])).
% 0.45/0.38 thf(f504,plain,(
% 0.45/0.38 ! [X0 : $tType] : (coinductive_lnull @ X0 @ coinductive_LNil @ X0)),
% 0.45/0.38 inference(rectify,[],[f33])).
% 0.45/0.38 thf(f505,plain,(
% 0.45/0.38 ! [X0 : $tType] : (((coinductive_lnull @ X0 @ coinductive_LNil @ X0)) = $true)),
% 0.45/0.38 inference(fool_elimination,[],[f504])).
% 0.45/0.38 thf(f741,plain,(
% 0.45/0.38 ! [X0 : $tType,X2 : coinductive_llist @ X0,X1 : coinductive_llist @ X0] : (((((coinductive_lnull @ X0 @ X2)) != $true) | (((coinductive_lnull @ X0 @ X1)) != $true)) <=> (((coinductive_lnull @ X0 @ (lMirro999291890or_aux @ X0 @ X1 @ X2))) != $true))),
% 0.45/0.38 inference(flattening,[],[f329])).
% 0.45/0.38 thf(f839,plain,(
% 0.45/0.38 ((((coinductive_lnull @ a @ acc)) = $true) & (((coinductive_lnull @ a @ xs)) = $true)) <~> (((coinductive_lnull @ a @ (lMirro999291890or_aux @ a @ acc @ xs))) = $true)),
% 0.45/0.38 inference(ennf_transformation,[],[f407])).
% 0.45/0.38 thf(f959,plain,(
% 0.45/0.38 ! [X0 : $tType,X1 : coinductive_llist @ X0] : ((((coinductive_lnull @ X0 @ X1)) != $true) | (coinductive_LNil @ X0 = X1))),
% 0.45/0.38 inference(ennf_transformation,[],[f448])).
% 0.45/0.38 thf(f1142,plain,(
% 0.45/0.38 ! [X0 : $tType,X2 : coinductive_llist @ X0,X1 : coinductive_llist @ X0] : ((((((coinductive_lnull @ X0 @ X2)) != $true) | (((coinductive_lnull @ X0 @ X1)) != $true)) | (((coinductive_lnull @ X0 @ (lMirro999291890or_aux @ X0 @ X1 @ X2))) = $true)) & ((((coinductive_lnull @ X0 @ (lMirro999291890or_aux @ X0 @ X1 @ X2))) != $true) | ((((coinductive_lnull @ X0 @ X2)) = $true) & (((coinductive_lnull @ X0 @ X1)) = $true))))),
% 0.45/0.38 inference(nnf_transformation,[],[f741])).
% 0.45/0.38 thf(f1143,plain,(
% 0.45/0.38 ! [X0 : $tType,X2 : coinductive_llist @ X0,X1 : coinductive_llist @ X0] : (((((coinductive_lnull @ X0 @ X2)) != $true) | (((coinductive_lnull @ X0 @ X1)) != $true) | (((coinductive_lnull @ X0 @ (lMirro999291890or_aux @ X0 @ X1 @ X2))) = $true)) & ((((coinductive_lnull @ X0 @ (lMirro999291890or_aux @ X0 @ X1 @ X2))) != $true) | ((((coinductive_lnull @ X0 @ X2)) = $true) & (((coinductive_lnull @ X0 @ X1)) = $true))))),
% 0.45/0.38 inference(flattening,[],[f1142])).
% 0.45/0.38 thf(f1144,plain,(
% 0.45/0.38 ! [X0 : $tType,X1 : coinductive_llist @ X0,X2 : coinductive_llist @ X0] : (((((coinductive_lnull @ X0 @ X1)) != $true) | (((coinductive_lnull @ X0 @ X2)) != $true) | (((coinductive_lnull @ X0 @ (lMirro999291890or_aux @ X0 @ X2 @ X1))) = $true)) & ((((coinductive_lnull @ X0 @ (lMirro999291890or_aux @ X0 @ X2 @ X1))) != $true) | ((((coinductive_lnull @ X0 @ X1)) = $true) & (((coinductive_lnull @ X0 @ X2)) = $true))))),
% 0.45/0.38 inference(rectify,[],[f1143])).
% 0.45/0.38 thf(f1306,plain,(
% 0.45/0.38 ((((coinductive_lnull @ a @ (lMirro999291890or_aux @ a @ acc @ xs))) != $true) | ((((coinductive_lnull @ a @ acc)) != $true) | (((coinductive_lnull @ a @ xs)) != $true))) & ((((coinductive_lnull @ a @ (lMirro999291890or_aux @ a @ acc @ xs))) = $true) | ((((coinductive_lnull @ a @ acc)) = $true) & (((coinductive_lnull @ a @ xs)) = $true)))),
% 0.45/0.38 inference(nnf_transformation,[],[f839])).
% 0.45/0.38 thf(f1307,plain,(
% 0.45/0.38 ((((coinductive_lnull @ a @ (lMirro999291890or_aux @ a @ acc @ xs))) != $true) | (((coinductive_lnull @ a @ acc)) != $true) | (((coinductive_lnull @ a @ xs)) != $true)) & ((((coinductive_lnull @ a @ (lMirro999291890or_aux @ a @ acc @ xs))) = $true) | ((((coinductive_lnull @ a @ acc)) = $true) & (((coinductive_lnull @ a @ xs)) = $true)))),
% 0.45/0.38 inference(flattening,[],[f1306])).
% 0.45/0.38 thf(f1428,plain,(
% 0.45/0.38 ( ! [X0 : $tType,X1 : coinductive_llist @ X0] : ((((lMirro999291890or_aux @ X0 @ X1 @ coinductive_LNil @ X0)) = X1)) )),
% 0.45/0.38 inference(cnf_transformation,[],[f9])).
% 0.45/0.38 thf(f1472,plain,(
% 0.45/0.38 ( ! [X0 : $tType,X2 : coinductive_llist @ X0,X1 : coinductive_llist @ X0] : ((((coinductive_lnull @ X0 @ (lMirro999291890or_aux @ X0 @ X2 @ X1))) != $true) | (((coinductive_lnull @ X0 @ X2)) = $true)) )),
% 0.45/0.38 inference(cnf_transformation,[],[f1144])).
% 0.45/0.38 thf(f1473,plain,(
% 0.45/0.38 ( ! [X0 : $tType,X2 : coinductive_llist @ X0,X1 : coinductive_llist @ X0] : ((((coinductive_lnull @ X0 @ (lMirro999291890or_aux @ X0 @ X2 @ X1))) != $true) | (((coinductive_lnull @ X0 @ X1)) = $true)) )),
% 0.45/0.38 inference(cnf_transformation,[],[f1144])).
% 0.45/0.38 thf(f1704,plain,(
% 0.45/0.38 ( ! [X0 : $tType] : ((((coinductive_lnull @ X0 @ coinductive_LNil @ X0)) = $true)) )),
% 0.45/0.38 inference(cnf_transformation,[],[f505])).
% 0.45/0.38 thf(f1738,plain,(
% 0.45/0.38 ( ! [X0 : $tType,X1 : coinductive_llist @ X0] : ((((coinductive_lnull @ X0 @ X1)) != $true) | (coinductive_LNil @ X0 = X1)) )),
% 0.45/0.38 inference(cnf_transformation,[],[f959])).
% 0.45/0.38 thf(f1769,plain,(
% 0.45/0.38 (((coinductive_lnull @ a @ (lMirro999291890or_aux @ a @ acc @ xs))) = $true) | (((coinductive_lnull @ a @ xs)) = $true)),
% 0.45/0.38 inference(cnf_transformation,[],[f1307])).
% 0.45/0.38 thf(f1770,plain,(
% 0.45/0.38 (((coinductive_lnull @ a @ acc)) = $true) | (((coinductive_lnull @ a @ (lMirro999291890or_aux @ a @ acc @ xs))) = $true)),
% 0.45/0.38 inference(cnf_transformation,[],[f1307])).
% 0.45/0.38 thf(f1771,plain,(
% 0.45/0.38 (((coinductive_lnull @ a @ acc)) != $true) | (((coinductive_lnull @ a @ xs)) != $true) | (((coinductive_lnull @ a @ (lMirro999291890or_aux @ a @ acc @ xs))) != $true)),
% 0.45/0.38 inference(cnf_transformation,[],[f1307])).
% 0.45/0.38 thf(f1891,definition,(
% 0.45/0.38 spl83_2 <=> (((coinductive_lnull @ a @ xs)) = $true)),
% 0.45/0.38 introduced(definition,[new_symbols(definition,[spl83_2])],[avatar_definition])).
% 0.45/0.38 thf(f1893,plain,(
% 0.45/0.38 (((coinductive_lnull @ a @ xs)) = $true) | ~spl83_2),
% 0.45/0.38 inference(avatar_component_clause,[],[f1891])).
% 0.45/0.38 thf(f1895,definition,(
% 0.45/0.38 spl83_3 <=> (((coinductive_lnull @ a @ (lMirro999291890or_aux @ a @ acc @ xs))) = $true)),
% 0.45/0.38 introduced(definition,[new_symbols(definition,[spl83_3])],[avatar_definition])).
% 0.45/0.38 thf(f1896,plain,(
% 0.45/0.38 (((coinductive_lnull @ a @ (lMirro999291890or_aux @ a @ acc @ xs))) != $true) | spl83_3),
% 0.45/0.38 inference(avatar_component_clause,[],[f1895])).
% 0.45/0.38 thf(f1897,plain,(
% 0.45/0.38 (((coinductive_lnull @ a @ (lMirro999291890or_aux @ a @ acc @ xs))) = $true) | ~spl83_3),
% 0.45/0.38 inference(avatar_component_clause,[],[f1895])).
% 0.45/0.38 thf(f1898,plain,(
% 0.45/0.38 spl83_2 | spl83_3),
% 0.45/0.38 inference(avatar_split_clause,[],[f1769,f1895,f1891])).
% 0.45/0.38 thf(f1900,definition,(
% 0.45/0.38 spl83_4 <=> (((coinductive_lnull @ a @ acc)) = $true)),
% 0.45/0.38 introduced(definition,[new_symbols(definition,[spl83_4])],[avatar_definition])).
% 0.45/0.38 thf(f1902,plain,(
% 0.45/0.38 (((coinductive_lnull @ a @ acc)) = $true) | ~spl83_4),
% 0.45/0.38 inference(avatar_component_clause,[],[f1900])).
% 0.45/0.38 thf(f1903,plain,(
% 0.45/0.38 spl83_4 | spl83_3),
% 0.45/0.38 inference(avatar_split_clause,[],[f1770,f1895,f1900])).
% 0.45/0.38 thf(f1919,plain,(
% 0.45/0.38 ~spl83_2 | ~spl83_4 | ~spl83_3),
% 0.45/0.38 inference(avatar_split_clause,[],[f1771,f1895,f1900,f1891])).
% 0.45/0.38 thf(f1931,plain,(
% 0.45/0.38 ($true != $true) | (((coinductive_lnull @ a @ acc)) = $true) | ~spl83_3),
% 0.45/0.38 inference(superposition,[],[f1472,f1897])).
% 0.45/0.38 thf(f1932,plain,(
% 0.45/0.38 (((coinductive_lnull @ a @ acc)) = $true) | ~spl83_3),
% 0.45/0.38 inference(trivial_inequality_removal,[],[f1931])).
% 0.45/0.38 thf(f1939,plain,(
% 0.45/0.38 spl83_4 | ~spl83_3),
% 0.45/0.38 inference(avatar_split_clause,[],[f1932,f1895,f1900])).
% 0.45/0.38 thf(f1940,plain,(
% 0.45/0.38 ($true != $true) | (acc = coinductive_LNil @ a) | ~spl83_4),
% 0.45/0.38 inference(superposition,[],[f1738,f1902])).
% 0.45/0.38 thf(f1941,plain,(
% 0.45/0.38 (acc = coinductive_LNil @ a) | ~spl83_4),
% 0.45/0.38 inference(trivial_inequality_removal,[],[f1940])).
% 0.45/0.38 thf(f1943,definition,(
% 0.45/0.38 spl83_9 <=> (acc = coinductive_LNil @ a)),
% 0.45/0.38 introduced(definition,[new_symbols(definition,[spl83_9])],[avatar_definition])).
% 0.45/0.38 thf(f1945,plain,(
% 0.45/0.38 (acc = coinductive_LNil @ a) | ~spl83_9),
% 0.45/0.38 inference(avatar_component_clause,[],[f1943])).
% 0.45/0.38 thf(f1946,plain,(
% 0.45/0.38 spl83_9 | ~spl83_4),
% 0.45/0.38 inference(avatar_split_clause,[],[f1941,f1900,f1943])).
% 0.45/0.38 thf(f1949,plain,(
% 0.45/0.38 (((coinductive_lnull @ a @ xs)) = $true) | ($true != $true) | ~spl83_3),
% 0.45/0.38 inference(superposition,[],[f1473,f1897])).
% 0.45/0.38 thf(f1950,plain,(
% 0.45/0.38 (((coinductive_lnull @ a @ xs)) = $true) | ~spl83_3),
% 0.45/0.38 inference(trivial_inequality_removal,[],[f1949])).
% 0.45/0.38 thf(f1951,plain,(
% 0.45/0.38 spl83_2 | ~spl83_3),
% 0.45/0.38 inference(avatar_split_clause,[],[f1950,f1895,f1891])).
% 0.45/0.38 thf(f1955,plain,(
% 0.45/0.38 ($true != $true) | (xs = coinductive_LNil @ a) | ~spl83_2),
% 0.45/0.38 inference(superposition,[],[f1738,f1893])).
% 0.45/0.38 thf(f1956,plain,(
% 0.45/0.38 (xs = coinductive_LNil @ a) | ~spl83_2),
% 0.45/0.38 inference(trivial_inequality_removal,[],[f1955])).
% 0.45/0.38 thf(f1958,definition,(
% 0.45/0.38 spl83_10 <=> (xs = coinductive_LNil @ a)),
% 0.45/0.38 introduced(definition,[new_symbols(definition,[spl83_10])],[avatar_definition])).
% 0.45/0.38 thf(f1960,plain,(
% 0.45/0.38 (xs = coinductive_LNil @ a) | ~spl83_10),
% 0.45/0.38 inference(avatar_component_clause,[],[f1958])).
% 0.45/0.38 thf(f1961,plain,(
% 0.45/0.38 spl83_10 | ~spl83_2),
% 0.45/0.38 inference(avatar_split_clause,[],[f1956,f1891,f1958])).
% 0.45/0.38 thf(f1983,plain,(
% 0.45/0.38 ($true != ((coinductive_lnull @ a @ (lMirro999291890or_aux @ a @ coinductive_LNil @ a @ xs)))) | (spl83_3 | ~spl83_9)),
% 0.45/0.38 inference(forward_demodulation,[],[f1896,f1945])).
% 0.45/0.38 thf(f1984,plain,(
% 0.45/0.38 ($true != ((coinductive_lnull @ a @ (lMirro999291890or_aux @ a @ coinductive_LNil @ a @ coinductive_LNil @ a)))) | (spl83_3 | ~spl83_9 | ~spl83_10)),
% 0.45/0.38 inference(forward_demodulation,[],[f1983,f1960])).
% 0.45/0.38 thf(f1985,plain,(
% 0.45/0.38 ($true != ((coinductive_lnull @ a @ coinductive_LNil @ a))) | (spl83_3 | ~spl83_9 | ~spl83_10)),
% 0.45/0.38 inference(forward_demodulation,[],[f1984,f1428])).
% 0.45/0.38 thf(f1986,plain,(
% 0.45/0.38 $false | (spl83_3 | ~spl83_9 | ~spl83_10)),
% 0.45/0.38 inference(forward_subsumption_resolution,[],[f1985,f1704])).
% 0.45/0.38 thf(f1987,plain,(
% 0.45/0.38 spl83_3 | ~spl83_9 | ~spl83_10),
% 0.45/0.38 inference(avatar_contradiction_clause,[],[f1986])).
% 0.45/0.38 cnf(s2, plain, spl83_2 | spl83_3, inference(sat_conversion,[],[f1898])).
% 0.45/0.38 cnf(s3, plain, spl83_3 | spl83_4, inference(sat_conversion,[],[f1903])).
% 0.45/0.38 cnf(s7, plain, ~spl83_2 | ~spl83_3 | ~spl83_4, inference(sat_conversion,[],[f1919])).
% 0.45/0.38 cnf(s12, plain, ~spl83_3 | spl83_4, inference(sat_conversion,[],[f1939])).
% 0.45/0.38 cnf(s13, plain, ~spl83_4 | spl83_9, inference(sat_conversion,[],[f1946])).
% 0.45/0.38 cnf(s14, plain, spl83_2 | ~spl83_3, inference(sat_conversion,[],[f1951])).
% 0.45/0.38 cnf(s17, plain, ~spl83_2 | spl83_10, inference(sat_conversion,[],[f1961])).
% 0.45/0.38 cnf(s18, plain, spl83_3 | ~spl83_9 | ~spl83_10, inference(sat_conversion,[],[f1987])).
% 0.45/0.38 cnf(s19, plain, spl83_2, inference(rat,[],[s2,s14])).
% 0.45/0.38 cnf(s20, plain, spl83_10, inference(rat,[],[s17,s19])).
% 0.45/0.38 cnf(s21, plain, spl83_3, inference(rat,[],[s13,s3,s18,s20])).
% 0.45/0.38 cnf(s22, plain, spl83_4, inference(rat,[],[s12,s21])).
% 0.45/0.38 cnf(s24, plain, $false, inference(rat,[],[s7,s19,s22,s21])).
% 0.45/0.38 thf(f1988,plain,(
% 0.45/0.38 $false),
% 0.45/0.38 inference(avatar_sat_refutation,[],[s24])).
% 0.45/0.38 % SZS output end Proof for theBenchmark
% 0.45/0.38 % (2457665)------------------------------
% 0.45/0.38 % (2457665)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.45/0.38 % (2457665)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.45/0.38 % (2457665)CaDiCaL version: 2.1.3
% 0.45/0.38 % (2457665)Termination reason: Refutation
% 0.45/0.38 % (2457665)Time elapsed: 0.040 s
% 0.45/0.38 % (2457665)Peak memory usage: 14 MB
% 0.45/0.38 % (2457665)Instructions burned: 144 (million)
% 0.45/0.38 % (2457645)Success in time 0.091 s
% 0.45/0.38 % Vampire exiting
%------------------------------------------------------------------------------