%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT178^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 07:48:29 AM UTC 2026
% Result : Theorem 0.22s 0.36s
% Output : Refutation 0.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : DAT178^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.16 % Computer : n006.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Tue Sep 29 18:05:55 UTC 2026
% 0.09/0.16 % CPUTime :
% 0.09/0.16 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 Running higher-order theorem proving
% 0.09/0.24 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.36 % (1113397)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.36 % (1113403)lrs+10_16_si=on:nwc=1.5:random_seed=1765970138:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.36 % (1113408)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.36 % (1113408)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
% 0.22/0.36 % (1113403)Instruction limit reached!
% 0.22/0.36 % (1113403)------------------------------
% 0.22/0.36 % (1113403)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.36 % (1113403)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.36 % (1113403)CaDiCaL version: 2.1.3
% 0.22/0.36 % (1113403)Termination reason: Instruction limit
% 0.22/0.36 % (1113403)Termination phase: Property scanning
% 0.22/0.36 % (1113403)Time elapsed: 0.005 s
% 0.22/0.36 % (1113403)Peak memory usage: 10 MB
% 0.22/0.36 % (1113403)Instructions burned: 21 (million)
% 0.22/0.36 % (1113402)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4217850214:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.36 % (1113404)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=515756793:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.36 % (1113406)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=908950163:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.36 % (1113405)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=2177935087: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)
% 0.22/0.36 % (1113407)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1855523826:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.36 % (1113408)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=3026342883:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.36 % (1113404)Instruction limit reached!
% 0.22/0.36 % (1113404)------------------------------
% 0.22/0.36 % (1113404)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.36 % (1113404)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.36 % (1113404)CaDiCaL version: 2.1.3
% 0.22/0.36 % (1113404)Termination reason: Instruction limit
% 0.22/0.36 % (1113404)Termination phase: shuffling
% 0.22/0.36 % (1113404)Time elapsed: 0.002 s
% 0.22/0.36 % (1113404)Peak memory usage: 10 MB
% 0.22/0.36 % (1113404)Instructions burned: 3 (million)
% 0.22/0.36 % (1113410)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3323724047:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.22/0.36 % (1113410)Instruction limit reached!
% 0.22/0.36 % (1113410)------------------------------
% 0.22/0.36 % (1113410)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.36 % (1113410)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.36 % (1113410)CaDiCaL version: 2.1.3
% 0.22/0.36 % (1113410)Termination reason: Instruction limit
% 0.22/0.36 % (1113410)Termination phase: shuffling
% 0.22/0.36 % (1113410)Time elapsed: 0.001 s
% 0.22/0.36 % (1113410)Peak memory usage: 10 MB
% 0.22/0.36 % (1113410)Instructions burned: 3 (million)
% 0.22/0.36 % (1113406)Instruction limit reached!
% 0.22/0.36 % (1113406)------------------------------
% 0.22/0.36 % (1113406)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.36 % (1113406)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.36 % (1113406)CaDiCaL version: 2.1.3
% 0.22/0.36 % (1113406)Termination reason: Instruction limit
% 0.22/0.36 % (1113406)Termination phase: Property scanning
% 0.22/0.36 % (1113406)Time elapsed: 0.012 s
% 0.22/0.36 % (1113406)Peak memory usage: 10 MB
% 0.22/0.36 % (1113406)Instructions burned: 25 (million)
% 0.22/0.36 % (1113419)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.22/0.36 % (1113417)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=4043049701:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.22/0.36 % (1113419)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1225759217:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.22/0.36 % (1113419)Instruction limit reached!
% 0.22/0.36 % (1113419)------------------------------
% 0.22/0.36 % (1113419)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.36 % (1113419)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.36 % (1113419)CaDiCaL version: 2.1.3
% 0.22/0.36 % (1113419)Termination reason: Instruction limit
% 0.22/0.36 % (1113419)Termination phase: shuffling
% 0.22/0.36 % (1113419)Time elapsed: 0.002 s
% 0.22/0.36 % (1113419)Peak memory usage: 10 MB
% 0.22/0.36 % (1113419)Instructions burned: 8 (million)
% 0.22/0.36 % (1113417)Instruction limit reached!
% 0.22/0.36 % (1113417)------------------------------
% 0.22/0.36 % (1113417)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.36 % (1113417)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.36 % (1113417)CaDiCaL version: 2.1.3
% 0.22/0.36 % (1113417)Termination reason: Instruction limit
% 0.22/0.36 % (1113417)Termination phase: shuffling
% 0.22/0.36 % (1113417)Time elapsed: 0.003 s
% 0.22/0.36 % (1113417)Peak memory usage: 10 MB
% 0.22/0.36 % (1113417)Instructions burned: 5 (million)
% 0.22/0.36 % (1113420)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=784033799:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.22/0.36 % (1113423)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
% 0.22/0.36 % (1113423)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.22/0.36 % (1113423)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1556594733:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.22/0.36 % (1113407)Instruction limit reached!
% 0.22/0.36 % (1113407)------------------------------
% 0.22/0.36 % (1113407)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.36 % (1113407)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.36 % (1113407)CaDiCaL version: 2.1.3
% 0.22/0.36 % (1113407)Termination reason: Instruction limit
% 0.22/0.36 % (1113407)Termination phase: shuffling
% 0.22/0.36 % (1113407)Time elapsed: 0.037 s
% 0.22/0.36 % (1113407)Peak memory usage: 12 MB
% 0.22/0.36 % (1113407)Instructions burned: 80 (million)
% 0.22/0.36 % (1113420)Instruction limit reached!
% 0.22/0.36 % (1113420)------------------------------
% 0.22/0.36 % (1113420)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.36 % (1113420)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.36 % (1113420)CaDiCaL version: 2.1.3
% 0.22/0.36 % (1113420)Termination reason: Instruction limit
% 0.22/0.36 % (1113420)Termination phase: shuffling
% 0.22/0.36 % (1113420)Time elapsed: 0.006 s
% 0.22/0.36 % (1113420)Peak memory usage: 10 MB
% 0.22/0.36 % (1113420)Instructions burned: 13 (million)
% 0.22/0.36 % (1113402)Instruction limit reached!
% 0.22/0.36 % (1113402)------------------------------
% 0.22/0.36 % (1113402)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.36 % (1113402)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.36 % (1113402)CaDiCaL version: 2.1.3
% 0.22/0.36 % (1113402)Termination reason: Instruction limit
% 0.22/0.36 % (1113402)Termination phase: Property scanning
% 0.22/0.36 % (1113402)Time elapsed: 0.040 s
% 0.22/0.36 % (1113402)Peak memory usage: 12 MB
% 0.22/0.36 % (1113402)Instructions burned: 88 (million)
% 0.22/0.36 % (1113423)Instruction limit reached!
% 0.22/0.36 % (1113423)------------------------------
% 0.22/0.36 % (1113423)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.36 % (1113423)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.36 % (1113423)CaDiCaL version: 2.1.3
% 0.22/0.36 % (1113423)Termination reason: Instruction limit
% 0.22/0.36 % (1113423)Termination phase: Property scanning
% 0.22/0.36 % (1113423)Time elapsed: 0.008 s
% 0.22/0.36 % (1113423)Peak memory usage: 10 MB
% 0.22/0.36 % (1113423)Instructions burned: 33 (million)
% 0.22/0.36 % (1113424)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=867513045:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.22/0.36 % (1113428)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.22/0.36 % (1113430)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=2893476737:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.22/0.36 % (1113408) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1113397-1113408"...
% 0.22/0.36 % (1113427)lrs+10_1_si=on:cs=on:random_seed=305288009:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.22/0.36 % (1113428)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=2515011068:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.22/0.36 % (1113408)...printing done.
% 0.22/0.36 % (1113429)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2708353778:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.22/0.36 % (1113408)Refutation found. Thanks to Tanya!
% 0.22/0.36 % SZS status Theorem for theBenchmark
% 0.22/0.36 % SZS output start Proof for theBenchmark
% 0.22/0.36 thf(type_def_5, type, coinductive_llist: $tType > $tType).
% 0.22/0.36 thf(type_def_6, type, set: $tType > $tType).
% 0.22/0.36 thf(type_def_7, type, itself: $tType > $tType).
% 0.22/0.36 thf(type_def_8, type, a: $tType).
% 0.22/0.36 thf(type_def_9, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.36 thf(func_def_0, type, bounded_lattice: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.22/0.36 thf(func_def_1, type, type: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.22/0.36 thf(func_def_2, type, minus: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.22/0.36 thf(func_def_3, type, top: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.22/0.36 thf(func_def_4, type, lattice: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.22/0.36 thf(func_def_5, type, semilattice_sup: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.22/0.36 thf(func_def_6, type, bounded_lattice_top: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.22/0.36 thf(func_def_7, type, coindu328551480prefix: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > $o))).
% 0.22/0.36 thf(func_def_8, type, coinductive_gen_lset: !>[X0: $tType]:((set @ X0 > coinductive_llist @ X0 > set @ X0))).
% 0.22/0.36 thf(func_def_9, type, coinductive_lappend: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.22/0.36 thf(func_def_10, type, coindu351974385stinct: !>[X0: $tType]:((coinductive_llist @ X0 > $o))).
% 0.22/0.36 thf(func_def_11, type, coinductive_lfilter: !>[X0: $tType]:(((X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.22/0.36 thf(func_def_12, type, coinductive_lfinite: !>[X0: $tType]:((coinductive_llist @ X0 > $o))).
% 0.22/0.36 thf(func_def_13, type, coinductive_llast: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 0.22/0.36 thf(func_def_14, type, coinductive_llexord: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > $o))).
% 0.22/0.36 thf(func_def_15, type, coinductive_LCons: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.22/0.36 thf(func_def_16, type, coinductive_LNil: !>[X0: $tType]:(coinductive_llist @ X0)).
% 0.22/0.36 thf(func_def_17, type, coinductive_lnull: !>[X0: $tType]:((coinductive_llist @ X0 > $o))).
% 0.22/0.36 thf(func_def_18, type, coinductive_lset: !>[X0: $tType]:((coinductive_llist @ X0 > set @ X0))).
% 0.22/0.36 thf(func_def_19, type, coinductive_lmember: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > $o))).
% 0.22/0.36 thf(func_def_20, type, coindu1478340336prefix: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > $o))).
% 0.22/0.36 thf(func_def_21, type, minus_minus: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.22/0.36 thf(func_def_22, type, undefined: !>[X0: $tType]:(X0)).
% 0.22/0.36 thf(func_def_23, type, lList2435255213lllsts: !>[X0: $tType]:((set @ X0 > set @ coinductive_llist @ X0))).
% 0.22/0.36 thf(func_def_24, type, lList21511617539llstsp: !>[X0: $tType]:(((X0 > $o) > coinductive_llist @ X0 > $o))).
% 0.22/0.36 thf(func_def_25, type, lList2236698231inlsts: !>[X0: $tType]:((set @ X0 > set @ coinductive_llist @ X0))).
% 0.22/0.36 thf(func_def_26, type, lList21916056377ts_rec: !>[X0: $tType, X1: $tType]:((X0 > (X1 > coinductive_llist @ X1 > X0 > X0) > coinductive_llist @ X1 > X0))).
% 0.22/0.36 thf(func_def_27, type, lList2860480441nlstsp: !>[X0: $tType]:(((X0 > $o) > coinductive_llist @ X0 > $o))).
% 0.22/0.36 thf(func_def_28, type, lList22096119349pslsts: !>[X0: $tType]:((set @ X0 > set @ coinductive_llist @ X0))).
% 0.22/0.36 thf(func_def_29, type, lList21612149805nflsts: !>[X0: $tType]:((set @ X0 > set @ coinductive_llist @ X0))).
% 0.22/0.36 thf(func_def_30, type, lList2370560421utlast: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.22/0.36 thf(func_def_31, type, lList2170638824_llast: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 0.22/0.36 thf(func_def_32, type, lList2281150353e_lrev: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.22/0.36 thf(func_def_33, type, lList21148268032oslsts: !>[X0: $tType]:((set @ X0 > set @ coinductive_llist @ X0))).
% 0.22/0.36 thf(func_def_34, type, sup_sup: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.22/0.36 thf(func_def_35, type, top_top: !>[X0: $tType]:(X0)).
% 0.22/0.36 thf(func_def_36, type, type2: !>[X0: $tType]:(itself @ X0)).
% 0.22/0.36 thf(func_def_37, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.22/0.36 thf(func_def_38, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.22/0.36 thf(func_def_39, type, a2: set @ a).
% 0.22/0.36 thf(func_def_40, type, p: (coinductive_llist @ a > $o)).
% 0.22/0.36 thf(func_def_41, type, l: coinductive_llist @ a).
% 0.22/0.36 thf(func_def_42, type, la: coinductive_llist @ a).
% 0.22/0.36 thf(func_def_43, type, xs: coinductive_llist @ a).
% 0.22/0.36 thf(func_def_47, type, vOR: ($o > $o > $o)).
% 0.22/0.36 thf(func_def_48, type, vAND: ($o > $o > $o)).
% 0.22/0.36 thf(func_def_49, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.22/0.36 thf(func_def_50, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.22/0.36 thf(func_def_51, type, db0: !>[X0: $tType]:(X0)).
% 0.22/0.36 thf(func_def_52, type, db1: !>[X0: $tType]:(X0)).
% 0.22/0.36 thf(func_def_53, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.22/0.36 thf(func_def_54, type, vNOT: ($o > $o)).
% 0.22/0.36 thf(func_def_55, type, db2: !>[X0: $tType]:(X0)).
% 0.22/0.36 thf(func_def_56, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.22/0.36 thf(func_def_57, type, vIMP: ($o > $o > $o)).
% 0.22/0.36 thf(func_def_58, type, db3: !>[X0: $tType]:(X0)).
% 0.22/0.36 thf(func_def_59, type, sP0: !>[X0: $tType]:((coinductive_llist @ X0 > (coinductive_llist @ X0 > $o) > $o))).
% 0.22/0.36 thf(func_def_60, type, sP1: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > $o))).
% 0.22/0.36 thf(func_def_61, type, sP2: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > $o))).
% 0.22/0.36 thf(func_def_62, type, sP3: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > (X0 > $o) > $o))).
% 0.22/0.36 thf(func_def_63, type, sP4: !>[X0: $tType]:(((X0 > X0 > $o) > $o))).
% 0.22/0.36 thf(func_def_64, type, sP5: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > $o))).
% 0.22/0.36 thf(func_def_65, type, sP6: !>[X0: $tType]:(((X0 > coinductive_llist @ X0 > $o) > $o))).
% 0.22/0.36 thf(func_def_66, type, sP7: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > coinductive_llist @ X0 > set @ X0 > $o))).
% 0.22/0.36 thf(func_def_67, type, sP8: !>[X0: $tType]:((set @ X0 > (coinductive_llist @ X0 > $o) > $o))).
% 0.22/0.36 thf(func_def_68, type, sP9: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > (X0 > $o) > coinductive_llist @ X0 > $o))).
% 0.22/0.36 thf(func_def_69, type, sP10: !>[X0: $tType]:((coinductive_llist @ X0 > (coinductive_llist @ X0 > $o) > (X0 > $o) > $o))).
% 0.22/0.36 thf(func_def_70, type, sP11: !>[X0: $tType]:(((X0 > $o) > (coinductive_llist @ X0 > $o) > $o))).
% 0.22/0.36 thf(func_def_71, type, sP12: !>[X0: $tType]:((set @ X0 > (coinductive_llist @ X0 > $o) > $o))).
% 0.22/0.36 thf(func_def_72, type, sP13: !>[X0: $tType]:((coinductive_llist @ X0 > (X0 > $o) > $o))).
% 0.22/0.36 thf(func_def_73, type, sP14: !>[X0: $tType]:((set @ X0 > coinductive_llist @ X0 > $o))).
% 0.22/0.36 thf(func_def_74, type, sP15: !>[X0: $tType]:((coinductive_llist @ X0 > $o))).
% 0.22/0.36 thf(func_def_75, type, sP16: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > $o))).
% 0.22/0.36 thf(func_def_76, type, sP17: !>[X0: $tType]:((coinductive_llist @ X0 > set @ X0 > $o))).
% 0.22/0.36 thf(func_def_77, type, sP18: !>[X0: $tType]:((set @ X0 > (coinductive_llist @ X0 > $o) > $o))).
% 0.22/0.36 thf(func_def_78, type, sP19: !>[X0: $tType]:((coinductive_llist @ X0 > set @ X0 > $o))).
% 0.22/0.36 thf(func_def_79, type, sP20: !>[X0: $tType]:(((X0 > X0 > $o) > $o))).
% 0.22/0.36 thf(func_def_80, type, sP21: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > X0 > $o))).
% 0.22/0.36 thf(func_def_81, type, sP22: !>[X0: $tType]:((coinductive_llist @ X0 > set @ X0 > $o))).
% 0.22/0.36 thf(func_def_82, type, sP23: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > X0 > $o))).
% 0.22/0.36 thf(func_def_83, type, sP24: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > $o))).
% 0.22/0.36 thf(func_def_84, type, sP25: !>[X0: $tType]:((coinductive_llist @ X0 > (X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > $o))).
% 0.22/0.36 thf(func_def_85, type, sP26: !>[X0: $tType]:((coinductive_llist @ X0 > (X0 > $o) > $o))).
% 0.22/0.36 thf(func_def_86, type, sK27: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.22/0.36 thf(func_def_87, type, sK28: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.22/0.36 thf(func_def_88, type, sK29: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.22/0.36 thf(func_def_89, type, sK30: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > X0))).
% 0.22/0.36 thf(func_def_90, type, sK31: !>[X0: $tType]:((set @ X0 > X0))).
% 0.22/0.36 thf(func_def_91, type, sK32: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.22/0.36 thf(func_def_92, type, sK33: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 0.22/0.36 thf(func_def_93, type, sK34: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > (X0 > $o) > coinductive_llist @ X0))).
% 0.22/0.36 thf(func_def_94, type, sK35: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > (X0 > $o) > X0))).
% 0.22/0.36 thf(func_def_95, type, sK36: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.22/0.36 thf(func_def_96, type, sK37: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.22/0.36 thf(func_def_97, type, sK38: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.22/0.36 thf(func_def_98, type, sK39: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 0.22/0.36 thf(func_def_99, type, sK40: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > X0))).
% 0.22/0.36 thf(func_def_100, type, sK41: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.22/0.36 thf(func_def_101, type, sK42: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > X0))).
% 0.22/0.36 thf(func_def_102, type, sK43: !>[X0: $tType]:(((X0 > coinductive_llist @ X0 > $o) > X0))).
% 0.22/0.36 thf(func_def_103, type, sK44: !>[X0: $tType]:(((X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.22/0.36 thf(func_def_104, type, sK45: !>[X0: $tType]:(((X0 > coinductive_llist @ X0 > $o) > X0))).
% 0.22/0.36 thf(func_def_105, type, sK46: !>[X0: $tType]:(((X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.22/0.36 thf(func_def_106, type, sK47: !>[X0: $tType]:(((X0 > coinductive_llist @ X0 > $o) > X0))).
% 0.22/0.36 thf(func_def_107, type, sK48: !>[X0: $tType]:((set @ X0 > (coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.22/0.36 thf(func_def_108, type, sK49: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > (X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.22/0.36 thf(func_def_109, type, sK50: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > (X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.22/0.36 thf(func_def_110, type, sK51: !>[X0: $tType]:(((X0 > $o) > (coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.22/0.36 thf(func_def_111, type, sK52: !>[X0: $tType]:((set @ X0 > (coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.22/0.36 thf(func_def_112, type, sK53: !>[X0: $tType]:((set @ X0 > (coinductive_llist @ X0 > $o) > X0))).
% 0.22/0.36 thf(func_def_113, type, sK54: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.22/0.36 thf(func_def_114, type, sK55: !>[X0: $tType]:(X0)).
% 0.22/0.36 thf(func_def_115, type, sK56: !>[X0: $tType]:((coinductive_llist @ X0 > (X0 > $o) > coinductive_llist @ X0))).
% 0.22/0.36 thf(func_def_116, type, sK57: !>[X0: $tType]:((coinductive_llist @ X0 > (X0 > $o) > X0))).
% 0.22/0.36 thf(func_def_117, type, sK58: !>[X0: $tType]:((coinductive_llist @ X0 > (X0 > X0 > $o) > X0))).
% 0.22/0.36 thf(func_def_118, type, sK59: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.22/0.36 thf(func_def_119, type, sK60: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.22/0.36 thf(func_def_120, type, sK61: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.22/0.36 thf(func_def_121, type, sK62: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.22/0.36 thf(func_def_122, type, sK63: !>[X0: $tType]:((set @ X0 > coinductive_llist @ X0 > X0))).
% 0.22/0.36 thf(func_def_123, type, sK64: !>[X0: $tType]:((set @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.22/0.36 thf(func_def_124, type, sK65: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.22/0.36 thf(func_def_125, type, sK66: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 0.22/0.36 thf(func_def_126, type, sK67: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > X0))).
% 0.22/0.36 thf(func_def_127, type, sK68: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.22/0.36 thf(func_def_128, type, sK69: !>[X0: $tType]:((coinductive_llist @ X0 > set @ X0 > coinductive_llist @ X0))).
% 0.22/0.36 thf(func_def_129, type, sK70: !>[X0: $tType]:((coinductive_llist @ X0 > set @ X0 > X0))).
% 0.22/0.36 thf(func_def_130, type, sK71: !>[X0: $tType]:((set @ X0 > (coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.22/0.36 thf(func_def_131, type, sK72: !>[X0: $tType]:((set @ X0 > (coinductive_llist @ X0 > $o) > X0))).
% 0.22/0.36 thf(func_def_132, type, sK73: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > coinductive_llist @ X0))).
% 0.22/0.36 thf(func_def_133, type, sK74: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > coinductive_llist @ X0))).
% 0.22/0.36 thf(func_def_134, type, sK75: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > X0))).
% 0.22/0.36 thf(func_def_135, type, sK76: !>[X0: $tType]:((coinductive_llist @ X0 > set @ X0 > X0))).
% 0.22/0.36 thf(func_def_136, type, sK77: !>[X0: $tType]:((coinductive_llist @ X0 > set @ X0 > coinductive_llist @ X0))).
% 0.22/0.36 thf(func_def_137, type, sK78: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > coinductive_llist @ X0))).
% 0.22/0.36 thf(func_def_138, type, sK79: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > X0))).
% 0.22/0.36 thf(func_def_139, type, sK80: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > coinductive_llist @ X0))).
% 0.22/0.36 thf(func_def_140, type, sK81: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.22/0.36 thf(func_def_141, type, sK82: !>[X0: $tType]:(((X0 > $o) > coinductive_llist @ X0 > (X0 > $o) > X0))).
% 0.22/0.36 thf(func_def_142, type, sK83: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.22/0.36 thf(func_def_143, type, sK84: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.22/0.36 thf(func_def_144, type, sK85: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.22/0.36 thf(func_def_145, type, sK86: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > X0 > coinductive_llist @ X0))).
% 0.22/0.36 thf(func_def_146, type, sK87: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > X0 > X0))).
% 0.22/0.36 thf(func_def_147, type, sK88: !>[X0: $tType]:((X0 > (coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.22/0.36 thf(func_def_148, type, sK89: !>[X0: $tType]:((coinductive_llist @ X0 > set @ X0 > coinductive_llist @ X0))).
% 0.22/0.36 thf(func_def_149, type, sK90: !>[X0: $tType]:((coinductive_llist @ X0 > set @ X0 > X0))).
% 0.22/0.36 thf(func_def_150, type, sK91: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > X0 > X0))).
% 0.22/0.36 thf(func_def_151, type, sK92: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > X0 > coinductive_llist @ X0))).
% 0.22/0.36 thf(func_def_152, type, sK93: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > X0 > coinductive_llist @ X0))).
% 0.22/0.36 thf(func_def_153, type, sK94: !>[X0: $tType]:(((X0 > $o) > coinductive_llist @ X0 > X0))).
% 0.22/0.36 thf(func_def_154, type, sK95: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.22/0.36 thf(func_def_155, type, sK96: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > X0))).
% 0.22/0.36 thf(func_def_156, type, sK97: !>[X0: $tType]:((coinductive_llist @ X0 > (X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.22/0.36 thf(func_def_157, type, sK98: !>[X0: $tType]:((coinductive_llist @ X0 > (X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.22/0.36 thf(func_def_158, type, sK99: !>[X0: $tType]:((coinductive_llist @ X0 > (X0 > $o) > coinductive_llist @ X0))).
% 0.22/0.36 thf(func_def_159, type, sK100: !>[X0: $tType]:((coinductive_llist @ X0 > (X0 > $o) > X0))).
% 0.22/0.36 thf(func_def_160, type, sK101: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.22/0.36 thf(func_def_161, type, sF102: coinductive_llist @ a).
% 0.22/0.36 thf(func_def_162, type, sF103: $o).
% 0.22/0.36 thf(func_def_163, type, sK104: !>[X0: $tType]:((set @ X0 > (X0 > $o) > set @ X0 > X0))).
% 0.22/0.36 thf(func_def_164, type, sK105: !>[X0: $tType]:((set @ X0 > set @ X0 > (X0 > $o) > X0))).
% 0.22/0.36 thf(func_def_165, type, sK106: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 0.22/0.36 thf(func_def_166, type, sK107: !>[X0: $tType]:(((X0 > $o) > set @ X0 > X0))).
% 0.22/0.36 thf(func_def_167, type, sK108: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.22/0.36 thf(func_def_168, type, sK109: !>[X0: $tType]:((set @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.22/0.36 thf(func_def_169, type, sK110: !>[X0: $tType]:((set @ X0 > coinductive_llist @ X0 > X0))).
% 0.22/0.36 thf(func_def_170, type, sK111: !>[X0: $tType]:((set @ X0 > (X0 > $o) > set @ X0 > X0))).
% 0.22/0.36 thf(func_def_171, type, sK112: !>[X0: $tType]:((set @ X0 > (X0 > $o) > set @ X0 > X0))).
% 0.22/0.36 thf(func_def_172, type, sK113: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 0.22/0.36 thf(func_def_173, type, sK114: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 0.22/0.36 thf(func_def_174, type, sK115: !>[X0: $tType]:((coinductive_llist @ X0 > (X0 > $o) > X0))).
% 0.22/0.36 thf(func_def_175, type, sK116: !>[X0: $tType]:((coinductive_llist @ X0 > (X0 > $o) > X0))).
% 0.22/0.36 thf(func_def_176, type, sK117: !>[X0: $tType]:((coinductive_llist @ X0 > (X0 > $o) > X0))).
% 0.22/0.36 thf(func_def_177, type, sK118: !>[X0: $tType]:((set @ X0 > coinductive_llist @ X0 > X0))).
% 0.22/0.36 thf(func_def_178, type, sK119: !>[X0: $tType]:((set @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.22/0.36 thf(func_def_179, type, sK120: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.22/0.36 thf(func_def_180, type, sK121: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 0.22/0.36 thf(func_def_181, type, sK122: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.22/0.36 thf(func_def_182, type, sK123: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 0.22/0.36 thf(func_def_183, type, sK124: !>[X0: $tType]:((X0 > (X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.22/0.36 thf(func_def_184, type, sK125: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > X0))).
% 0.22/0.36 thf(f1,axiom,(
% 0.22/0.36 (p @ coinductive_LNil @ a)),
% 0.22/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_init)).
% 0.22/0.36 thf(f2,axiom,(
% 0.22/0.36 (la = coinductive_LNil @ a)),
% 0.22/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_LNil__fin_Ohyps)).
% 0.22/0.36 thf(f4,axiom,(
% 0.22/0.36 ! [X0 : $tType] : (((lList2281150353e_lrev @ X0 @ coinductive_LNil @ X0)) = coinductive_LNil @ X0)),
% 0.22/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_lrev__LNil)).
% 0.22/0.36 thf(f273,conjecture,(
% 0.22/0.36 (p @ (lList2281150353e_lrev @ a @ la))),
% 0.22/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 0.22/0.36 thf(f274,negated_conjecture,(
% 0.22/0.36 ~(p @ (lList2281150353e_lrev @ a @ la))),
% 0.22/0.36 inference(negated_conjecture,[status(cth)],[f273])).
% 0.22/0.36 thf(f620,plain,(
% 0.22/0.36 ~(p @ (lList2281150353e_lrev @ a @ la))),
% 0.22/0.36 inference(rectify,[],[f274])).
% 0.22/0.36 thf(f621,plain,(
% 0.22/0.36 ~ (((p @ (lList2281150353e_lrev @ a @ la))) = $true)),
% 0.22/0.36 inference(fool_elimination,[],[f620])).
% 0.22/0.36 thf(f693,plain,(
% 0.22/0.36 (p @ coinductive_LNil @ a)),
% 0.22/0.36 inference(rectify,[],[f1])).
% 0.80/0.36 thf(f694,plain,(
% 0.80/0.36 (((p @ coinductive_LNil @ a)) = $true)),
% 0.80/0.36 inference(fool_elimination,[],[f693])).
% 0.80/0.36 thf(f771,plain,(
% 0.80/0.36 (((p @ (lList2281150353e_lrev @ a @ la))) != $true)),
% 0.80/0.36 inference(flattening,[],[f621])).
% 0.80/0.36 thf(f1275,plain,(
% 0.80/0.36 ( ! [X0 : $tType] : ((coinductive_LNil @ X0 = ((lList2281150353e_lrev @ X0 @ coinductive_LNil @ X0)))) )),
% 0.80/0.36 inference(cnf_transformation,[],[f4])).
% 0.80/0.36 thf(f1523,plain,(
% 0.80/0.36 (coinductive_LNil @ a = la)),
% 0.80/0.36 inference(cnf_transformation,[],[f2])).
% 0.80/0.36 thf(f1536,plain,(
% 0.80/0.36 (((p @ coinductive_LNil @ a)) = $true)),
% 0.80/0.36 inference(cnf_transformation,[],[f694])).
% 0.80/0.36 thf(f1573,plain,(
% 0.80/0.36 (((p @ (lList2281150353e_lrev @ a @ la))) != $true)),
% 0.80/0.36 inference(cnf_transformation,[],[f771])).
% 0.80/0.36 thf(f1701,definition,(
% 0.80/0.36 (sF102 = ((lList2281150353e_lrev @ a @ la)))),
% 0.80/0.36 introduced(definition,[new_symbols(definition,[sF102])],[function_definition])).
% 0.80/0.36 thf(f1702,plain,(
% 0.80/0.36 (((lList2281150353e_lrev @ a @ la)) = sF102)),
% 0.80/0.36 inference(reorient_equations,[],[f1701])).
% 0.80/0.36 thf(f1703,definition,(
% 0.80/0.36 (sF103 = ((p @ sF102)))),
% 0.80/0.36 introduced(definition,[new_symbols(definition,[sF103])],[function_definition])).
% 0.80/0.36 thf(f1704,plain,(
% 0.80/0.36 (((p @ sF102)) = sF103)),
% 0.80/0.36 inference(reorient_equations,[],[f1703])).
% 0.80/0.36 thf(f1705,plain,(
% 0.80/0.36 (sF103 != $true)),
% 0.80/0.36 inference(definition_folding,[],[f1573,f1704,f1702])).
% 0.80/0.36 thf(f1833,plain,(
% 0.80/0.36 (sF103 = $true) | ($false = ((p @ sF102)))),
% 0.80/0.36 inference(iff_proxy_clausification,[],[f1704])).
% 0.80/0.36 thf(f2302,definition,(
% 0.80/0.36 spl126_5 <=> (sF103 = $true)),
% 0.80/0.36 introduced(definition,[new_symbols(definition,[spl126_5])],[avatar_definition])).
% 0.80/0.36 thf(f2306,definition,(
% 0.80/0.36 spl126_6 <=> ($false = ((p @ sF102)))),
% 0.80/0.36 introduced(definition,[new_symbols(definition,[spl126_6])],[avatar_definition])).
% 0.80/0.36 thf(f2308,plain,(
% 0.80/0.36 ($false = ((p @ sF102))) | ~spl126_6),
% 0.80/0.36 inference(avatar_component_clause,[],[f2306])).
% 0.80/0.36 thf(f2309,plain,(
% 0.80/0.36 spl126_5 | spl126_6),
% 0.80/0.36 inference(avatar_split_clause,[],[f1833,f2306,f2302])).
% 0.80/0.36 thf(f2322,plain,(
% 0.80/0.36 ~spl126_5),
% 0.80/0.36 inference(avatar_split_clause,[],[f1705,f2302])).
% 0.80/0.36 thf(f2337,plain,(
% 0.80/0.36 ($true = ((p @ la)))),
% 0.80/0.36 inference(forward_demodulation,[],[f1536,f1523])).
% 0.80/0.36 thf(f2340,plain,(
% 0.80/0.36 (la = ((lList2281150353e_lrev @ a @ la)))),
% 0.80/0.36 inference(constrained_superposition,[],[f1275,f1523])).
% 0.80/0.36 thf(f2341,plain,(
% 0.80/0.36 (la = sF102)),
% 0.80/0.36 inference(forward_demodulation,[],[f2340,f1702])).
% 0.80/0.36 thf(f2345,plain,(
% 0.80/0.36 (((p @ sF102)) = $true)),
% 0.80/0.36 inference(constrained_superposition,[],[f2337,f2341])).
% 0.80/0.36 thf(f2346,plain,(
% 0.80/0.36 ($false = $true) | ~spl126_6),
% 0.80/0.36 inference(forward_demodulation,[],[f2345,f2308])).
% 0.80/0.36 thf(f2347,plain,(
% 0.80/0.36 $false | ~spl126_6),
% 0.80/0.36 inference(trivial_inequality_removal,[],[f2346])).
% 0.80/0.36 thf(f2348,plain,(
% 0.80/0.36 ~spl126_6),
% 0.80/0.36 inference(avatar_contradiction_clause,[],[f2347])).
% 0.80/0.36 cnf(s5, plain, spl126_5 | spl126_6, inference(sat_conversion,[],[f2309])).
% 0.80/0.36 cnf(s11, plain, ~spl126_5, inference(sat_conversion,[],[f2322])).
% 0.80/0.36 cnf(s12, plain, ~spl126_6, inference(sat_conversion,[],[f2348])).
% 0.80/0.36 cnf(s13, plain, $false, inference(rat,[],[s5,s12,s11])).
% 0.80/0.36 thf(f2349,plain,(
% 0.80/0.36 $false),
% 0.80/0.36 inference(avatar_sat_refutation,[],[s13])).
% 0.80/0.36 % SZS output end Proof for theBenchmark
% 0.80/0.36 % (1113408)------------------------------
% 0.80/0.36 % (1113408)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.80/0.36 % (1113408)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.80/0.36 % (1113408)CaDiCaL version: 2.1.3
% 0.80/0.36 % (1113408)Termination reason: Refutation
% 0.80/0.36 % (1113408)Time elapsed: 0.057 s
% 0.80/0.36 % (1113408)Peak memory usage: 14 MB
% 0.80/0.36 % (1113408)Instructions burned: 119 (million)
% 0.80/0.36 % (1113397)Success in time 0.109 s
% 0.80/0.36 % Vampire exiting
%------------------------------------------------------------------------------