%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT147^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 07:48:57 AM UTC 2026
% Result : Theorem 0.77s 0.44s
% Output : Refutation 0.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT147^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 17:59:41 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.77/0.44 % (3728601)Will run a generic schedule for satisfiability detection.
% 0.77/0.44 % (3728621)dis+10_1_sil=32000:sp=arity:random_seed=334724348:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.77/0.44 % (3728619)% WARNING: option uhcvi not known.
% 0.77/0.44 % (3728618)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2585317776_2999 on theBenchmark for (2999ds/0Mi)
% 0.77/0.44 % (3728619)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3186070402:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.77/0.44 % (3728620)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2125021714:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.77/0.44 % (3728622)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3589020880:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.77/0.44 % (3728623)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3123156114:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.77/0.44 % (3728624)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3700493811:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.77/0.44 % (3728619)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.77/0.44 % (3728622)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.77/0.44 % (3728621)Instruction limit reached!
% 0.77/0.44 % (3728621)------------------------------
% 0.77/0.44 % (3728621)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.44 % (3728621)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.44 % (3728621)CaDiCaL version: 2.1.3
% 0.77/0.44 % (3728621)Termination reason: Instruction limit
% 0.77/0.44 % (3728621)Termination phase: Saturation
% 0.77/0.44 % (3728621)Time elapsed: 0.025 s
% 0.77/0.44 % (3728621)Peak memory usage: 12 MB
% 0.77/0.44 % (3728621)Instructions burned: 104 (million)
% 0.77/0.44 % (3728638)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=754854654:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.77/0.44 % Exception at run slice level
% 0.77/0.44 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.77/0.44 % (3728619)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.77/0.44 % Exception at run slice level
% 0.77/0.44 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.77/0.44 % (3728646)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1912490977:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.77/0.44 % (3728622)Instruction limit reached!
% 0.77/0.44 % (3728622)------------------------------
% 0.77/0.44 % (3728622)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.44 % (3728622)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.44 % (3728622)CaDiCaL version: 2.1.3
% 0.77/0.44 % (3728622)Termination reason: Instruction limit
% 0.77/0.44 % (3728622)Termination phase: Saturation
% 0.77/0.44 % (3728622)Time elapsed: 0.054 s
% 0.77/0.44 % (3728622)Peak memory usage: 13 MB
% 0.77/0.44 % (3728622)Instructions burned: 118 (million)
% 0.77/0.44 % (3728653)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=42983070:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.77/0.44 % (3728623)Instruction limit reached!
% 0.77/0.44 % (3728623)------------------------------
% 0.77/0.44 % (3728623)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.44 % (3728623)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.44 % (3728623)CaDiCaL version: 2.1.3
% 0.77/0.44 % (3728623)Termination reason: Instruction limit
% 0.77/0.44 % (3728623)Termination phase: Saturation
% 0.77/0.44 % (3728623)Time elapsed: 0.061 s
% 0.77/0.44 % (3728623)Peak memory usage: 13 MB
% 0.77/0.44 % (3728623)Instructions burned: 132 (million)
% 0.77/0.44 % (3728653)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.77/0.44 % (3728655)ott-21_1_sil=16000:fs=off:random_seed=2219425760:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 0.77/0.44 % (3728653)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.77/0.44 % (3728657)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2236561424:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 0.77/0.44 % (3728624)Instruction limit reached!
% 0.77/0.44 % (3728624)------------------------------
% 0.77/0.44 % (3728624)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.44 % (3728624)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.44 % (3728624)CaDiCaL version: 2.1.3
% 0.77/0.44 % (3728624)Termination reason: Instruction limit
% 0.77/0.44 % (3728624)Termination phase: Saturation
% 0.77/0.44 % (3728624)Time elapsed: 0.083 s
% 0.77/0.44 % (3728624)Peak memory usage: 14 MB
% 0.77/0.44 % (3728624)Instructions burned: 160 (million)
% 0.77/0.44 % (3728664)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3712564307:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 0.77/0.44 % (3728646)Instruction limit reached!
% 0.77/0.44 % (3728646)------------------------------
% 0.77/0.44 % (3728646)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.44 % (3728646)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.44 % (3728646)CaDiCaL version: 2.1.3
% 0.77/0.44 % (3728646)Termination reason: Instruction limit
% 0.77/0.44 % (3728646)Termination phase: Saturation
% 0.77/0.44 % (3728646)Time elapsed: 0.062 s
% 0.77/0.44 % (3728646)Peak memory usage: 13 MB
% 0.77/0.44 % (3728646)Instructions burned: 133 (million)
% 0.77/0.44 % (3728676)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3398908863:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 0.77/0.44 % Exception at run slice level
% 0.77/0.44 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.77/0.44 % (3728619) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3728601-3728619"...
% 0.77/0.44 % (3728619)...printing done.
% 0.77/0.44 % (3728683)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=3993381173:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 0.77/0.44 % (3728619)Refutation found. Thanks to Tanya!
% 0.77/0.44 % SZS status Theorem for theBenchmark
% 0.77/0.44 % SZS output start Proof for theBenchmark
% 0.77/0.44 thf(type_def_5, type, coinductive_llist: $tType > $tType).
% 0.77/0.44 thf(type_def_6, type, stream: $tType > $tType).
% 0.77/0.44 thf(type_def_7, type, set: $tType > $tType).
% 0.77/0.44 thf(type_def_8, type, itself: $tType > $tType).
% 0.77/0.44 thf(type_def_9, type, a: $tType).
% 0.77/0.44 thf(type_def_10, type, sTfun: ($tType * $tType) > $tType).
% 0.77/0.44 thf(func_def_0, type, bounded_lattice: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.77/0.44 thf(func_def_1, type, type: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.77/0.44 thf(func_def_2, type, bot: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.77/0.44 thf(func_def_3, type, lattice: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.77/0.44 thf(func_def_4, type, distrib_lattice: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.77/0.44 thf(func_def_5, type, semilattice_inf: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.77/0.44 thf(func_def_6, type, semilattice_sup: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.77/0.44 thf(func_def_7, type, bounded_lattice_bot: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.77/0.44 thf(func_def_8, type, bounde1808546759up_bot: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.77/0.44 thf(func_def_9, type, coinductive_gen_lset: !>[X0: $tType]:((set @ X0 > coinductive_llist @ X0 > set @ X0))).
% 0.77/0.44 thf(func_def_10, type, coinductive_lappend: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.77/0.44 thf(func_def_11, type, coinductive_lconcat: !>[X0: $tType]:((coinductive_llist @ coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.77/0.44 thf(func_def_12, type, coindu351974385stinct: !>[X0: $tType]:((coinductive_llist @ X0 > $o))).
% 0.77/0.44 thf(func_def_13, type, coindu218763757pWhile: !>[X0: $tType]:(((X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.77/0.44 thf(func_def_14, type, coinductive_lfilter: !>[X0: $tType]:(((X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.77/0.44 thf(func_def_15, type, coinductive_lfinite: !>[X0: $tType]:((coinductive_llist @ X0 > $o))).
% 0.77/0.44 thf(func_def_16, type, coinductive_llast: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 0.77/0.44 thf(func_def_17, type, coinductive_LCons: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.77/0.44 thf(func_def_18, type, coinductive_LNil: !>[X0: $tType]:(coinductive_llist @ X0)).
% 0.77/0.44 thf(func_def_19, type, coindu1381640503_llist: !>[X0: $tType, X1: $tType]:((X0 > (X1 > coinductive_llist @ X1 > X0) > coinductive_llist @ X1 > X0))).
% 0.77/0.44 thf(func_def_20, type, coinductive_lhd: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 0.77/0.44 thf(func_def_21, type, coinductive_lnull: !>[X0: $tType]:((coinductive_llist @ X0 > $o))).
% 0.77/0.44 thf(func_def_22, type, coinductive_lset: !>[X0: $tType]:((coinductive_llist @ X0 > set @ X0))).
% 0.77/0.44 thf(func_def_23, type, coinductive_ltl: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.77/0.44 thf(func_def_24, type, coinductive_lmember: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > $o))).
% 0.77/0.44 thf(func_def_25, type, coinductive_lsetp: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > $o))).
% 0.77/0.44 thf(func_def_26, type, coindu1478340336prefix: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > $o))).
% 0.77/0.44 thf(func_def_27, type, coindu501562517eWhile: !>[X0: $tType]:(((X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.77/0.44 thf(func_def_28, type, coindu1441602521_llist: !>[X0: $tType, X1: $tType]:(((X0 > $o) > (X0 > X1) > (X0 > X0) > X0 > coinductive_llist @ X1))).
% 0.77/0.44 thf(func_def_29, type, coindu1724414836stream: !>[X0: $tType]:((stream @ X0 > coinductive_llist @ X0))).
% 0.77/0.44 thf(func_def_30, type, coindu1183105481stream: !>[X0: $tType]:((coinductive_llist @ X0 > stream @ X0 > $o))).
% 0.77/0.44 thf(func_def_31, type, coindu2010755910_llist: !>[X0: $tType]:((coinductive_llist @ X0 > stream @ X0))).
% 0.77/0.44 thf(func_def_32, type, coindu139217191stream: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X0) > X0 > stream @ X1))).
% 0.77/0.44 thf(func_def_33, type, if: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 0.77/0.44 thf(func_def_34, type, inf_inf: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.77/0.44 thf(func_def_35, type, sup_sup: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.77/0.44 thf(func_def_36, type, bot_bot: !>[X0: $tType]:(X0)).
% 0.77/0.44 thf(func_def_37, type, type2: !>[X0: $tType]:(itself @ X0)).
% 0.77/0.44 thf(func_def_38, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.77/0.44 thf(func_def_39, type, disjnt: !>[X0: $tType]:((set @ X0 > set @ X0 > $o))).
% 0.77/0.44 thf(func_def_40, type, is_empty: !>[X0: $tType]:((set @ X0 > $o))).
% 0.77/0.44 thf(func_def_41, type, sinterleave: !>[X0: $tType]:((stream @ X0 > stream @ X0 > stream @ X0))).
% 0.77/0.44 thf(func_def_42, type, smember: !>[X0: $tType]:((X0 > stream @ X0 > $o))).
% 0.77/0.44 thf(func_def_43, type, shd: !>[X0: $tType]:((stream @ X0 > X0))).
% 0.77/0.44 thf(func_def_44, type, sset: !>[X0: $tType]:((stream @ X0 > set @ X0))).
% 0.77/0.44 thf(func_def_45, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.77/0.44 thf(func_def_46, type, x: a).
% 0.77/0.44 thf(func_def_47, type, xs: stream @ a).
% 0.77/0.44 thf(func_def_48, type, xsa: stream @ a).
% 0.77/0.44 thf(func_def_52, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.77/0.44 thf(func_def_53, type, db1: !>[X0: $tType]:(X0)).
% 0.77/0.44 thf(func_def_54, type, db0: !>[X0: $tType]:(X0)).
% 0.77/0.44 thf(func_def_55, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.77/0.44 thf(func_def_56, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.77/0.44 thf(func_def_57, type, vIMP: ($o > $o > $o)).
% 0.77/0.44 thf(func_def_58, type, vNOT: ($o > $o)).
% 0.77/0.44 thf(func_def_59, type, vAND: ($o > $o > $o)).
% 0.77/0.44 thf(func_def_60, type, vOR: ($o > $o > $o)).
% 0.77/0.44 thf(func_def_61, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.77/0.44 thf(func_def_62, type, db2: !>[X0: $tType]:(X0)).
% 0.77/0.44 thf(func_def_63, type, db3: !>[X0: $tType]:(X0)).
% 0.77/0.44 thf(func_def_64, type, db4: !>[X0: $tType]:(X0)).
% 0.77/0.44 thf(func_def_65, type, sK0: !>[X0: $tType]:(((X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.77/0.44 thf(func_def_66, type, sK1: !>[X0: $tType]:(((X0 > coinductive_llist @ X0 > $o) > X0))).
% 0.77/0.44 thf(func_def_67, type, sK2: !>[X0: $tType]:(((X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.77/0.44 thf(func_def_68, type, sK3: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > coinductive_llist @ X0 > X0))).
% 0.77/0.44 thf(func_def_69, type, sK4: !>[X0: $tType]:(((X0 > $o) > coinductive_llist @ X0 > X0))).
% 0.77/0.44 thf(func_def_70, type, sK5: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > coinductive_llist @ X0 > X0))).
% 0.77/0.44 thf(func_def_71, type, sK6: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.77/0.44 thf(func_def_72, type, sK7: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.77/0.44 thf(func_def_73, type, sK8: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > coinductive_llist @ X0 > X0))).
% 0.77/0.44 thf(func_def_74, type, sK9: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.77/0.44 thf(func_def_75, type, sK10: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.77/0.44 thf(func_def_76, type, sK11: !>[X0: $tType]:(((coinductive_llist @ X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.77/0.44 thf(func_def_77, type, sK12: !>[X0: $tType]:(((coinductive_llist @ X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.77/0.44 thf(func_def_78, type, sK13: !>[X0: $tType]:(((coinductive_llist @ X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.77/0.44 thf(func_def_79, type, sK14: !>[X0: $tType]:(((coinductive_llist @ X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.77/0.44 thf(func_def_80, type, sK15: !>[X0: $tType]:((set @ X0 > X0))).
% 0.77/0.44 thf(func_def_81, type, sK16: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > $o) > coinductive_llist @ X0))).
% 0.77/0.44 thf(func_def_82, type, sK17: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > $o) > coinductive_llist @ X0))).
% 0.77/0.44 thf(func_def_83, type, sK18: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.77/0.44 thf(func_def_84, type, sK19: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.77/0.44 thf(func_def_85, type, sK20: !>[X0: $tType]:((coinductive_llist @ coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.77/0.44 thf(func_def_86, type, sK21: !>[X0: $tType]:((coinductive_llist @ coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.77/0.44 thf(func_def_87, type, sK22: !>[X0: $tType]:((coinductive_llist @ coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.77/0.44 thf(func_def_88, type, sK23: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.77/0.44 thf(func_def_89, type, sK24: !>[X0: $tType]:(X0)).
% 0.77/0.44 thf(func_def_90, type, sK25: !>[X0: $tType]:(X0)).
% 0.77/0.44 thf(func_def_91, type, sK26: !>[X0: $tType]:(X0)).
% 0.77/0.44 thf(func_def_92, type, sK27: !>[X0: $tType]:(X0)).
% 0.77/0.44 thf(func_def_93, type, sK28: !>[X0: $tType]:(X0)).
% 0.77/0.44 thf(func_def_94, type, sK29: !>[X0: $tType]:(X0)).
% 0.77/0.44 thf(func_def_95, type, sK30: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > coinductive_llist @ X0 > (X0 > $o) > coinductive_llist @ X0))).
% 0.77/0.44 thf(func_def_96, type, sK31: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > coinductive_llist @ X0 > (X0 > $o) > coinductive_llist @ X0))).
% 0.77/0.44 thf(func_def_97, type, sK32: !>[X0: $tType]:(((X0 > coinductive_llist @ X0 > $o) > X0))).
% 0.77/0.44 thf(func_def_98, type, sK33: !>[X0: $tType]:(((X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.77/0.44 thf(func_def_99, type, sK34: !>[X0: $tType]:(((X0 > coinductive_llist @ X0 > $o) > X0))).
% 0.77/0.44 thf(func_def_100, type, sK35: !>[X0: $tType]:(((X0 > coinductive_llist @ X0 > $o) > X0))).
% 0.77/0.44 thf(func_def_101, type, sK36: !>[X0: $tType]:(((X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.77/0.44 thf(func_def_102, type, sK37: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > X0))).
% 0.77/0.44 thf(func_def_103, type, sK38: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > coinductive_llist @ X0))).
% 0.77/0.44 thf(func_def_104, type, sK39: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > coinductive_llist @ X0))).
% 0.77/0.44 thf(func_def_105, type, sK40: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > X0 > X0))).
% 0.77/0.44 thf(func_def_106, type, sK41: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > X0 > coinductive_llist @ X0))).
% 0.77/0.44 thf(func_def_107, type, sK42: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > X0 > coinductive_llist @ X0))).
% 0.77/0.44 thf(func_def_108, type, sK43: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > X0 > X0))).
% 0.77/0.44 thf(func_def_109, type, sK44: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > X0 > coinductive_llist @ X0))).
% 0.77/0.44 thf(func_def_110, type, sK45: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > X0 > coinductive_llist @ X0))).
% 0.77/0.44 thf(func_def_111, type, sK46: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > X0))).
% 0.77/0.44 thf(func_def_112, type, sK47: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > coinductive_llist @ X0))).
% 0.77/0.44 thf(func_def_113, type, sK48: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > coinductive_llist @ X0))).
% 0.77/0.44 thf(func_def_114, type, sK49: !>[X0: $tType]:(((coinductive_llist @ X0 > X0 > $o) > coinductive_llist @ X0))).
% 0.77/0.44 thf(func_def_115, type, sK50: !>[X0: $tType]:(((coinductive_llist @ X0 > X0 > $o) > X0))).
% 0.77/0.44 thf(func_def_116, type, sK51: !>[X0: $tType]:(((coinductive_llist @ X0 > X0 > $o) > X0))).
% 0.77/0.44 thf(func_def_117, type, sK52: !>[X0: $tType]:(((coinductive_llist @ X0 > X0 > $o) > X0))).
% 0.77/0.44 thf(func_def_118, type, sK53: !>[X0: $tType]:(((coinductive_llist @ X0 > X0 > $o) > coinductive_llist @ X0))).
% 0.77/0.44 thf(func_def_119, type, sK54: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.77/0.44 thf(func_def_120, type, sK55: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > X0))).
% 0.77/0.44 thf(func_def_121, type, sK56: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > X0))).
% 0.77/0.44 thf(func_def_122, type, sK57: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.77/0.44 thf(func_def_123, type, sK58: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > coinductive_llist @ X0))).
% 0.77/0.44 thf(func_def_124, type, sK59: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > coinductive_llist @ X0))).
% 0.77/0.44 thf(func_def_125, type, sK60: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > coinductive_llist @ X0))).
% 0.77/0.44 thf(func_def_126, type, sK61: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > coinductive_llist @ X0))).
% 0.77/0.44 thf(func_def_127, type, sK62: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.77/0.44 thf(func_def_128, type, sK63: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 0.77/0.44 thf(func_def_129, type, sK64: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.77/0.44 thf(func_def_130, type, sK65: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.77/0.44 thf(func_def_131, type, sK66: !>[X0: $tType]:((set @ X0 > set @ X0 > (X0 > $o) > X0))).
% 0.77/0.44 thf(func_def_132, type, sK67: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 0.77/0.44 thf(func_def_133, type, sK68: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 0.77/0.44 thf(func_def_134, type, sK69: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 0.77/0.44 thf(func_def_135, type, sK70: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 0.77/0.44 thf(func_def_136, type, sK71: !>[X0: $tType]:((set @ X0 > (X0 > $o) > set @ X0 > X0))).
% 0.77/0.44 thf(func_def_137, type, sK72: !>[X0: $tType]:((set @ X0 > X0))).
% 0.77/0.44 thf(func_def_138, type, sK73: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.77/0.44 thf(func_def_139, type, sK74: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.77/0.44 thf(func_def_140, type, sK75: !>[X0: $tType]:((set @ X0 > X0))).
% 0.77/0.44 thf(func_def_141, type, sK76: !>[X0: $tType]:(((X0 > $o) > coinductive_llist @ X0 > X0))).
% 0.77/0.44 thf(func_def_142, type, sK77: !>[X0: $tType]:(((X0 > $o) > coinductive_llist @ X0 > X0))).
% 0.77/0.44 thf(func_def_143, type, sK78: !>[X0: $tType]:(((X0 > $o) > coinductive_llist @ X0 > X0))).
% 0.77/0.44 thf(func_def_144, type, sK79: !>[X0: $tType]:(((X0 > $o) > coinductive_llist @ X0 > X0))).
% 0.77/0.44 thf(func_def_145, type, sK80: !>[X0: $tType]:(((X0 > $o) > coinductive_llist @ X0 > X0))).
% 0.77/0.44 thf(f1,axiom,(
% 0.77/0.44 ~(coinductive_lnull @ a @ (coindu1724414836stream @ a @ xsa)) => (member @ a @ (coinductive_lhd @ a @ (coindu1724414836stream @ a @ xsa)) @ (coinductive_lset @ a @ (coindu1724414836stream @ a @ xsa)))),
% 0.77/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__092_060open_062_092_060not_062_Alnull_A_Illist__of__stream_Axs_J_A_092_060Longrightarrow_062_Alhd_A_Illist__of__stream_Axs_J_A_092_060in_062_Alset_A_Illist__of__stream_Axs_J_092_060close_062)).
% 0.77/0.44 thf(f3,axiom,(
% 0.77/0.44 ! [X0 : $tType,X1 : stream @ X0] : (((coinductive_lhd @ X0 @ (coindu1724414836stream @ X0 @ X1))) = ((shd @ X0 @ X1)))),
% 0.77/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_lhd__llist__of__stream)).
% 0.77/0.44 thf(f4,axiom,(
% 0.77/0.44 ! [X0 : $tType,X1 : stream @ X0] : ~(coinductive_lnull @ X0 @ (coindu1724414836stream @ X0 @ X1))),
% 0.77/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_lnull__llist__of__stream)).
% 0.77/0.44 thf(f279,axiom,(
% 0.77/0.44 ! [X0 : $o] : ((X0 = $false) | (X0 = $true))),
% 0.77/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_T)).
% 0.77/0.44 thf(f282,conjecture,(
% 0.77/0.44 (member @ a @ (shd @ a @ xsa) @ (coinductive_lset @ a @ (coindu1724414836stream @ a @ xsa)))),
% 0.77/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 0.77/0.44 thf(f283,negated_conjecture,(
% 0.77/0.44 ~(member @ a @ (shd @ a @ xsa) @ (coinductive_lset @ a @ (coindu1724414836stream @ a @ xsa)))),
% 0.77/0.44 inference(negated_conjecture,[status(cth)],[f282])).
% 0.77/0.44 thf(f284,plain,(
% 0.77/0.44 ~(coinductive_lnull @ a @ (coindu1724414836stream @ a @ xsa)) => (member @ a @ (coinductive_lhd @ a @ (coindu1724414836stream @ a @ xsa)) @ (coinductive_lset @ a @ (coindu1724414836stream @ a @ xsa)))),
% 0.77/0.44 inference(rectify,[],[f1])).
% 0.77/0.44 thf(f285,plain,(
% 0.77/0.44 ~ (((coinductive_lnull @ a @ (coindu1724414836stream @ a @ xsa))) = $true) => (((member @ a @ (coinductive_lhd @ a @ (coindu1724414836stream @ a @ xsa)) @ (coinductive_lset @ a @ (coindu1724414836stream @ a @ xsa)))) = $true)),
% 0.77/0.44 inference(fool_elimination,[],[f284])).
% 0.77/0.44 thf(f287,plain,(
% 0.77/0.44 ! [X0 : $tType,X1 : stream @ X0] : ~(coinductive_lnull @ X0 @ (coindu1724414836stream @ X0 @ X1))),
% 0.77/0.44 inference(rectify,[],[f4])).
% 0.77/0.44 thf(f288,plain,(
% 0.77/0.44 ! [X0 : $tType,X1 : stream @ X0] : ~ (((coinductive_lnull @ X0 @ (coindu1724414836stream @ X0 @ X1))) = $true)),
% 0.77/0.44 inference(fool_elimination,[],[f287])).
% 0.77/0.44 thf(f727,plain,(
% 0.77/0.44 ! [X0 : $o] : (($false = X0) | ($true = X0))),
% 0.77/0.44 inference(fool_elimination,[],[f279])).
% 0.77/0.44 thf(f732,plain,(
% 0.77/0.44 ~(member @ a @ (shd @ a @ xsa) @ (coinductive_lset @ a @ (coindu1724414836stream @ a @ xsa)))),
% 0.77/0.44 inference(rectify,[],[f283])).
% 0.77/0.44 thf(f733,plain,(
% 0.77/0.44 ~ (((member @ a @ (shd @ a @ xsa) @ (coinductive_lset @ a @ (coindu1724414836stream @ a @ xsa)))) = $true)),
% 0.77/0.44 inference(fool_elimination,[],[f732])).
% 0.77/0.44 thf(f734,plain,(
% 0.77/0.44 (((coinductive_lnull @ a @ (coindu1724414836stream @ a @ xsa))) != $true) => (((member @ a @ (coinductive_lhd @ a @ (coindu1724414836stream @ a @ xsa)) @ (coinductive_lset @ a @ (coindu1724414836stream @ a @ xsa)))) = $true)),
% 0.77/0.44 inference(flattening,[],[f285])).
% 0.77/0.44 thf(f735,plain,(
% 0.77/0.44 ! [X0 : $tType,X1 : stream @ X0] : (((coinductive_lnull @ X0 @ (coindu1724414836stream @ X0 @ X1))) != $true)),
% 0.77/0.44 inference(flattening,[],[f288])).
% 0.77/0.44 thf(f791,plain,(
% 0.77/0.44 (((member @ a @ (shd @ a @ xsa) @ (coinductive_lset @ a @ (coindu1724414836stream @ a @ xsa)))) != $true)),
% 0.77/0.44 inference(flattening,[],[f733])).
% 0.77/0.44 thf(f792,plain,(
% 0.77/0.44 (((member @ a @ (coinductive_lhd @ a @ (coindu1724414836stream @ a @ xsa)) @ (coinductive_lset @ a @ (coindu1724414836stream @ a @ xsa)))) = $true) | (((coinductive_lnull @ a @ (coindu1724414836stream @ a @ xsa))) = $true)),
% 0.77/0.44 inference(ennf_transformation,[],[f734])).
% 0.77/0.44 thf(f1021,plain,(
% 0.77/0.44 (((member @ a @ (coinductive_lhd @ a @ (coindu1724414836stream @ a @ xsa)) @ (coinductive_lset @ a @ (coindu1724414836stream @ a @ xsa)))) = $true) | (((coinductive_lnull @ a @ (coindu1724414836stream @ a @ xsa))) = $true)),
% 0.77/0.44 inference(cnf_transformation,[],[f792])).
% 0.77/0.44 thf(f1023,plain,(
% 0.77/0.44 ( ! [X0 : $tType,X1 : stream @ X0] : ((((coinductive_lhd @ X0 @ (coindu1724414836stream @ X0 @ X1))) = ((shd @ X0 @ X1)))) )),
% 0.77/0.44 inference(cnf_transformation,[],[f3])).
% 0.77/0.44 thf(f1024,plain,(
% 0.77/0.44 ( ! [X0 : $tType,X1 : stream @ X0] : ((((coinductive_lnull @ X0 @ (coindu1724414836stream @ X0 @ X1))) != $true)) )),
% 0.77/0.44 inference(cnf_transformation,[],[f735])).
% 0.77/0.44 thf(f1375,plain,(
% 0.77/0.44 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.77/0.44 inference(cnf_transformation,[],[f727])).
% 0.77/0.44 thf(f1378,plain,(
% 0.77/0.44 (((member @ a @ (shd @ a @ xsa) @ (coinductive_lset @ a @ (coindu1724414836stream @ a @ xsa)))) != $true)),
% 0.77/0.44 inference(cnf_transformation,[],[f791])).
% 0.77/0.44 thf(f1820,definition,(
% 0.77/0.44 spl81_1 <=> (((coinductive_lnull @ a @ (coindu1724414836stream @ a @ xsa))) = $true)),
% 0.77/0.44 introduced(definition,[new_symbols(definition,[spl81_1])],[avatar_definition])).
% 0.77/0.44 thf(f1822,plain,(
% 0.77/0.44 (((coinductive_lnull @ a @ (coindu1724414836stream @ a @ xsa))) = $true) | ~spl81_1),
% 0.77/0.44 inference(avatar_component_clause,[],[f1820])).
% 0.77/0.44 thf(f1824,definition,(
% 0.77/0.44 spl81_2 <=> (((member @ a @ (coinductive_lhd @ a @ (coindu1724414836stream @ a @ xsa)) @ (coinductive_lset @ a @ (coindu1724414836stream @ a @ xsa)))) = $true)),
% 0.77/0.44 introduced(definition,[new_symbols(definition,[spl81_2])],[avatar_definition])).
% 0.77/0.44 thf(f1826,plain,(
% 0.77/0.44 (((member @ a @ (coinductive_lhd @ a @ (coindu1724414836stream @ a @ xsa)) @ (coinductive_lset @ a @ (coindu1724414836stream @ a @ xsa)))) = $true) | ~spl81_2),
% 0.77/0.44 inference(avatar_component_clause,[],[f1824])).
% 0.77/0.44 thf(f1827,plain,(
% 0.77/0.44 spl81_1 | spl81_2),
% 0.77/0.44 inference(avatar_split_clause,[],[f1021,f1824,f1820])).
% 0.77/0.44 thf(f1830,plain,(
% 0.77/0.44 ($true != $true) | (((member @ a @ (shd @ a @ xsa) @ (coinductive_lset @ a @ (coindu1724414836stream @ a @ xsa)))) = $false)),
% 0.77/0.44 inference(constrained_superposition,[],[f1378,f1375])).
% 0.77/0.44 thf(f1832,plain,(
% 0.77/0.44 (((member @ a @ (shd @ a @ xsa) @ (coinductive_lset @ a @ (coindu1724414836stream @ a @ xsa)))) = $false)),
% 0.77/0.44 inference(trivial_inequality_removal,[],[f1830])).
% 0.77/0.44 thf(f1840,plain,(
% 0.77/0.44 ( ! [X0 : $tType,X1 : stream @ X0] : (($true != $true) | (((coinductive_lnull @ X0 @ (coindu1724414836stream @ X0 @ X1))) = $false)) )),
% 0.77/0.44 inference(constrained_superposition,[],[f1024,f1375])).
% 0.77/0.44 thf(f1841,plain,(
% 0.77/0.44 ( ! [X0 : $tType,X1 : stream @ X0] : ((((coinductive_lnull @ X0 @ (coindu1724414836stream @ X0 @ X1))) = $false)) )),
% 0.77/0.44 inference(trivial_inequality_removal,[],[f1840])).
% 0.77/0.44 thf(f4017,plain,(
% 0.77/0.44 (((member @ a @ (shd @ a @ xsa) @ (coinductive_lset @ a @ (coindu1724414836stream @ a @ xsa)))) = $true) | ~spl81_2),
% 0.77/0.44 inference(forward_demodulation,[],[f1826,f1023])).
% 0.77/0.44 thf(f4018,plain,(
% 0.77/0.44 ($true = $false) | ~spl81_2),
% 0.77/0.44 inference(forward_demodulation,[],[f4017,f1832])).
% 0.77/0.44 thf(f4019,plain,(
% 0.77/0.44 $false | ~spl81_2),
% 0.77/0.44 inference(trivial_inequality_removal,[],[f4018])).
% 0.77/0.44 thf(f4020,plain,(
% 0.77/0.44 ~spl81_2),
% 0.77/0.44 inference(avatar_contradiction_clause,[],[f4019])).
% 0.77/0.44 thf(f4021,plain,(
% 0.77/0.44 ($true = $false) | ~spl81_1),
% 0.77/0.44 inference(forward_demodulation,[],[f1822,f1841])).
% 0.77/0.44 thf(f4022,plain,(
% 0.77/0.44 $false | ~spl81_1),
% 0.77/0.44 inference(trivial_inequality_removal,[],[f4021])).
% 0.77/0.44 thf(f4023,plain,(
% 0.77/0.44 ~spl81_1),
% 0.77/0.44 inference(avatar_contradiction_clause,[],[f4022])).
% 0.77/0.44 cnf(s1, plain, spl81_1 | spl81_2, inference(sat_conversion,[],[f1827])).
% 0.77/0.44 cnf(s137, plain, ~spl81_2, inference(sat_conversion,[],[f4020])).
% 0.77/0.44 cnf(s138, plain, ~spl81_1, inference(sat_conversion,[],[f4023])).
% 0.77/0.44 cnf(s171, plain, $false, inference(rat,[],[s1,s137,s138])).
% 0.77/0.44 thf(f4026,plain,(
% 0.77/0.44 $false),
% 0.77/0.44 inference(avatar_sat_refutation,[],[s171])).
% 0.77/0.44 % SZS output end Proof for theBenchmark
% 0.77/0.44 % (3728619)------------------------------
% 0.77/0.44 % (3728619)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.44 % (3728619)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.44 % (3728619)CaDiCaL version: 2.1.3
% 0.77/0.44 % (3728619)Termination reason: Refutation
% 0.77/0.44 % (3728619)Time elapsed: 0.155 s
% 0.77/0.44 % (3728619)Peak memory usage: 15 MB
% 0.77/0.44 % (3728619)Instructions burned: 297 (million)
% 0.77/0.44 % (3728601)Success in time 0.208 s
% 0.77/0.44 % Vampire exiting
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