%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT150^1 : 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 : n016.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 2.86s 0.67s
% Output : Refutation 2.86s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT150^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.20 % Computer : n016.cluster.edu
% 0.12/0.20 % Model : x86_64 x86_64
% 0.12/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.20 % Memory : 8046.5625MB
% 0.12/0.20 % OS : Linux 6.8.0-71-generic
% 0.12/0.20 % CPULimit : 300
% 0.12/0.20 % WCLimit : 300
% 0.12/0.20 % DateTime : Tue Sep 29 18:06:53 UTC 2026
% 0.12/0.20 % CPUTime :
% 0.12/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.23 Running first-order model finding
% 0.12/0.23 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
% 2.86/0.67 % (703498)Will run a generic schedule for satisfiability detection.
% 2.86/0.67 % (703512)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=478783904_2999 on theBenchmark for (2999ds/0Mi)
% 2.86/0.67 % (703513)% WARNING: option uhcvi not known.
% 2.86/0.67 % (703513)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1998294786:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 2.86/0.67 % (703514)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3002479266:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 2.86/0.67 % (703515)dis+10_1_sil=32000:sp=arity:random_seed=1880593152:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 2.86/0.67 % (703516)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3235429964:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 2.86/0.67 % (703517)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=932892637:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 2.86/0.67 % (703518)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1192842880:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 2.86/0.67 % Exception at run slice level
% 2.86/0.67 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.86/0.67 % (703513)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.86/0.67 % (703516)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.86/0.67 % (703533)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=866830794:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 2.86/0.67 % (703513)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.86/0.67 % Exception at run slice level
% 2.86/0.67 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.86/0.67 % (703515)Instruction limit reached!
% 2.86/0.67 % (703515)------------------------------
% 2.86/0.67 % (703515)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.86/0.67 % (703515)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.86/0.67 % (703515)CaDiCaL version: 2.1.3
% 2.86/0.67 % (703515)Termination reason: Instruction limit
% 2.86/0.67 % (703515)Termination phase: Saturation
% 2.86/0.67 % (703515)Time elapsed: 0.047 s
% 2.86/0.67 % (703515)Peak memory usage: 12 MB
% 2.86/0.67 % (703515)Instructions burned: 104 (million)
% 2.86/0.67 % (703516)Instruction limit reached!
% 2.86/0.67 % (703516)------------------------------
% 2.86/0.67 % (703516)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.86/0.67 % (703516)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.86/0.67 % (703516)CaDiCaL version: 2.1.3
% 2.86/0.67 % (703516)Termination reason: Instruction limit
% 2.86/0.67 % (703516)Termination phase: Saturation
% 2.86/0.67 % (703516)Time elapsed: 0.053 s
% 2.86/0.67 % (703516)Peak memory usage: 13 MB
% 2.86/0.67 % (703516)Instructions burned: 117 (million)
% 2.86/0.67 % (703544)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=436408546:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 2.86/0.67 % (703517)Instruction limit reached!
% 2.86/0.67 % (703517)------------------------------
% 2.86/0.67 % (703517)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.86/0.67 % (703517)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.86/0.67 % (703517)CaDiCaL version: 2.1.3
% 2.86/0.67 % (703517)Termination reason: Instruction limit
% 2.86/0.67 % (703517)Termination phase: Saturation
% 2.86/0.67 % (703517)Time elapsed: 0.060 s
% 2.86/0.67 % (703517)Peak memory usage: 13 MB
% 2.86/0.67 % (703517)Instructions burned: 132 (million)
% 2.86/0.67 % (703546)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=757195260:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 2.86/0.67 % (703549)ott-21_1_sil=16000:fs=off:random_seed=760939843:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 2.86/0.67 % (703518)Instruction limit reached!
% 2.86/0.67 % (703518)------------------------------
% 2.86/0.67 % (703518)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.86/0.67 % (703518)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.86/0.67 % (703518)CaDiCaL version: 2.1.3
% 2.86/0.67 % (703518)Termination reason: Instruction limit
% 2.86/0.67 % (703518)Termination phase: Saturation
% 2.86/0.67 % (703518)Time elapsed: 0.076 s
% 2.86/0.67 % (703518)Peak memory usage: 14 MB
% 2.86/0.67 % (703518)Instructions burned: 160 (million)
% 2.86/0.67 % (703554)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=756882817:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 2.86/0.67 % (703546)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.86/0.67 % (703544)Instruction limit reached!
% 2.86/0.67 % (703544)------------------------------
% 2.86/0.67 % (703544)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.86/0.67 % (703544)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.86/0.67 % (703544)CaDiCaL version: 2.1.3
% 2.86/0.67 % (703544)Termination reason: Instruction limit
% 2.86/0.67 % (703544)Termination phase: Saturation
% 2.86/0.67 % (703544)Time elapsed: 0.034 s
% 2.86/0.67 % (703544)Peak memory usage: 13 MB
% 2.86/0.67 % (703544)Instructions burned: 134 (million)
% 2.86/0.67 % (703562)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1577319838:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 2.86/0.67 % (703570)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=531229814:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 2.86/0.67 % (703546)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.86/0.67 % Exception at run slice level
% 2.86/0.67 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.86/0.67 % (703549)Instruction limit reached!
% 2.86/0.67 % (703549)------------------------------
% 2.86/0.67 % (703549)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.86/0.67 % (703549)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.86/0.67 % (703549)CaDiCaL version: 2.1.3
% 2.86/0.67 % (703549)Termination reason: Instruction limit
% 2.86/0.67 % (703549)Termination phase: Saturation
% 2.86/0.67 % (703549)Time elapsed: 0.082 s
% 2.86/0.67 % (703549)Peak memory usage: 14 MB
% 2.86/0.67 % (703549)Instructions burned: 182 (million)
% 2.86/0.67 % (703592)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=3094068753:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 2.86/0.67 % (703598)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=244751957:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2997 on theBenchmark for (2997ds/692Mi)
% 2.86/0.67 % (703598)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.86/0.67 % Exception at run slice level
% 2.86/0.67 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.86/0.67 % (703615)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=4280414827:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 2.86/0.67 % (703615)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.86/0.67 % (703554)Instruction limit reached!
% 2.86/0.67 % (703554)------------------------------
% 2.86/0.67 % (703554)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.86/0.67 % (703554)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.86/0.67 % (703554)CaDiCaL version: 2.1.3
% 2.86/0.67 % (703554)Termination reason: Instruction limit
% 2.86/0.67 % (703554)Termination phase: Saturation
% 2.86/0.67 % (703554)Time elapsed: 0.258 s
% 2.86/0.67 % (703554)Peak memory usage: 15 MB
% 2.86/0.67 % (703554)Instructions burned: 478 (million)
% 2.86/0.67 % (703640)fmb+10_1_sil=64000:random_seed=553379220:i=22061:nm=2:gsp=on_2996 on theBenchmark for (2996ds/22061Mi)
% 2.86/0.67 % (703570) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-703498-703570"...
% 2.86/0.67 % (703570)...printing done.
% 2.86/0.67 % (703570)Refutation found. Thanks to Tanya!
% 2.86/0.67 % SZS status Theorem for theBenchmark
% 2.86/0.67 % SZS output start Proof for theBenchmark
% 2.86/0.67 thf(type_def_5, type, coinductive_llist: $tType > $tType).
% 2.86/0.67 thf(type_def_6, type, stream: $tType > $tType).
% 2.86/0.67 thf(type_def_7, type, set: $tType > $tType).
% 2.86/0.67 thf(type_def_8, type, nat: $tType).
% 2.86/0.67 thf(type_def_9, type, itself: $tType > $tType).
% 2.86/0.67 thf(type_def_10, type, a: $tType).
% 2.86/0.67 thf(type_def_11, type, sTfun: ($tType * $tType) > $tType).
% 2.86/0.67 thf(func_def_0, type, finite_finite: !>[X0: $tType]:((itself @ X0 > $o))).
% 2.86/0.67 thf(func_def_1, type, type: !>[X0: $tType]:((itself @ X0 > $o))).
% 2.86/0.67 thf(func_def_2, type, zero: !>[X0: $tType]:((itself @ X0 > $o))).
% 2.86/0.67 thf(func_def_3, type, bot: !>[X0: $tType]:((itself @ X0 > $o))).
% 2.86/0.67 thf(func_def_4, type, ord: !>[X0: $tType]:((itself @ X0 > $o))).
% 2.86/0.67 thf(func_def_5, type, top: !>[X0: $tType]:((itself @ X0 > $o))).
% 2.86/0.67 thf(func_def_6, type, order: !>[X0: $tType]:((itself @ X0 > $o))).
% 2.86/0.67 thf(func_def_7, type, no_bot: !>[X0: $tType]:((itself @ X0 > $o))).
% 2.86/0.67 thf(func_def_8, type, monoid_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 2.86/0.67 thf(func_def_9, type, linorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 2.86/0.67 thf(func_def_10, type, preorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 2.86/0.67 thf(func_def_11, type, countable: !>[X0: $tType]:((itself @ X0 > $o))).
% 2.86/0.67 thf(func_def_12, type, order_bot: !>[X0: $tType]:((itself @ X0 > $o))).
% 2.86/0.67 thf(func_def_13, type, order_top: !>[X0: $tType]:((itself @ X0 > $o))).
% 2.86/0.67 thf(func_def_14, type, complete_Sup: !>[X0: $tType]:((itself @ X0 > $o))).
% 2.86/0.67 thf(func_def_15, type, linordered_semidom: !>[X0: $tType]:((itself @ X0 > $o))).
% 2.86/0.67 thf(func_def_16, type, comple1141879883l_ccpo: !>[X0: $tType]:((itself @ X0 > $o))).
% 2.86/0.67 thf(func_def_17, type, ordere779506340up_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 2.86/0.67 thf(func_def_18, type, comple187826305attice: !>[X0: $tType]:((itself @ X0 > $o))).
% 2.86/0.67 thf(func_def_19, type, canoni770627133id_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 2.86/0.67 thf(func_def_20, type, counta840220525attice: !>[X0: $tType]:((itself @ X0 > $o))).
% 2.86/0.67 thf(func_def_21, type, condit378418413attice: !>[X0: $tType]:((itself @ X0 > $o))).
% 2.86/0.67 thf(func_def_22, type, coinductive_gen_lset: !>[X0: $tType]:((set @ X0 > coinductive_llist @ X0 > set @ X0))).
% 2.86/0.67 thf(func_def_23, type, coindu68654304_llist: !>[X0: $tType]:(((nat > X0) > coinductive_llist @ X0))).
% 2.86/0.67 thf(func_def_24, type, coinductive_lfinite: !>[X0: $tType]:((coinductive_llist @ X0 > $o))).
% 2.86/0.67 thf(func_def_25, type, coinductive_lmap: !>[X0: $tType, X1: $tType]:(((X0 > X1) > coinductive_llist @ X0 > coinductive_llist @ X1))).
% 2.86/0.67 thf(func_def_26, type, coinductive_lset: !>[X0: $tType]:((coinductive_llist @ X0 > set @ X0))).
% 2.86/0.67 thf(func_def_27, type, coindu543516966_llist: !>[X0: $tType]:(((X0 > $o) > coinductive_llist @ X0 > $o))).
% 2.86/0.67 thf(func_def_28, type, coinductive_lmember: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > $o))).
% 2.86/0.67 thf(func_def_29, type, coinductive_lnth: !>[X0: $tType]:((coinductive_llist @ X0 > nat > X0))).
% 2.86/0.67 thf(func_def_30, type, coindu780009021istsum: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 2.86/0.67 thf(func_def_31, type, coindu1724414836stream: !>[X0: $tType]:((stream @ X0 > coinductive_llist @ X0))).
% 2.86/0.67 thf(func_def_32, type, coindu176146587of_seq: !>[X0: $tType]:(((nat > X0) > stream @ X0))).
% 2.86/0.67 thf(func_def_33, type, coindu1183105481stream: !>[X0: $tType]:((coinductive_llist @ X0 > stream @ X0 > $o))).
% 2.86/0.67 thf(func_def_34, type, coindu2010755910_llist: !>[X0: $tType]:((coinductive_llist @ X0 > stream @ X0))).
% 2.86/0.67 thf(func_def_35, type, complete_Sup_Sup: !>[X0: $tType]:((set @ X0 > X0))).
% 2.86/0.67 thf(func_def_36, type, comple2143767107ompact: !>[X0: $tType]:(((set @ X0 > X0) > (X0 > X0 > $o) > X0 > $o))).
% 2.86/0.67 thf(func_def_37, type, condit1810911227_above: !>[X0: $tType]:((set @ X0 > $o))).
% 2.86/0.67 thf(func_def_38, type, from_nat: !>[X0: $tType]:((nat > X0))).
% 2.86/0.67 thf(func_def_39, type, swap: !>[X0: $tType, X1: $tType]:((X0 > X0 > (X0 > X1) > X0 > X1))).
% 2.86/0.67 thf(func_def_40, type, zero_zero: !>[X0: $tType]:(X0)).
% 2.86/0.67 thf(func_def_41, type, bot_bot: !>[X0: $tType]:(X0)).
% 2.86/0.67 thf(func_def_42, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 2.86/0.67 thf(func_def_43, type, top_top: !>[X0: $tType]:(X0)).
% 2.86/0.67 thf(func_def_44, type, type2: !>[X0: $tType]:(itself @ X0)).
% 2.86/0.67 thf(func_def_45, type, ball: !>[X0: $tType]:((set @ X0 > (X0 > $o) > $o))).
% 2.86/0.67 thf(func_def_46, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 2.86/0.67 thf(func_def_47, type, pow: !>[X0: $tType]:((set @ X0 > set @ set @ X0))).
% 2.86/0.67 thf(func_def_48, type, bind: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > set @ X1) > set @ X1))).
% 2.86/0.67 thf(func_def_49, type, image: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > set @ X1))).
% 2.86/0.67 thf(func_def_50, type, the_elem: !>[X0: $tType]:((set @ X0 > X0))).
% 2.86/0.67 thf(func_def_51, type, smap2: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > stream @ X0 > stream @ X1 > stream @ X2))).
% 2.86/0.67 thf(func_def_52, type, smember: !>[X0: $tType]:((X0 > stream @ X0 > $o))).
% 2.86/0.67 thf(func_def_53, type, smerge: !>[X0: $tType]:((stream @ stream @ X0 > stream @ X0))).
% 2.86/0.67 thf(func_def_54, type, snth: !>[X0: $tType]:((stream @ X0 > nat > X0))).
% 2.86/0.67 thf(func_def_55, type, pred_stream: !>[X0: $tType]:(((X0 > $o) > stream @ X0 > $o))).
% 2.86/0.67 thf(func_def_56, type, smap: !>[X0: $tType, X1: $tType]:(((X0 > X1) > stream @ X0 > stream @ X1))).
% 2.86/0.67 thf(func_def_57, type, sset: !>[X0: $tType]:((stream @ X0 > set @ X0))).
% 2.86/0.67 thf(func_def_58, type, stream_all: !>[X0: $tType]:(((X0 > $o) > stream @ X0 > $o))).
% 2.86/0.67 thf(func_def_59, type, streams: !>[X0: $tType]:((set @ X0 > set @ stream @ X0))).
% 2.86/0.67 thf(func_def_60, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 2.86/0.67 thf(func_def_61, type, f: (nat > a)).
% 2.86/0.67 thf(func_def_63, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 2.86/0.67 thf(func_def_64, type, db2: !>[X0: $tType]:(X0)).
% 2.86/0.67 thf(func_def_65, type, db1: !>[X0: $tType]:(X0)).
% 2.86/0.67 thf(func_def_66, type, db0: !>[X0: $tType]:(X0)).
% 2.86/0.67 thf(func_def_67, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 2.86/0.67 thf(func_def_68, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 2.86/0.67 thf(func_def_71, type, vIMP: ($o > $o > $o)).
% 2.86/0.67 thf(func_def_72, type, vNOT: ($o > $o)).
% 2.86/0.67 thf(func_def_73, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 2.86/0.67 thf(func_def_74, type, vAND: ($o > $o > $o)).
% 2.86/0.67 thf(func_def_75, type, sP0: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 2.86/0.67 thf(func_def_76, type, sP1: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 2.86/0.67 thf(func_def_77, type, sP2: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 2.86/0.67 thf(func_def_78, type, sK3: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > X1) > set @ X0 > X0))).
% 2.86/0.67 thf(func_def_79, type, sK4: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > stream @ X1 > X1))).
% 2.86/0.67 thf(func_def_80, type, sK5: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > stream @ X1 > X1))).
% 2.86/0.67 thf(func_def_81, type, sK6: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > stream @ X1 > stream @ X1 > X1))).
% 2.86/0.67 thf(func_def_82, type, sK7: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > stream @ X1 > stream @ X1 > X1))).
% 2.86/0.67 thf(func_def_83, type, sK8: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > coinductive_llist @ X1 > coinductive_llist @ X1 > X1))).
% 2.86/0.67 thf(func_def_84, type, sK9: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > coinductive_llist @ X1 > coinductive_llist @ X1 > X1))).
% 2.86/0.67 thf(func_def_85, type, sK10: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > coinductive_llist @ X1 > X1))).
% 2.86/0.67 thf(func_def_86, type, sK11: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > coinductive_llist @ X1 > X1))).
% 2.86/0.67 thf(func_def_87, type, sK12: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 2.86/0.67 thf(func_def_88, type, sK13: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 2.86/0.67 thf(func_def_89, type, sK14: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 2.86/0.67 thf(func_def_90, type, sK15: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 2.86/0.67 thf(func_def_91, type, sK16: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 2.86/0.67 thf(func_def_92, type, sK17: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > set @ X0 > set @ X1))).
% 2.86/0.67 thf(func_def_93, type, sK18: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 2.86/0.67 thf(func_def_94, type, sK19: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.86/0.67 thf(func_def_95, type, sK20: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.86/0.67 thf(func_def_96, type, sK21: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 2.86/0.67 thf(func_def_97, type, sK22: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 2.86/0.67 thf(func_def_98, type, sK23: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.86/0.67 thf(func_def_99, type, sK24: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.86/0.67 thf(func_def_100, type, sK25: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 2.86/0.67 thf(func_def_101, type, sK26: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 2.86/0.67 thf(func_def_102, type, sK27: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 2.86/0.67 thf(func_def_103, type, sK28: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 2.86/0.67 thf(func_def_104, type, sK29: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 2.86/0.67 thf(func_def_105, type, sK30: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 2.86/0.67 thf(func_def_106, type, sK31: !>[X0: $tType, X1: $tType]:(((X0 > $o) > set @ X1 > (X1 > X0) > X1))).
% 2.86/0.67 thf(func_def_107, type, sK32: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > set @ X1 > X1))).
% 2.86/0.67 thf(func_def_108, type, sK33: !>[X0: $tType, X1: $tType]:(((X0 > $o) > set @ X1 > (X1 > X0) > X0))).
% 2.86/0.67 thf(func_def_109, type, sK34: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > set @ X1 > X1))).
% 2.86/0.67 thf(func_def_110, type, sK35: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > set @ X1 > X1))).
% 2.86/0.67 thf(func_def_111, type, sK36: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 2.86/0.67 thf(func_def_112, type, sK37: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > X1) > set @ X0 > X0))).
% 2.86/0.67 thf(func_def_113, type, sK38: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > coinductive_llist @ X1 > X1))).
% 2.86/0.67 thf(func_def_114, type, sK39: !>[X0: $tType]:(((X0 > $o) > set @ X0 > X0))).
% 2.86/0.67 thf(func_def_115, type, sK40: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > set @ X0 > X0))).
% 2.86/0.67 thf(func_def_116, type, sK41: !>[X0: $tType]:(((X0 > $o) > stream @ X0 > (X0 > $o) > X0))).
% 2.86/0.67 thf(func_def_117, type, sK42: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > stream @ X0 > X0))).
% 2.86/0.67 thf(func_def_118, type, sK43: !>[X0: $tType]:((X0 > set @ X0 > X0))).
% 2.86/0.67 thf(func_def_119, type, sK44: !>[X0: $tType]:((X0 > set @ X0 > X0))).
% 2.86/0.67 thf(func_def_120, type, sK45: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 2.86/0.67 thf(func_def_121, type, sK46: !>[X0: $tType]:((X0 > set @ X0 > X0))).
% 2.86/0.67 thf(func_def_122, type, sK47: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > set @ X1 > X1))).
% 2.86/0.67 thf(func_def_123, type, sK48: !>[X0: $tType]:((set @ X0 > set @ set @ X0 > set @ X0))).
% 2.86/0.67 thf(func_def_124, type, sK49: !>[X0: $tType]:((set @ set @ X0 > X0 > set @ X0))).
% 2.86/0.67 thf(func_def_125, type, sK50: !>[X0: $tType]:(X0)).
% 2.86/0.67 thf(func_def_126, type, sK51: !>[X0: $tType]:((set @ X0 > X0))).
% 2.86/0.67 thf(func_def_127, type, sK52: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > coinductive_llist @ X0 > X0))).
% 2.86/0.67 thf(func_def_128, type, sK53: !>[X0: $tType]:(((X0 > $o) > coinductive_llist @ X0 > (X0 > $o) > X0))).
% 2.86/0.67 thf(func_def_129, type, sK54: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > X1) > (X0 > X1) > set @ X2 > set @ X0 > X2))).
% 2.86/0.67 thf(func_def_130, type, sK55: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > X1) > (X0 > X1) > set @ X2 > set @ X0 > X0))).
% 2.86/0.67 thf(func_def_131, type, sK56: !>[X0: $tType, X1: $tType]:((X0 > (X1 > X0) > X1))).
% 2.86/0.67 thf(func_def_132, type, sK57: !>[X0: $tType, X1: $tType]:((X0 > (X1 > X0) > X1))).
% 2.86/0.67 thf(func_def_133, type, sK58: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X0 > X1) > X1))).
% 2.86/0.67 thf(func_def_134, type, sK59: !>[X0: $tType]:((X0 > set @ X0 > X0))).
% 2.86/0.67 thf(func_def_135, type, sK60: !>[X0: $tType]:((X0 > set @ X0 > X0))).
% 2.86/0.67 thf(func_def_136, type, sK61: !>[X0: $tType]:((set @ X0 > X0 > X0))).
% 2.86/0.67 thf(func_def_137, type, sK62: !>[X0: $tType]:((X0 > set @ (X0 > $o) > X0 > $o))).
% 2.86/0.67 thf(func_def_138, type, sK63: !>[X0: $tType, X1: $tType]:((X1 > (X0 > X1) > set @ X0 > X0))).
% 2.86/0.67 thf(func_def_139, type, sK64: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X0 > set @ X1 > X1))).
% 2.86/0.67 thf(func_def_140, type, sK65: !>[X0: $tType]:((set @ X0 > X0))).
% 2.86/0.67 thf(func_def_141, type, sK66: !>[X0: $tType]:((X0 > set @ X0 > X0))).
% 2.86/0.67 thf(func_def_142, type, sK67: !>[X0: $tType]:((X0 > set @ X0 > X0))).
% 2.86/0.67 thf(func_def_143, type, sK68: !>[X0: $tType]:((X0 > set @ X0 > X0))).
% 2.86/0.67 thf(func_def_144, type, sK69: !>[X0: $tType]:((X0 > set @ X0 > X0))).
% 2.86/0.67 thf(func_def_145, type, sK70: !>[X0: $tType, X1: $tType]:((X1 > (X0 > X1) > set @ X0 > X0))).
% 2.86/0.67 thf(func_def_146, type, sK71: !>[X0: $tType]:((set @ X0 > X0))).
% 2.86/0.67 thf(func_def_147, type, sK72: !>[X0: $tType, X1: $tType]:((X1 > (X1 > X0) > set @ X1 > X1))).
% 2.86/0.67 thf(func_def_148, type, sK73: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > (X1 > X0) > X1))).
% 2.86/0.67 thf(func_def_149, type, sK74: !>[X0: $tType]:((X0 > set @ X0 > X0))).
% 2.86/0.67 thf(func_def_150, type, sK75: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 2.86/0.67 thf(func_def_151, type, sK76: !>[X0: $tType, X1: $tType]:((X0 > (X1 > X0) > set @ X1 > X1))).
% 2.86/0.67 thf(func_def_152, type, sK77: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1) > set @ X2 > (X2 > X1) > set @ X0 > X0))).
% 2.86/0.67 thf(func_def_153, type, sF78: stream @ a).
% 2.86/0.67 thf(func_def_154, type, sK79: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X0 > X1))).
% 2.86/0.67 thf(func_def_155, type, sK80: !>[X0: $tType]:((set @ X0 > X0 > X0))).
% 2.86/0.67 thf(func_def_156, type, sK81: !>[X0: $tType]:((set @ X0 > X0))).
% 2.86/0.67 thf(func_def_157, type, sK82: !>[X0: $tType]:((set @ set @ X0 > set @ X0))).
% 2.86/0.67 thf(func_def_158, type, sK83: !>[X0: $tType]:((set @ set @ X0 > set @ X0))).
% 2.86/0.67 thf(func_def_159, type, sK84: !>[X0: $tType]:((set @ X0 > X0))).
% 2.86/0.67 thf(func_def_160, type, sK85: !>[X0: $tType]:((set @ X0 > X0))).
% 2.86/0.67 thf(func_def_161, type, sK86: !>[X0: $tType]:(((X0 > $o) > X0))).
% 2.86/0.67 thf(func_def_162, type, sK87: !>[X0: $tType]:(((X0 > $o) > X0))).
% 2.86/0.67 thf(func_def_163, type, sK88: !>[X0: $tType]:((set @ X0 > X0))).
% 2.86/0.67 thf(func_def_164, type, sK89: !>[X0: $tType, X1: $tType]:((X0 > (X1 > X0) > set @ X1 > X1))).
% 2.86/0.67 thf(func_def_165, type, sK90: !>[X0: $tType, X1: $tType]:((X0 > (X1 > X0) > set @ X1 > X1))).
% 2.86/0.67 thf(func_def_166, type, sK91: !>[X0: $tType, X1: $tType]:((X1 > (X0 > X1) > X0))).
% 2.86/0.67 thf(func_def_167, type, sK92: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X1))).
% 2.86/0.67 thf(func_def_168, type, sK93: !>[X0: $tType]:(((X0 > $o) > coinductive_llist @ X0 > X0))).
% 2.86/0.67 thf(func_def_169, type, sK94: !>[X0: $tType]:(((X0 > $o) > coinductive_llist @ X0 > X0))).
% 2.86/0.67 thf(func_def_170, type, sK95: !>[X0: $tType]:(((X0 > $o) > coinductive_llist @ X0 > X0))).
% 2.86/0.67 thf(func_def_171, type, sK96: !>[X0: $tType]:((coinductive_llist @ X0 > (X0 > $o) > X0))).
% 2.86/0.67 thf(func_def_172, type, sK97: !>[X0: $tType]:((coinductive_llist @ X0 > (X0 > $o) > X0))).
% 2.86/0.67 thf(func_def_173, type, sK98: !>[X0: $tType]:((coinductive_llist @ X0 > (X0 > $o) > X0))).
% 2.86/0.67 thf(func_def_174, type, sK99: !>[X0: $tType]:((coinductive_llist @ X0 > (X0 > $o) > X0))).
% 2.86/0.67 thf(func_def_175, type, sK100: !>[X0: $tType]:((coinductive_llist @ X0 > (X0 > $o) > X0))).
% 2.86/0.67 thf(func_def_176, type, sK101: !>[X0: $tType]:((coinductive_llist @ X0 > (X0 > $o) > X0))).
% 2.86/0.67 thf(func_def_177, type, sK102: !>[X0: $tType]:((set @ X0 > X0 > X0))).
% 2.86/0.67 thf(func_def_178, type, sK103: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > $o) > (X1 > set @ X0) > X0))).
% 2.86/0.67 thf(func_def_179, type, sK104: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > $o) > (X1 > set @ X0) > X1))).
% 2.86/0.67 thf(func_def_180, type, sK105: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > $o) > (X1 > set @ X0) > X0))).
% 2.86/0.67 thf(func_def_181, type, sK106: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > $o) > (X1 > set @ X0) > X1))).
% 2.86/0.67 thf(func_def_182, type, sK107: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > $o) > (X1 > set @ X0) > X0))).
% 2.86/0.67 thf(func_def_183, type, sK108: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > $o) > (X1 > set @ X0) > X0))).
% 2.86/0.67 thf(func_def_184, type, sK109: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > $o) > (X1 > set @ X0) > X0))).
% 2.86/0.67 thf(func_def_185, type, sK110: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > $o) > (X1 > set @ X0) > X1))).
% 2.86/0.67 thf(func_def_186, type, sK111: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > $o) > (X1 > set @ X0) > X0))).
% 2.86/0.67 thf(func_def_187, type, sK112: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > $o) > (X1 > set @ X0) > X1))).
% 2.86/0.67 thf(func_def_188, type, sK113: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > $o) > (X1 > set @ X0) > X0))).
% 2.86/0.67 thf(func_def_189, type, sK114: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > $o) > (X1 > set @ X0) > X0))).
% 2.86/0.67 thf(func_def_190, type, sK115: !>[X0: $tType]:((set @ set @ X0 > (X0 > $o) > set @ X0))).
% 2.86/0.67 thf(func_def_191, type, sK116: !>[X0: $tType]:((set @ set @ X0 > (X0 > $o) > X0))).
% 2.86/0.67 thf(func_def_192, type, sK117: !>[X0: $tType]:((set @ set @ X0 > (X0 > $o) > X0))).
% 2.86/0.67 thf(func_def_193, type, sK118: !>[X0: $tType]:((set @ set @ X0 > (X0 > $o) > X0))).
% 2.86/0.67 thf(func_def_194, type, sK119: !>[X0: $tType]:((set @ set @ X0 > (X0 > $o) > set @ X0))).
% 2.86/0.67 thf(func_def_195, type, sK120: !>[X0: $tType]:((set @ set @ X0 > (X0 > $o) > X0))).
% 2.86/0.67 thf(func_def_196, type, sK121: !>[X0: $tType]:((X0 > set @ set @ X0 > set @ X0))).
% 2.86/0.67 thf(func_def_197, type, sK122: !>[X0: $tType]:((stream @ X0 > (X0 > $o) > X0))).
% 2.86/0.67 thf(func_def_198, type, sK123: !>[X0: $tType]:((stream @ X0 > (X0 > $o) > X0))).
% 2.86/0.67 thf(func_def_199, type, sK124: !>[X0: $tType]:((stream @ X0 > (X0 > $o) > X0))).
% 2.86/0.67 thf(func_def_200, type, sK125: !>[X0: $tType]:((stream @ X0 > (X0 > $o) > X0))).
% 2.86/0.67 thf(func_def_201, type, sK126: !>[X0: $tType]:((stream @ X0 > (X0 > $o) > X0))).
% 2.86/0.67 thf(func_def_202, type, sK127: !>[X0: $tType]:((stream @ X0 > (X0 > $o) > X0))).
% 2.86/0.67 thf(func_def_203, type, sK128: !>[X0: $tType]:(((X0 > $o) > stream @ X0 > X0))).
% 2.86/0.67 thf(func_def_204, type, sK129: !>[X0: $tType]:(((X0 > $o) > stream @ X0 > X0))).
% 2.86/0.67 thf(func_def_205, type, sK130: !>[X0: $tType]:(((X0 > $o) > stream @ X0 > X0))).
% 2.86/0.67 thf(func_def_206, type, sK131: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 2.86/0.67 thf(func_def_207, type, sK132: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > X0 > X1))).
% 2.86/0.67 thf(func_def_208, type, sK133: !>[X0: $tType, X1: $tType]:((set @ X1 > set @ X0 > (X1 > X0) > X1))).
% 2.86/0.67 thf(func_def_209, type, sK134: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > set @ X0 > set @ X1))).
% 2.86/0.67 thf(func_def_210, type, sK135: !>[X0: $tType]:(((X0 > $o) > set @ X0 > X0))).
% 2.86/0.67 thf(func_def_211, type, sK136: !>[X0: $tType, X1: $tType]:((stream @ X1 > stream @ X0 > (X1 > X0) > nat))).
% 2.86/0.67 thf(func_def_212, type, sK137: !>[X0: $tType]:((stream @ X0 > set @ X0 > nat))).
% 2.86/0.67 thf(func_def_213, type, sK138: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > X1 > X0) > stream @ X2 > stream @ X0 > stream @ X1 > nat))).
% 2.86/0.67 thf(func_def_215, type, sK140: nat).
% 2.86/0.67 thf(func_def_216, type, sK141: nat).
% 2.86/0.67 thf(func_def_217, type, sK142: (stream @ a > nat)).
% 2.86/0.67 thf(func_def_218, type, sK143: (stream @ a > nat)).
% 2.86/0.67 thf(f4,axiom,(
% 2.86/0.67 ! [X0 : $tType] : (coindu176146587of_seq @ X0 = (^[X1 : (nat > X0)] : ((coindu2010755910_llist @ X0 @ (coindu68654304_llist @ X0 @ X1)))))),
% 2.86/0.67 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_of__seq_Oabs__eq)).
% 2.86/0.67 thf(f5,axiom,(
% 2.86/0.67 ! [X0 : $tType,X1 : (nat > X0)] : (((coindu1724414836stream @ X0 @ (coindu176146587of_seq @ X0 @ X1))) = ((coindu68654304_llist @ X0 @ X1)))),
% 2.86/0.67 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_of__seq_Orep__eq)).
% 2.86/0.67 thf(f10,axiom,(
% 2.86/0.67 ! [X0 : $tType,X1 : stream @ X0] : (((coinductive_lnth @ X0 @ (coindu1724414836stream @ X0 @ X1))) = ((snth @ X0 @ X1)))),
% 2.86/0.67 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_lnth__list__of__stream)).
% 2.86/0.67 thf(f19,axiom,(
% 2.86/0.67 ! [X0 : $tType,X1 : stream @ X0,X2 : stream @ X0] : ((((coindu1724414836stream @ X0 @ X1)) = ((coindu1724414836stream @ X0 @ X2))) = (X1 = X2))),
% 2.86/0.67 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_stream_ORep__inject)).
% 2.86/0.67 thf(f20,axiom,(
% 2.86/0.67 ! [X0 : $tType,X1 : (nat > X0),X2 : nat] : (((coinductive_lnth @ X0 @ (coindu68654304_llist @ X0 @ X1) @ X2)) = ((X1 @ X2)))),
% 2.86/0.67 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_lnth__inf__llist)).
% 2.86/0.67 thf(f313,conjecture,(
% 2.86/0.67 (((snth @ a @ (coindu176146587of_seq @ a @ f))) = f)),
% 2.86/0.67 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 2.86/0.67 thf(f314,negated_conjecture,(
% 2.86/0.67 ~ (((snth @ a @ (coindu176146587of_seq @ a @ f))) = f)),
% 2.86/0.67 inference(negated_conjecture,[status(cth)],[f313])).
% 2.86/0.67 thf(f318,plain,(
% 2.86/0.67 ! [X0 : $tType] : (coindu176146587of_seq @ X0 = (^[Y0 : nat > X0]: (coindu2010755910_llist @ X0 @ (coindu68654304_llist @ X0 @ Y0))))),
% 2.86/0.67 inference(fool_elimination,[],[f4])).
% 2.86/0.67 thf(f336,plain,(
% 2.86/0.67 ! [X0 : $tType,X1 : stream @ X0,X2 : stream @ X0] : ((((coindu1724414836stream @ X0 @ X1) = (coindu1724414836stream @ X0 @ X2))) = ((X1 = X2)))),
% 2.86/0.67 inference(fool_elimination,[],[f19])).
% 2.86/0.67 thf(f860,plain,(
% 2.86/0.67 (f != ((snth @ a @ (coindu176146587of_seq @ a @ f))))),
% 2.86/0.67 inference(flattening,[],[f314])).
% 2.86/0.67 thf(f1193,plain,(
% 2.86/0.67 ( ! [X0 : $tType] : ((coindu176146587of_seq @ X0 = (^[Y0 : nat > X0]: (coindu2010755910_llist @ X0 @ (coindu68654304_llist @ X0 @ Y0))))) )),
% 2.86/0.67 inference(cnf_transformation,[],[f318])).
% 2.86/0.67 thf(f1194,plain,(
% 2.86/0.67 ( ! [X0 : $tType,X1 : (nat > X0)] : ((((coindu68654304_llist @ X0 @ X1)) = ((coindu1724414836stream @ X0 @ (coindu176146587of_seq @ X0 @ X1))))) )),
% 2.86/0.67 inference(cnf_transformation,[],[f5])).
% 2.86/0.67 thf(f1199,plain,(
% 2.86/0.67 ( ! [X0 : $tType,X1 : stream @ X0] : ((((snth @ X0 @ X1)) = ((coinductive_lnth @ X0 @ (coindu1724414836stream @ X0 @ X1))))) )),
% 2.86/0.67 inference(cnf_transformation,[],[f10])).
% 2.86/0.67 thf(f1214,plain,(
% 2.86/0.67 ( ! [X0 : $tType,X2 : stream @ X0,X1 : stream @ X0] : (((((coindu1724414836stream @ X0 @ X1) = (coindu1724414836stream @ X0 @ X2))) = ((X1 = X2)))) )),
% 2.86/0.67 inference(cnf_transformation,[],[f336])).
% 2.86/0.67 thf(f1215,plain,(
% 2.86/0.67 ( ! [X0 : $tType,X2 : nat,X1 : (nat > X0)] : ((((coinductive_lnth @ X0 @ (coindu68654304_llist @ X0 @ X1) @ X2)) = ((X1 @ X2)))) )),
% 2.86/0.67 inference(cnf_transformation,[],[f20])).
% 2.86/0.67 thf(f1588,plain,(
% 2.86/0.67 (f != ((snth @ a @ (coindu176146587of_seq @ a @ f))))),
% 2.86/0.67 inference(cnf_transformation,[],[f860])).
% 2.86/0.67 thf(f1594,plain,(
% 2.86/0.67 ( ! [X0 : $tType,X1 : (nat > X0)] : ((((coindu68654304_llist @ X0 @ X1)) = ((coindu1724414836stream @ X0 @ ((^[Y0 : nat > X0]: (coindu2010755910_llist @ X0 @ (coindu68654304_llist @ X0 @ Y0))) @ X1))))) )),
% 2.86/0.67 inference(definition_unfolding,[],[f1194,f1193])).
% 2.86/0.67 thf(f1631,plain,(
% 2.86/0.67 (f != ((snth @ a @ ((^[Y0 : nat > a]: (coindu2010755910_llist @ a @ (coindu68654304_llist @ a @ Y0))) @ f))))),
% 2.86/0.67 inference(definition_unfolding,[],[f1588,f1193])).
% 2.86/0.67 thf(f1665,definition,(
% 2.86/0.67 (sF78 = (((^[Y0 : nat > a]: (coindu2010755910_llist @ a @ (coindu68654304_llist @ a @ Y0))) @ f)))),
% 2.86/0.67 introduced(definition,[new_symbols(definition,[sF78])],[function_definition])).
% 2.86/0.67 thf(f1666,plain,(
% 2.86/0.67 ((((^[Y0 : nat > a]: (coindu2010755910_llist @ a @ (coindu68654304_llist @ a @ Y0))) @ f)) = sF78)),
% 2.86/0.67 inference(reorient_equations,[],[f1665])).
% 2.86/0.67 thf(f1667,plain,(
% 2.86/0.67 (f != ((snth @ a @ sF78)))),
% 2.86/0.67 inference(definition_folding,[],[f1631,f1666])).
% 2.86/0.67 thf(f2277,plain,(
% 2.86/0.67 ( ! [X0 : $tType,X2 : stream @ X0,X1 : stream @ X0] : (($true = (((coindu1724414836stream @ X0 @ X1) = (coindu1724414836stream @ X0 @ X2)))) | (((X1 = X2)) = $false)) )),
% 2.86/0.67 inference(iff_proxy_clausification,[],[f1214])).
% 2.86/0.67 thf(f2281,plain,(
% 2.86/0.67 ( ! [X0 : $tType,X2 : stream @ X0,X1 : stream @ X0] : ((((coindu1724414836stream @ X0 @ X1)) = ((coindu1724414836stream @ X0 @ X2))) | (((X1 = X2)) = $false)) )),
% 2.86/0.67 inference(equality_proxy_clausification,[],[f2277])).
% 2.86/0.67 thf(f2282,plain,(
% 2.86/0.67 ( ! [X0 : $tType,X2 : stream @ X0,X1 : stream @ X0] : ((((coindu1724414836stream @ X0 @ X1)) = ((coindu1724414836stream @ X0 @ X2))) | (X1 != X2)) )),
% 2.86/0.67 inference(equality_proxy_clausification,[],[f2281])).
% 2.86/0.67 thf(f2305,plain,(
% 2.86/0.67 ( ! [X0 : $tType,X1 : (nat > X0)] : ((((coindu68654304_llist @ X0 @ X1)) = ((coindu1724414836stream @ X0 @ (coindu2010755910_llist @ X0 @ (coindu68654304_llist @ X0 @ X1)))))) )),
% 2.86/0.67 inference(beta-eta_normalization,[],[f1594])).
% 2.86/0.67 thf(f2316,plain,(
% 2.86/0.67 (sF78 = ((coindu2010755910_llist @ a @ (coindu68654304_llist @ a @ f))))),
% 2.86/0.67 inference(beta-eta_normalization,[],[f1666])).
% 2.86/0.67 thf(f2789,plain,(
% 2.86/0.67 (f != ((coinductive_lnth @ a @ (coindu1724414836stream @ a @ sF78))))),
% 2.86/0.67 inference(constrained_superposition,[],[f1667,f1199])).
% 2.86/0.67 thf(f2790,plain,(
% 2.86/0.67 (((f @ sK141)) != ((coinductive_lnth @ a @ (coindu1724414836stream @ a @ sF78) @ sK141)))),
% 2.86/0.67 inference(negative_extensionality,[],[f2789])).
% 2.86/0.67 thf(f6708,plain,(
% 2.86/0.67 ( ! [X0 : stream @ a] : ((((f @ sK141)) != ((coinductive_lnth @ a @ (coindu1724414836stream @ a @ X0) @ sK141))) | (sF78 != X0)) )),
% 2.86/0.67 inference(constrained_superposition,[],[f2790,f2282])).
% 2.86/0.67 thf(f6864,plain,(
% 2.86/0.67 ( ! [X0 : (nat > a)] : ((((f @ sK141)) != ((coinductive_lnth @ a @ (coindu68654304_llist @ a @ X0) @ sK141))) | (sF78 != ((coindu2010755910_llist @ a @ (coindu68654304_llist @ a @ X0))))) )),
% 2.86/0.67 inference(constrained_superposition,[],[f6708,f2305])).
% 2.86/0.67 thf(f6873,plain,(
% 2.86/0.67 ( ! [X0 : (nat > a)] : ((sF78 != ((coindu2010755910_llist @ a @ (coindu68654304_llist @ a @ X0)))) | (((f @ sK141)) != ((X0 @ sK141)))) )),
% 2.86/0.67 inference(forward_demodulation,[],[f6864,f1215])).
% 2.86/0.67 thf(f6900,plain,(
% 2.86/0.67 (sF78 != sF78) | (((f @ sK141)) != ((f @ sK141)))),
% 2.86/0.67 inference(constrained_superposition,[],[f6873,f2316])).
% 2.86/0.67 thf(f6903,plain,(
% 2.86/0.67 $false),
% 2.86/0.67 inference(trivial_inequality_removal,[],[f6900])).
% 2.86/0.67 % SZS output end Proof for theBenchmark
% 2.86/0.67 % (703570)------------------------------
% 2.86/0.67 % (703570)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.86/0.67 % (703570)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.86/0.67 % (703570)CaDiCaL version: 2.1.3
% 2.86/0.67 % (703570)Termination reason: Refutation
% 2.86/0.67 % (703570)Time elapsed: 0.269 s
% 2.86/0.67 % (703570)Peak memory usage: 19 MB
% 2.86/0.67 % (703570)Instructions burned: 985 (million)
% 2.86/0.67 % (703498)Success in time 0.43 s
% 2.86/0.67 % Vampire exiting
%------------------------------------------------------------------------------