%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT176^1 : 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 : n011.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 07:49:00 AM UTC 2026
% Result : Theorem 3.23s 0.72s
% Output : Refutation 3.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT176^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n011.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 18:06:01 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 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
% 3.23/0.72 % (455196)Will run a generic schedule for satisfiability detection.
% 3.23/0.72 % (455202)% WARNING: option uhcvi not known.
% 3.23/0.72 % (455202)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1492552592:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 3.23/0.72 % (455201)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1321022876_2999 on theBenchmark for (2999ds/0Mi)
% 3.23/0.72 % (455203)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2748356174:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 3.23/0.72 % (455204)dis+10_1_sil=32000:sp=arity:random_seed=2392584964:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 3.23/0.72 % (455202)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.23/0.72 % (455205)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1368607639:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 3.23/0.72 % (455206)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=853226167:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 3.23/0.72 % (455207)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=543793285:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 3.23/0.72 % (455202)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.23/0.72 % (455205)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.23/0.72 % Exception at run slice level
% 3.23/0.72 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.23/0.72 % (455215)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=214326318:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 3.23/0.72 % (455204)Instruction limit reached!
% 3.23/0.72 % (455204)------------------------------
% 3.23/0.72 % (455204)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.23/0.72 % (455204)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.23/0.72 % (455204)CaDiCaL version: 2.1.3
% 3.23/0.72 % (455204)Termination reason: Instruction limit
% 3.23/0.72 % (455204)Termination phase: Saturation
% 3.23/0.72 % (455204)Time elapsed: 0.051 s
% 3.23/0.72 % (455204)Peak memory usage: 12 MB
% 3.23/0.72 % (455204)Instructions burned: 107 (million)
% 3.23/0.72 % (455205)Instruction limit reached!
% 3.23/0.72 % (455205)------------------------------
% 3.23/0.72 % (455205)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.23/0.72 % (455205)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.23/0.72 % (455205)CaDiCaL version: 2.1.3
% 3.23/0.72 % (455205)Termination reason: Instruction limit
% 3.23/0.72 % (455205)Termination phase: Saturation
% 3.23/0.72 % (455205)Time elapsed: 0.054 s
% 3.23/0.72 % (455205)Peak memory usage: 13 MB
% 3.23/0.72 % (455205)Instructions burned: 116 (million)
% 3.23/0.72 % (455206)Instruction limit reached!
% 3.23/0.72 % (455206)------------------------------
% 3.23/0.72 % (455206)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.23/0.72 % (455206)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.23/0.72 % (455206)CaDiCaL version: 2.1.3
% 3.23/0.72 % (455206)Termination reason: Instruction limit
% 3.23/0.72 % (455206)Termination phase: Saturation
% 3.23/0.72 % (455206)Time elapsed: 0.066 s
% 3.23/0.72 % (455206)Peak memory usage: 13 MB
% 3.23/0.72 % (455206)Instructions burned: 132 (million)
% 3.23/0.72 % (455217)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3800494052:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 3.23/0.72 % Exception at run slice level
% 3.23/0.72 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.23/0.72 % (455218)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=1323412269:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 3.23/0.72 % (455207)Instruction limit reached!
% 3.23/0.72 % (455207)------------------------------
% 3.23/0.72 % (455207)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.23/0.72 % (455207)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.23/0.72 % (455207)CaDiCaL version: 2.1.3
% 3.23/0.72 % (455207)Termination reason: Instruction limit
% 3.23/0.72 % (455207)Termination phase: Saturation
% 3.23/0.72 % (455207)Time elapsed: 0.079 s
% 3.23/0.72 % (455207)Peak memory usage: 13 MB
% 3.23/0.72 % (455207)Instructions burned: 159 (million)
% 3.23/0.72 % (455219)ott-21_1_sil=16000:fs=off:random_seed=862253491:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 3.23/0.72 % (455218)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.23/0.72 % (455222)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1791649358:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 3.23/0.72 % (455223)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2317179802:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 3.23/0.72 % (455218)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.23/0.72 % Exception at run slice level
% 3.23/0.72 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.23/0.72 % (455217)Instruction limit reached!
% 3.23/0.72 % (455217)------------------------------
% 3.23/0.72 % (455217)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.23/0.72 % (455217)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.23/0.72 % (455217)CaDiCaL version: 2.1.3
% 3.23/0.72 % (455217)Termination reason: Instruction limit
% 3.23/0.72 % (455217)Termination phase: Saturation
% 3.23/0.72 % (455217)Time elapsed: 0.063 s
% 3.23/0.72 % (455217)Peak memory usage: 13 MB
% 3.23/0.72 % (455217)Instructions burned: 131 (million)
% 3.23/0.72 % (455227)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=2375278645:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 3.23/0.72 % (455228)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=40542666:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 3.23/0.72 % (455219)Instruction limit reached!
% 3.23/0.72 % (455219)------------------------------
% 3.23/0.72 % (455219)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.23/0.72 % (455219)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.23/0.72 % (455219)CaDiCaL version: 2.1.3
% 3.23/0.72 % (455219)Termination reason: Instruction limit
% 3.23/0.72 % (455219)Termination phase: Saturation
% 3.23/0.72 % (455219)Time elapsed: 0.079 s
% 3.23/0.72 % (455219)Peak memory usage: 14 MB
% 3.23/0.72 % (455219)Instructions burned: 181 (million)
% 3.23/0.72 % (455231)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=4083049524: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)
% 3.23/0.72 % Exception at run slice level
% 3.23/0.72 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.23/0.72 % (455231)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.23/0.72 % (455233)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=3083346196:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 3.23/0.72 % (455233)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.23/0.72 % (455222)Instruction limit reached!
% 3.23/0.72 % (455222)------------------------------
% 3.23/0.72 % (455222)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.23/0.72 % (455222)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.23/0.72 % (455222)CaDiCaL version: 2.1.3
% 3.23/0.72 % (455222)Termination reason: Instruction limit
% 3.23/0.72 % (455222)Termination phase: Saturation
% 3.23/0.72 % (455222)Time elapsed: 0.263 s
% 3.23/0.72 % (455222)Peak memory usage: 14 MB
% 3.23/0.72 % (455222)Instructions burned: 478 (million)
% 3.23/0.72 % (455235)fmb+10_1_sil=64000:random_seed=4284165281:i=22061:nm=2:gsp=on_2995 on theBenchmark for (2995ds/22061Mi)
% 3.23/0.72 % (455235)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.23/0.72 % Exception at run slice level
% 3.23/0.72 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.23/0.72 % (455218)Instruction limit reached!
% 3.23/0.72 % (455218)------------------------------
% 3.23/0.72 % (455218)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.23/0.72 % (455218)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.23/0.72 % (455218)CaDiCaL version: 2.1.3
% 3.23/0.72 % (455218)Termination reason: Instruction limit
% 3.23/0.72 % (455218)Termination phase: Saturation
% 3.23/0.72 % (455218)Time elapsed: 0.332 s
% 3.23/0.72 % (455218)Peak memory usage: 16 MB
% 3.23/0.72 % (455218)Instructions burned: 684 (million)
% 3.23/0.72 % (455237)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=801071615:i=9515:nm=5_2995 on theBenchmark for (2995ds/9515Mi)
% 3.23/0.72 % (455238)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=107621075:fmbsr=1.7:i=920_2995 on theBenchmark for (2995ds/920Mi)
% 3.23/0.72 % (455202) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-455196-455202"...
% 3.23/0.72 % (455202)...printing done.
% 3.23/0.72 % (455202)Refutation found. Thanks to Tanya!
% 3.23/0.72 % SZS status Theorem for theBenchmark
% 3.23/0.72 % SZS output start Proof for theBenchmark
% 3.23/0.72 thf(type_def_5, type, coinductive_llist: $tType > $tType).
% 3.23/0.72 thf(type_def_6, type, set: $tType > $tType).
% 3.23/0.72 thf(type_def_7, type, itself: $tType > $tType).
% 3.23/0.72 thf(type_def_8, type, a: $tType).
% 3.23/0.72 thf(type_def_9, type, sTfun: ($tType * $tType) > $tType).
% 3.23/0.72 thf(func_def_0, type, bounded_lattice: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.23/0.72 thf(func_def_1, type, type: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.23/0.72 thf(func_def_2, type, minus: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.23/0.72 thf(func_def_3, type, uminus: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.23/0.72 thf(func_def_4, type, bot: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.23/0.72 thf(func_def_5, type, top: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.23/0.72 thf(func_def_6, type, group_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.23/0.72 thf(func_def_7, type, lattice: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.23/0.72 thf(func_def_8, type, ab_group_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.23/0.72 thf(func_def_9, type, boolean_algebra: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.23/0.72 thf(func_def_10, type, distrib_lattice: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.23/0.72 thf(func_def_11, type, semilattice_inf: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.23/0.72 thf(func_def_12, type, semilattice_sup: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.23/0.72 thf(func_def_13, type, bounded_lattice_bot: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.23/0.72 thf(func_def_14, type, bounded_lattice_top: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.23/0.72 thf(func_def_15, type, cancel146912293up_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.23/0.72 thf(func_def_16, type, bounde1561333602nf_top: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.23/0.72 thf(func_def_17, type, bounde1808546759up_bot: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.23/0.72 thf(func_def_18, type, coinductive_LCons: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 3.23/0.72 thf(func_def_19, type, coinductive_LNil: !>[X0: $tType]:(coinductive_llist @ X0)).
% 3.23/0.72 thf(func_def_20, type, minus_minus: !>[X0: $tType]:((X0 > X0 > X0))).
% 3.23/0.72 thf(func_def_21, type, uminus_uminus: !>[X0: $tType]:((X0 > X0))).
% 3.23/0.72 thf(func_def_22, type, lList2435255213lllsts: !>[X0: $tType]:((set @ X0 > set @ coinductive_llist @ X0))).
% 3.23/0.72 thf(func_def_23, type, lList2236698231inlsts: !>[X0: $tType]:((set @ X0 > set @ coinductive_llist @ X0))).
% 3.23/0.72 thf(func_def_24, type, lList21916056377ts_rec: !>[X0: $tType, X1: $tType]:((X0 > (X1 > coinductive_llist @ X1 > X0 > X0) > coinductive_llist @ X1 > X0))).
% 3.23/0.72 thf(func_def_25, type, lList22096119349pslsts: !>[X0: $tType]:((set @ X0 > set @ coinductive_llist @ X0))).
% 3.23/0.72 thf(func_def_26, type, lList21612149805nflsts: !>[X0: $tType]:((set @ X0 > set @ coinductive_llist @ X0))).
% 3.23/0.72 thf(func_def_27, type, lList21148268032oslsts: !>[X0: $tType]:((set @ X0 > set @ coinductive_llist @ X0))).
% 3.23/0.72 thf(func_def_28, type, inf_inf: !>[X0: $tType]:((X0 > X0 > X0))).
% 3.23/0.72 thf(func_def_29, type, sup_sup: !>[X0: $tType]:((X0 > X0 > X0))).
% 3.23/0.72 thf(func_def_30, type, bot_bot: !>[X0: $tType]:(X0)).
% 3.23/0.72 thf(func_def_31, type, top_top: !>[X0: $tType]:(X0)).
% 3.23/0.72 thf(func_def_32, type, type2: !>[X0: $tType]:(itself @ X0)).
% 3.23/0.72 thf(func_def_33, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 3.23/0.72 thf(func_def_34, type, disjnt: !>[X0: $tType]:((set @ X0 > set @ X0 > $o))).
% 3.23/0.72 thf(func_def_35, type, insert: !>[X0: $tType]:((X0 > set @ X0 > set @ X0))).
% 3.23/0.72 thf(func_def_36, type, is_empty: !>[X0: $tType]:((set @ X0 > $o))).
% 3.23/0.72 thf(func_def_37, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 3.23/0.72 thf(func_def_38, type, x: coinductive_llist @ a).
% 3.23/0.72 thf(func_def_40, type, vNOT: ($o > $o)).
% 3.23/0.72 thf(func_def_43, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 3.23/0.72 thf(func_def_44, type, db0: !>[X0: $tType]:(X0)).
% 3.23/0.72 thf(func_def_45, type, vAND: ($o > $o > $o)).
% 3.23/0.72 thf(func_def_46, type, db2: !>[X0: $tType]:(X0)).
% 3.23/0.72 thf(func_def_47, type, db1: !>[X0: $tType]:(X0)).
% 3.23/0.72 thf(func_def_48, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 3.23/0.72 thf(func_def_49, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 3.23/0.72 thf(func_def_50, type, vOR: ($o > $o > $o)).
% 3.23/0.72 thf(func_def_51, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 3.23/0.72 thf(func_def_52, type, vIMP: ($o > $o > $o)).
% 3.23/0.72 thf(func_def_53, type, sK0: !>[X0: $tType]:((set @ X0 > X0))).
% 3.23/0.72 thf(func_def_54, type, sK1: !>[X0: $tType]:(X0)).
% 3.23/0.72 thf(func_def_55, type, sK2: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 3.23/0.72 thf(func_def_56, type, sK3: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 3.23/0.72 thf(func_def_57, type, sK4: !>[X0: $tType]:((set @ X0 > X0))).
% 3.23/0.72 thf(func_def_58, type, sK5: !>[X0: $tType]:((set @ X0 > coinductive_llist @ X0 > X0))).
% 3.23/0.72 thf(func_def_59, type, sK6: !>[X0: $tType]:((set @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 3.23/0.72 thf(func_def_60, type, sK7: !>[X0: $tType]:((set @ X0 > coinductive_llist @ X0 > X0))).
% 3.23/0.72 thf(func_def_61, type, sK8: !>[X0: $tType]:((set @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 3.23/0.72 thf(func_def_62, type, sK9: !>[X0: $tType]:(X0)).
% 3.23/0.72 thf(func_def_63, type, sK10: !>[X0: $tType]:(X0)).
% 3.23/0.72 thf(func_def_64, type, sK11: !>[X0: $tType]:(X0)).
% 3.23/0.72 thf(func_def_65, type, sK12: !>[X0: $tType]:(X0)).
% 3.23/0.72 thf(func_def_66, type, sK13: !>[X0: $tType]:(X0)).
% 3.23/0.72 thf(func_def_67, type, sK14: !>[X0: $tType]:(X0)).
% 3.23/0.72 thf(func_def_68, type, sK15: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 3.23/0.72 thf(func_def_69, type, sK16: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 3.23/0.72 thf(func_def_70, type, sK17: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0))).
% 3.23/0.72 thf(func_def_71, type, sK18: !>[X0: $tType]:((set @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 3.23/0.72 thf(func_def_72, type, sK19: !>[X0: $tType]:((set @ X0 > coinductive_llist @ X0 > X0))).
% 3.23/0.72 thf(func_def_73, type, sK20: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > set @ X0 > X0))).
% 3.23/0.72 thf(func_def_74, type, sK21: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > set @ X0 > coinductive_llist @ X0))).
% 3.23/0.72 thf(func_def_75, type, sK22: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 3.23/0.72 thf(func_def_76, type, sK23: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > set @ X0 > coinductive_llist @ X0))).
% 3.23/0.72 thf(func_def_77, type, sK24: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > set @ X0 > X0))).
% 3.23/0.72 thf(func_def_78, type, sK25: !>[X0: $tType]:((set @ X0 > (coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 3.23/0.72 thf(func_def_79, type, sK26: !>[X0: $tType]:((set @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 3.23/0.72 thf(func_def_80, type, sK27: !>[X0: $tType]:((set @ X0 > coinductive_llist @ X0 > X0))).
% 3.23/0.72 thf(func_def_81, type, sK28: !>[X0: $tType]:((coinductive_llist @ X0 > set @ X0 > X0))).
% 3.23/0.72 thf(func_def_82, type, sK29: !>[X0: $tType]:((coinductive_llist @ X0 > set @ X0 > coinductive_llist @ X0))).
% 3.23/0.72 thf(func_def_83, type, sK30: !>[X0: $tType]:((coinductive_llist @ X0 > set @ X0 > X0))).
% 3.23/0.72 thf(func_def_84, type, sK31: !>[X0: $tType]:((coinductive_llist @ X0 > set @ X0 > coinductive_llist @ X0))).
% 3.23/0.72 thf(func_def_85, type, sK32: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 3.23/0.72 thf(func_def_86, type, sK33: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 3.23/0.72 thf(func_def_87, type, sK34: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0))).
% 3.23/0.72 thf(func_def_88, type, sK35: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 3.23/0.72 thf(func_def_89, type, sK36: !>[X0: $tType]:((set @ X0 > X0))).
% 3.23/0.72 thf(func_def_90, type, sK37: !>[X0: $tType]:((set @ X0 > set @ X0 > (X0 > $o) > X0))).
% 3.23/0.72 thf(func_def_91, type, sK38: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 3.23/0.72 thf(func_def_92, type, sK39: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 3.23/0.72 thf(func_def_93, type, sK40: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 3.23/0.72 thf(func_def_94, type, sK41: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 3.23/0.72 thf(func_def_95, type, sK42: !>[X0: $tType]:((set @ X0 > (X0 > $o) > set @ X0 > X0))).
% 3.23/0.72 thf(func_def_96, type, sK43: !>[X0: $tType]:(((X0 > $o) > X0))).
% 3.23/0.72 thf(func_def_97, type, sK44: !>[X0: $tType]:(((X0 > $o) > X0))).
% 3.23/0.72 thf(func_def_98, type, sK45: !>[X0: $tType]:((set @ X0 > X0))).
% 3.23/0.72 thf(func_def_100, type, sK47: !>[X0: $tType]:(((X0 > $o) > X0))).
% 3.23/0.72 thf(f5,axiom,(
% 3.23/0.72 ! [X0 : $tType,X1 : coinductive_llist @ X0] : (~(member @ coinductive_llist @ X0 @ X1 @ (lList2236698231inlsts @ X0 @ top_top @ set @ X0)) => (member @ coinductive_llist @ X0 @ X1 @ (lList21612149805nflsts @ X0 @ top_top @ set @ X0)))),
% 3.23/0.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_fin__inf__cases)).
% 3.23/0.72 thf(f12,axiom,(
% 3.23/0.72 ! [X0 : $tType,X1 : set @ X0] : (! [X2 : X0] : (member @ X0 @ X2 @ X1) => (top_top @ set @ X0 = X1))),
% 3.23/0.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_UNIV__eq__I)).
% 3.23/0.72 thf(f14,axiom,(
% 3.23/0.72 ! [X0 : $tType,X1 : coinductive_llist @ X0] : (member @ coinductive_llist @ X0 @ X1 @ (lList2435255213lllsts @ X0 @ top_top @ set @ X0))),
% 3.23/0.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_alllsts__UNIV)).
% 3.23/0.72 thf(f15,axiom,(
% 3.23/0.72 ! [X0 : $tType] : (lList21612149805nflsts @ X0 = (^[X1 : set @ X0] : ((minus_minus @ set @ coinductive_llist @ X0 @ (lList2435255213lllsts @ X0 @ X1) @ (lList2236698231inlsts @ X0 @ top_top @ set @ X0)))))),
% 3.23/0.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_inflsts__def)).
% 3.23/0.72 thf(f21,axiom,(
% 3.23/0.72 ! [X0 : $tType,X1 : X0,X2 : set @ X0,X3 : set @ X0] : ((member @ X0 @ X1 @ (minus_minus @ set @ X0 @ X2 @ X3)) => ~((member @ X0 @ X1 @ X2) => (member @ X0 @ X1 @ X3)))),
% 3.23/0.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_DiffE)).
% 3.23/0.72 thf(f299,conjecture,(
% 3.23/0.72 (~(member @ coinductive_llist @ a @ x @ (lList21612149805nflsts @ a @ top_top @ set @ a)) = ((member @ coinductive_llist @ a @ x @ (lList2236698231inlsts @ a @ top_top @ set @ a))))),
% 3.23/0.72 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 3.23/0.72 thf(f300,negated_conjecture,(
% 3.23/0.72 ~ (~(member @ coinductive_llist @ a @ x @ (lList21612149805nflsts @ a @ top_top @ set @ a)) = ((member @ coinductive_llist @ a @ x @ (lList2236698231inlsts @ a @ top_top @ set @ a))))),
% 3.23/0.72 inference(negated_conjecture,[status(cth)],[f299])).
% 3.23/0.72 thf(f309,plain,(
% 3.23/0.72 ! [X0 : $tType,X1 : coinductive_llist @ X0] : (~(member @ coinductive_llist @ X0 @ X1 @ (lList2236698231inlsts @ X0 @ top_top @ set @ X0)) => (member @ coinductive_llist @ X0 @ X1 @ (lList21612149805nflsts @ X0 @ top_top @ set @ X0)))),
% 3.23/0.72 inference(rectify,[],[f5])).
% 3.23/0.72 thf(f310,plain,(
% 3.23/0.72 ! [X0 : $tType,X1 : coinductive_llist @ X0] : (~ (((member @ coinductive_llist @ X0 @ X1 @ (lList2236698231inlsts @ X0 @ top_top @ set @ X0))) = $true) => (((member @ coinductive_llist @ X0 @ X1 @ (lList21612149805nflsts @ X0 @ top_top @ set @ X0))) = $true))),
% 3.23/0.72 inference(fool_elimination,[],[f309])).
% 3.23/0.72 thf(f323,plain,(
% 3.23/0.72 ! [X0 : $tType,X1 : set @ X0] : (! [X2 : X0] : (member @ X0 @ X2 @ X1) => (top_top @ set @ X0 = X1))),
% 3.23/0.72 inference(rectify,[],[f12])).
% 3.23/0.72 thf(f324,plain,(
% 3.23/0.72 ! [X0 : $tType,X1 : set @ X0] : (! [X2 : X0] : (((member @ X0 @ X2 @ X1)) = $true) => (top_top @ set @ X0 = X1))),
% 3.23/0.72 inference(fool_elimination,[],[f323])).
% 3.23/0.72 thf(f327,plain,(
% 3.23/0.72 ! [X0 : $tType,X1 : coinductive_llist @ X0] : (member @ coinductive_llist @ X0 @ X1 @ (lList2435255213lllsts @ X0 @ top_top @ set @ X0))),
% 3.23/0.72 inference(rectify,[],[f14])).
% 3.23/0.72 thf(f328,plain,(
% 3.23/0.72 ! [X0 : $tType,X1 : coinductive_llist @ X0] : (((member @ coinductive_llist @ X0 @ X1 @ (lList2435255213lllsts @ X0 @ top_top @ set @ X0))) = $true)),
% 3.23/0.72 inference(fool_elimination,[],[f327])).
% 3.23/0.72 thf(f329,plain,(
% 3.23/0.72 ! [X0 : $tType] : (lList21612149805nflsts @ X0 = (^[Y0 : set @ X0]: (minus_minus @ set @ coinductive_llist @ X0 @ (lList2435255213lllsts @ X0 @ Y0) @ (lList2236698231inlsts @ X0 @ top_top @ set @ X0))))),
% 3.23/0.72 inference(fool_elimination,[],[f15])).
% 3.23/0.72 thf(f338,plain,(
% 3.23/0.72 ! [X0 : $tType,X1 : X0,X2 : set @ X0,X3 : set @ X0] : ((member @ X0 @ X1 @ (minus_minus @ set @ X0 @ X2 @ X3)) => ~((member @ X0 @ X1 @ X2) => (member @ X0 @ X1 @ X3)))),
% 3.23/0.72 inference(rectify,[],[f21])).
% 3.23/0.72 thf(f339,plain,(
% 3.23/0.72 ! [X0 : $tType,X1 : X0,X2 : set @ X0,X3 : set @ X0] : ((((member @ X0 @ X1 @ (minus_minus @ set @ X0 @ X2 @ X3))) = $true) => ~((((member @ X0 @ X1 @ X2)) = $true) => (((member @ X0 @ X1 @ X3)) = $true)))),
% 3.23/0.72 inference(fool_elimination,[],[f338])).
% 3.23/0.72 thf(f741,plain,(
% 3.23/0.72 ~ (~(member @ coinductive_llist @ a @ x @ (lList21612149805nflsts @ a @ top_top @ set @ a)) = ((member @ coinductive_llist @ a @ x @ (lList2236698231inlsts @ a @ top_top @ set @ a))))),
% 3.23/0.72 inference(rectify,[],[f300])).
% 3.23/0.72 thf(f742,plain,(
% 3.23/0.72 ~ (((member @ coinductive_llist @ a @ x @ (lList2236698231inlsts @ a @ top_top @ set @ a))) = ((~ (member @ coinductive_llist @ a @ x @ (lList21612149805nflsts @ a @ top_top @ set @ a)))))),
% 3.23/0.72 inference(fool_elimination,[],[f741])).
% 3.23/0.72 thf(f743,plain,(
% 3.23/0.72 ! [X0 : $tType,X1 : coinductive_llist @ X0] : ((((member @ coinductive_llist @ X0 @ X1 @ (lList2236698231inlsts @ X0 @ top_top @ set @ X0))) != $true) => (((member @ coinductive_llist @ X0 @ X1 @ (lList21612149805nflsts @ X0 @ top_top @ set @ X0))) = $true))),
% 3.23/0.72 inference(flattening,[],[f310])).
% 3.23/0.72 thf(f764,plain,(
% 3.23/0.72 (((member @ coinductive_llist @ a @ x @ (lList2236698231inlsts @ a @ top_top @ set @ a))) != ((~ (member @ coinductive_llist @ a @ x @ (lList21612149805nflsts @ a @ top_top @ set @ a)))))),
% 3.23/0.72 inference(flattening,[],[f742])).
% 3.23/0.72 thf(f768,plain,(
% 3.23/0.72 ! [X0 : $tType,X1 : coinductive_llist @ X0] : ((((member @ coinductive_llist @ X0 @ X1 @ (lList21612149805nflsts @ X0 @ top_top @ set @ X0))) = $true) | (((member @ coinductive_llist @ X0 @ X1 @ (lList2236698231inlsts @ X0 @ top_top @ set @ X0))) = $true))),
% 3.23/0.72 inference(ennf_transformation,[],[f743])).
% 3.23/0.72 thf(f775,plain,(
% 3.23/0.72 ! [X0 : $tType,X1 : set @ X0] : ((top_top @ set @ X0 = X1) | ? [X2 : X0] : (((member @ X0 @ X2 @ X1)) != $true))),
% 3.23/0.72 inference(ennf_transformation,[],[f324])).
% 3.23/0.72 thf(f781,plain,(
% 3.23/0.72 ! [X0 : $tType,X1 : X0,X2 : set @ X0,X3 : set @ X0] : (((((member @ X0 @ X1 @ X3)) != $true) & (((member @ X0 @ X1 @ X2)) = $true)) | (((member @ X0 @ X1 @ (minus_minus @ set @ X0 @ X2 @ X3))) != $true))),
% 3.23/0.72 inference(ennf_transformation,[],[f339])).
% 3.23/0.72 thf(f941,plain,(
% 3.23/0.72 ! [X0 : $tType,X1 : set @ X0] : ((top_top @ set @ X0 = X1) | ($true != ((member @ X0 @ (sK0 @ X0 @ X1) @ X1))))),
% 3.23/0.72 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X2,sK0 @ X0 @ X1)],[f775])).
% 3.23/0.72 thf(f962,plain,(
% 3.23/0.72 ( ! [X0 : $tType,X1 : coinductive_llist @ X0] : ((((member @ coinductive_llist @ X0 @ X1 @ (lList21612149805nflsts @ X0 @ top_top @ set @ X0))) = $true) | (((member @ coinductive_llist @ X0 @ X1 @ (lList2236698231inlsts @ X0 @ top_top @ set @ X0))) = $true)) )),
% 3.23/0.72 inference(cnf_transformation,[],[f768])).
% 3.23/0.72 thf(f970,plain,(
% 3.23/0.72 ( ! [X0 : $tType,X1 : set @ X0] : (($true != ((member @ X0 @ (sK0 @ X0 @ X1) @ X1))) | (top_top @ set @ X0 = X1)) )),
% 3.23/0.72 inference(cnf_transformation,[],[f941])).
% 3.23/0.72 thf(f972,plain,(
% 3.23/0.72 ( ! [X0 : $tType,X1 : coinductive_llist @ X0] : ((((member @ coinductive_llist @ X0 @ X1 @ (lList2435255213lllsts @ X0 @ top_top @ set @ X0))) = $true)) )),
% 3.23/0.72 inference(cnf_transformation,[],[f328])).
% 3.23/0.72 thf(f973,plain,(
% 3.23/0.72 ( ! [X0 : $tType] : ((lList21612149805nflsts @ X0 = (^[Y0 : set @ X0]: (minus_minus @ set @ coinductive_llist @ X0 @ (lList2435255213lllsts @ X0 @ Y0) @ (lList2236698231inlsts @ X0 @ top_top @ set @ X0))))) )),
% 3.23/0.72 inference(cnf_transformation,[],[f329])).
% 3.23/0.72 thf(f980,plain,(
% 3.23/0.72 ( ! [X0 : $tType,X2 : set @ X0,X3 : set @ X0,X1 : X0] : ((((member @ X0 @ X1 @ (minus_minus @ set @ X0 @ X2 @ X3))) != $true) | (((member @ X0 @ X1 @ X3)) != $true)) )),
% 3.23/0.72 inference(cnf_transformation,[],[f781])).
% 3.23/0.72 thf(f1283,plain,(
% 3.23/0.72 (((member @ coinductive_llist @ a @ x @ (lList2236698231inlsts @ a @ top_top @ set @ a))) != ((~ (member @ coinductive_llist @ a @ x @ (lList21612149805nflsts @ a @ top_top @ set @ a)))))),
% 3.23/0.72 inference(cnf_transformation,[],[f764])).
% 3.23/0.72 thf(f1288,plain,(
% 3.23/0.72 ( ! [X0 : $tType,X1 : coinductive_llist @ X0] : (($true = ((member @ coinductive_llist @ X0 @ X1 @ ((^[Y0 : set @ X0]: (minus_minus @ set @ coinductive_llist @ X0 @ (lList2435255213lllsts @ X0 @ Y0) @ (lList2236698231inlsts @ X0 @ top_top @ set @ X0))) @ top_top @ set @ X0)))) | (((member @ coinductive_llist @ X0 @ X1 @ (lList2236698231inlsts @ X0 @ top_top @ set @ X0))) = $true)) )),
% 3.23/0.72 inference(definition_unfolding,[],[f962,f973])).
% 3.23/0.72 thf(f1304,plain,(
% 3.23/0.72 (((member @ coinductive_llist @ a @ x @ (lList2236698231inlsts @ a @ top_top @ set @ a))) != ((~ (member @ coinductive_llist @ a @ x @ ((^[Y0 : set @ a]: (minus_minus @ set @ coinductive_llist @ a @ (lList2435255213lllsts @ a @ Y0) @ (lList2236698231inlsts @ a @ top_top @ set @ a))) @ top_top @ set @ a)))))),
% 3.23/0.72 inference(definition_unfolding,[],[f1283,f973])).
% 3.23/0.72 thf(f1309,plain,(
% 3.23/0.72 (((member @ coinductive_llist @ a @ x @ (lList2236698231inlsts @ a @ top_top @ set @ a))) = $true) | ($true = ((~ (member @ coinductive_llist @ a @ x @ ((^[Y0 : set @ a]: (minus_minus @ set @ coinductive_llist @ a @ (lList2435255213lllsts @ a @ Y0) @ (lList2236698231inlsts @ a @ top_top @ set @ a))) @ top_top @ set @ a)))))),
% 3.23/0.72 inference(xor_proxy_clausification,[],[f1304])).
% 3.23/0.72 thf(f1310,plain,(
% 3.23/0.72 (((member @ coinductive_llist @ a @ x @ (lList2236698231inlsts @ a @ top_top @ set @ a))) = $false) | ($false = ((~ (member @ coinductive_llist @ a @ x @ ((^[Y0 : set @ a]: (minus_minus @ set @ coinductive_llist @ a @ (lList2435255213lllsts @ a @ Y0) @ (lList2236698231inlsts @ a @ top_top @ set @ a))) @ top_top @ set @ a)))))),
% 3.23/0.72 inference(xor_proxy_clausification,[],[f1304])).
% 3.23/0.72 thf(f1311,plain,(
% 3.23/0.72 (((member @ coinductive_llist @ a @ x @ (lList2236698231inlsts @ a @ top_top @ set @ a))) = $false) | ($true = ((member @ coinductive_llist @ a @ x @ ((^[Y0 : set @ a]: (minus_minus @ set @ coinductive_llist @ a @ (lList2435255213lllsts @ a @ Y0) @ (lList2236698231inlsts @ a @ top_top @ set @ a))) @ top_top @ set @ a))))),
% 3.23/0.72 inference(not_proxy_clausification,[],[f1310])).
% 3.23/0.72 thf(f1312,plain,(
% 3.23/0.72 (((member @ coinductive_llist @ a @ x @ (lList2236698231inlsts @ a @ top_top @ set @ a))) = $false) | ($true = ((member @ coinductive_llist @ a @ x @ (minus_minus @ set @ coinductive_llist @ a @ (lList2435255213lllsts @ a @ top_top @ set @ a) @ (lList2236698231inlsts @ a @ top_top @ set @ a)))))),
% 3.23/0.72 inference(beta-eta_normalization,[],[f1311])).
% 3.23/0.72 thf(f1313,plain,(
% 3.23/0.72 (((member @ coinductive_llist @ a @ x @ (lList2236698231inlsts @ a @ top_top @ set @ a))) = $true) | ($false = ((member @ coinductive_llist @ a @ x @ ((^[Y0 : set @ a]: (minus_minus @ set @ coinductive_llist @ a @ (lList2435255213lllsts @ a @ Y0) @ (lList2236698231inlsts @ a @ top_top @ set @ a))) @ top_top @ set @ a))))),
% 3.23/0.72 inference(not_proxy_clausification,[],[f1309])).
% 3.23/0.72 thf(f1314,plain,(
% 3.23/0.72 (((member @ coinductive_llist @ a @ x @ (lList2236698231inlsts @ a @ top_top @ set @ a))) = $true) | ($false = ((member @ coinductive_llist @ a @ x @ (minus_minus @ set @ coinductive_llist @ a @ (lList2435255213lllsts @ a @ top_top @ set @ a) @ (lList2236698231inlsts @ a @ top_top @ set @ a)))))),
% 3.23/0.72 inference(beta-eta_normalization,[],[f1313])).
% 3.23/0.72 thf(f1694,plain,(
% 3.23/0.72 ( ! [X0 : $tType,X1 : coinductive_llist @ X0] : (($true = ((member @ coinductive_llist @ X0 @ X1 @ (minus_minus @ set @ coinductive_llist @ X0 @ (lList2435255213lllsts @ X0 @ top_top @ set @ X0) @ (lList2236698231inlsts @ X0 @ top_top @ set @ X0))))) | (((member @ coinductive_llist @ X0 @ X1 @ (lList2236698231inlsts @ X0 @ top_top @ set @ X0))) = $true)) )),
% 3.23/0.72 inference(beta-eta_normalization,[],[f1288])).
% 3.23/0.72 thf(f1703,definition,(
% 3.23/0.72 spl46_1 <=> ($true = ((member @ coinductive_llist @ a @ x @ (minus_minus @ set @ coinductive_llist @ a @ (lList2435255213lllsts @ a @ top_top @ set @ a) @ (lList2236698231inlsts @ a @ top_top @ set @ a)))))),
% 3.23/0.72 introduced(definition,[new_symbols(definition,[spl46_1])],[avatar_definition])).
% 3.23/0.72 thf(f1705,plain,(
% 3.23/0.72 ($true = ((member @ coinductive_llist @ a @ x @ (minus_minus @ set @ coinductive_llist @ a @ (lList2435255213lllsts @ a @ top_top @ set @ a) @ (lList2236698231inlsts @ a @ top_top @ set @ a))))) | ~spl46_1),
% 3.23/0.72 inference(avatar_component_clause,[],[f1703])).
% 3.23/0.72 thf(f1707,definition,(
% 3.23/0.72 spl46_2 <=> (((member @ coinductive_llist @ a @ x @ (lList2236698231inlsts @ a @ top_top @ set @ a))) = $false)),
% 3.23/0.72 introduced(definition,[new_symbols(definition,[spl46_2])],[avatar_definition])).
% 3.23/0.72 thf(f1709,plain,(
% 3.23/0.72 (((member @ coinductive_llist @ a @ x @ (lList2236698231inlsts @ a @ top_top @ set @ a))) = $false) | ~spl46_2),
% 3.23/0.72 inference(avatar_component_clause,[],[f1707])).
% 3.23/0.72 thf(f1710,plain,(
% 3.23/0.72 spl46_1 | spl46_2),
% 3.23/0.72 inference(avatar_split_clause,[],[f1312,f1707,f1703])).
% 3.23/0.72 thf(f1712,definition,(
% 3.23/0.72 spl46_3 <=> ($false = ((member @ coinductive_llist @ a @ x @ (minus_minus @ set @ coinductive_llist @ a @ (lList2435255213lllsts @ a @ top_top @ set @ a) @ (lList2236698231inlsts @ a @ top_top @ set @ a)))))),
% 3.23/0.72 introduced(definition,[new_symbols(definition,[spl46_3])],[avatar_definition])).
% 3.23/0.72 thf(f1714,plain,(
% 3.23/0.72 ($false = ((member @ coinductive_llist @ a @ x @ (minus_minus @ set @ coinductive_llist @ a @ (lList2435255213lllsts @ a @ top_top @ set @ a) @ (lList2236698231inlsts @ a @ top_top @ set @ a))))) | ~spl46_3),
% 3.23/0.72 inference(avatar_component_clause,[],[f1712])).
% 3.23/0.72 thf(f1716,definition,(
% 3.23/0.72 spl46_4 <=> (((member @ coinductive_llist @ a @ x @ (lList2236698231inlsts @ a @ top_top @ set @ a))) = $true)),
% 3.23/0.72 introduced(definition,[new_symbols(definition,[spl46_4])],[avatar_definition])).
% 3.23/0.72 thf(f1718,plain,(
% 3.23/0.72 (((member @ coinductive_llist @ a @ x @ (lList2236698231inlsts @ a @ top_top @ set @ a))) = $true) | ~spl46_4),
% 3.23/0.72 inference(avatar_component_clause,[],[f1716])).
% 3.23/0.72 thf(f1719,plain,(
% 3.23/0.72 spl46_3 | spl46_4),
% 3.23/0.72 inference(avatar_split_clause,[],[f1314,f1716,f1712])).
% 3.23/0.72 thf(f2163,plain,(
% 3.23/0.72 ( ! [X0 : $tType] : (($true != $true) | (((lList2435255213lllsts @ X0 @ top_top @ set @ X0)) = top_top @ set @ coinductive_llist @ X0)) )),
% 3.23/0.72 inference(constrained_superposition,[],[f970,f972])).
% 3.23/0.72 thf(f2164,plain,(
% 3.23/0.72 ( ! [X0 : $tType] : ((((lList2435255213lllsts @ X0 @ top_top @ set @ X0)) = top_top @ set @ coinductive_llist @ X0)) )),
% 3.23/0.72 inference(trivial_inequality_removal,[],[f2163])).
% 3.23/0.72 thf(f3230,plain,(
% 3.23/0.72 ($false = ((member @ coinductive_llist @ a @ x @ (minus_minus @ set @ coinductive_llist @ a @ top_top @ set @ coinductive_llist @ a @ (lList2236698231inlsts @ a @ top_top @ set @ a))))) | ~spl46_3),
% 3.23/0.72 inference(constrained_superposition,[],[f1714,f2164])).
% 3.23/0.72 thf(f8520,plain,(
% 3.23/0.72 ( ! [X0 : $tType,X1 : coinductive_llist @ X0] : (($true = ((member @ coinductive_llist @ X0 @ X1 @ (minus_minus @ set @ coinductive_llist @ X0 @ top_top @ set @ coinductive_llist @ X0 @ (lList2236698231inlsts @ X0 @ top_top @ set @ X0))))) | (((member @ coinductive_llist @ X0 @ X1 @ (lList2236698231inlsts @ X0 @ top_top @ set @ X0))) = $true)) )),
% 3.23/0.72 inference(forward_demodulation,[],[f1694,f2164])).
% 3.23/0.72 thf(f8545,plain,(
% 3.23/0.72 ($true = $false) | (((member @ coinductive_llist @ a @ x @ (lList2236698231inlsts @ a @ top_top @ set @ a))) = $true) | ~spl46_3),
% 3.23/0.72 inference(constrained_superposition,[],[f8520,f3230])).
% 3.23/0.72 thf(f8570,plain,(
% 3.23/0.72 (((member @ coinductive_llist @ a @ x @ (lList2236698231inlsts @ a @ top_top @ set @ a))) = $true) | ~spl46_3),
% 3.23/0.72 inference(trivial_inequality_removal,[],[f8545])).
% 3.23/0.72 thf(f8574,plain,(
% 3.23/0.72 ($true = $false) | (~spl46_2 | ~spl46_3)),
% 3.23/0.72 inference(forward_demodulation,[],[f8570,f1709])).
% 3.23/0.72 thf(f8575,plain,(
% 3.23/0.72 $false | (~spl46_2 | ~spl46_3)),
% 3.23/0.72 inference(trivial_inequality_removal,[],[f8574])).
% 3.23/0.72 thf(f8576,plain,(
% 3.23/0.73 ~spl46_2 | ~spl46_3),
% 3.23/0.73 inference(avatar_contradiction_clause,[],[f8575])).
% 3.23/0.73 thf(f8578,plain,(
% 3.23/0.73 ($true = $false) | (~spl46_2 | ~spl46_4)),
% 3.23/0.73 inference(forward_demodulation,[],[f1718,f1709])).
% 3.23/0.73 thf(f8579,plain,(
% 3.23/0.73 $false | (~spl46_2 | ~spl46_4)),
% 3.23/0.73 inference(trivial_inequality_removal,[],[f8578])).
% 3.23/0.73 thf(f8580,plain,(
% 3.23/0.73 ~spl46_2 | ~spl46_4),
% 3.23/0.73 inference(avatar_contradiction_clause,[],[f8579])).
% 3.23/0.73 thf(f8581,plain,(
% 3.23/0.73 ($true = ((member @ coinductive_llist @ a @ x @ (minus_minus @ set @ coinductive_llist @ a @ top_top @ set @ coinductive_llist @ a @ (lList2236698231inlsts @ a @ top_top @ set @ a))))) | ~spl46_1),
% 3.23/0.73 inference(forward_demodulation,[],[f1705,f2164])).
% 3.23/0.73 thf(f15603,plain,(
% 3.23/0.73 ($true != $true) | (((member @ coinductive_llist @ a @ x @ (lList2236698231inlsts @ a @ top_top @ set @ a))) != $true) | ~spl46_1),
% 3.23/0.73 inference(constrained_superposition,[],[f980,f8581])).
% 3.23/0.73 thf(f15606,plain,(
% 3.23/0.73 (((member @ coinductive_llist @ a @ x @ (lList2236698231inlsts @ a @ top_top @ set @ a))) != $true) | ~spl46_1),
% 3.23/0.73 inference(trivial_inequality_removal,[],[f15603])).
% 3.23/0.73 thf(f15636,plain,(
% 3.23/0.73 spl46_4 | ~spl46_3),
% 3.23/0.73 inference(avatar_split_clause,[],[f8570,f1712,f1716])).
% 3.23/0.73 thf(f15637,plain,(
% 3.23/0.73 ~spl46_4 | ~spl46_1),
% 3.23/0.73 inference(avatar_split_clause,[],[f15606,f1703,f1716])).
% 3.23/0.73 cnf(s1, plain, spl46_1 | spl46_2, inference(sat_conversion,[],[f1710])).
% 3.23/0.73 cnf(s2, plain, spl46_3 | spl46_4, inference(sat_conversion,[],[f1719])).
% 3.23/0.73 cnf(s157, plain, ~spl46_2 | ~spl46_3, inference(sat_conversion,[],[f8576])).
% 3.23/0.73 cnf(s158, plain, ~spl46_2 | ~spl46_4, inference(sat_conversion,[],[f8580])).
% 3.23/0.73 cnf(s478, plain, ~spl46_3 | spl46_4, inference(sat_conversion,[],[f15636])).
% 3.23/0.73 cnf(s482, plain, ~spl46_1 | ~spl46_4, inference(sat_conversion,[],[f15637])).
% 3.23/0.73 cnf(s505, plain, ~spl46_2, inference(rat,[],[s2,s157,s158])).
% 3.23/0.73 cnf(s506, plain, spl46_1, inference(rat,[],[s1,s505])).
% 3.23/0.73 cnf(s507, plain, ~spl46_4, inference(rat,[],[s482,s506])).
% 3.23/0.73 cnf(s508, plain, ~spl46_3, inference(rat,[],[s478,s507])).
% 3.23/0.73 cnf(s509, plain, $false, inference(rat,[],[s2,s507,s508])).
% 3.23/0.73 thf(f15638,plain,(
% 3.23/0.73 $false),
% 3.23/0.73 inference(avatar_sat_refutation,[],[s509])).
% 3.23/0.73 % SZS output end Proof for theBenchmark
% 3.23/0.73 % (455202)------------------------------
% 3.23/0.73 % (455202)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.23/0.73 % (455202)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.23/0.73 % (455202)CaDiCaL version: 2.1.3
% 3.23/0.73 % (455202)Termination reason: Refutation
% 3.23/0.73 % (455202)Time elapsed: 0.444 s
% 3.23/0.73 % (455202)Peak memory usage: 20 MB
% 3.23/0.73 % (455202)Instructions burned: 1679 (million)
% 3.23/0.73 % (455196)Success in time 0.492 s
% 3.23/0.73 % Vampire exiting
%------------------------------------------------------------------------------