%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT117^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n009.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 07:48:54 AM UTC 2026
% Result : Theorem 2.76s 0.69s
% Output : Refutation 2.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT117^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.21 % Computer : n009.cluster.edu
% 0.11/0.21 % Model : x86_64 x86_64
% 0.11/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.21 % Memory : 8046.5625MB
% 0.11/0.21 % OS : Linux 6.8.0-71-generic
% 0.11/0.21 % CPULimit : 300
% 0.11/0.21 % WCLimit : 300
% 0.11/0.21 % DateTime : Tue Sep 29 17:58:01 UTC 2026
% 0.11/0.21 % CPUTime :
% 0.11/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.25 Running first-order model finding
% 0.11/0.25 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.76/0.69 % (148833)Will run a generic schedule for satisfiability detection.
% 2.76/0.69 % (148839)% WARNING: option uhcvi not known.
% 2.76/0.69 % (148839)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3313381311:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 2.76/0.69 % (148839)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.76/0.69 % (148841)dis+10_1_sil=32000:sp=arity:random_seed=328686758:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 2.76/0.69 % (148840)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3056745252:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 2.76/0.69 % (148843)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1374741933:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 2.76/0.69 % (148844)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=255740038:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 2.76/0.69 % (148842)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1982395814:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 2.76/0.69 % (148838)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2275436882_2999 on theBenchmark for (2999ds/0Mi)
% 2.76/0.69 % (148839)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.76/0.69 % (148842)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.76/0.69 % Exception at run slice level
% 2.76/0.69 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.76/0.69 % (148841)Instruction limit reached!
% 2.76/0.69 % (148841)------------------------------
% 2.76/0.69 % (148841)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.76/0.69 % (148841)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.76/0.69 % (148841)CaDiCaL version: 2.1.3
% 2.76/0.69 % (148841)Termination reason: Instruction limit
% 2.76/0.69 % (148841)Termination phase: Saturation
% 2.76/0.69 % (148841)Time elapsed: 0.085 s
% 2.76/0.69 % (148841)Peak memory usage: 12 MB
% 2.76/0.69 % (148841)Instructions burned: 105 (million)
% 2.76/0.69 % (148842)Instruction limit reached!
% 2.76/0.69 % (148842)------------------------------
% 2.76/0.69 % (148842)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.76/0.69 % (148842)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.76/0.69 % (148842)CaDiCaL version: 2.1.3
% 2.76/0.69 % (148842)Termination reason: Instruction limit
% 2.76/0.69 % (148842)Termination phase: Saturation
% 2.76/0.69 % (148842)Time elapsed: 0.094 s
% 2.76/0.69 % (148842)Peak memory usage: 12 MB
% 2.76/0.69 % (148842)Instructions burned: 116 (million)
% 2.76/0.69 % (148843)Instruction limit reached!
% 2.76/0.69 % (148843)------------------------------
% 2.76/0.69 % (148843)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.76/0.69 % (148843)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.76/0.69 % (148843)CaDiCaL version: 2.1.3
% 2.76/0.69 % (148843)Termination reason: Instruction limit
% 2.76/0.69 % (148843)Termination phase: Saturation
% 2.76/0.69 % (148843)Time elapsed: 0.108 s
% 2.76/0.69 % (148843)Peak memory usage: 13 MB
% 2.76/0.69 % (148843)Instructions burned: 132 (million)
% 2.76/0.69 % (148853)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3016259136:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 2.76/0.69 % (148852)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3539898986:i=714:nm=2_2998 on theBenchmark for (2998ds/714Mi)
% 2.76/0.69 % (148854)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=3512786299:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 2.76/0.69 % (148844)Instruction limit reached!
% 2.76/0.69 % (148844)------------------------------
% 2.76/0.69 % (148844)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.76/0.69 % (148844)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.76/0.69 % (148844)CaDiCaL version: 2.1.3
% 2.76/0.69 % (148844)Termination reason: Instruction limit
% 2.76/0.69 % (148844)Termination phase: Saturation
% 2.76/0.69 % (148844)Time elapsed: 0.134 s
% 2.76/0.69 % (148844)Peak memory usage: 13 MB
% 2.76/0.69 % (148844)Instructions burned: 160 (million)
% 2.76/0.69 % (148855)ott-21_1_sil=16000:fs=off:random_seed=3819017293:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 2.76/0.69 % (148853)Instruction limit reached!
% 2.76/0.69 % (148853)------------------------------
% 2.76/0.69 % (148853)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.76/0.69 % (148853)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.76/0.69 % (148853)CaDiCaL version: 2.1.3
% 2.76/0.69 % (148853)Termination reason: Instruction limit
% 2.76/0.69 % (148853)Termination phase: Saturation
% 2.76/0.69 % (148853)Time elapsed: 0.035 s
% 2.76/0.69 % (148853)Peak memory usage: 13 MB
% 2.76/0.69 % (148853)Instructions burned: 133 (million)
% 2.76/0.69 % (148861)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1480805480:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 2.76/0.69 % (148854)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.76/0.69 % (148859)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3721355353:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 2.76/0.69 % Exception at run slice level
% 2.76/0.69 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.76/0.69 % Exception at run slice level
% 2.76/0.69 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.76/0.69 % (148864)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3927445733:i=1179_2997 on theBenchmark for (2997ds/1179Mi)
% 2.76/0.69 % (148865)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=2358668098:i=889:ins=1_2997 on theBenchmark for (2997ds/889Mi)
% 2.76/0.69 % (148854)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.76/0.69 % Exception at run slice level
% 2.76/0.69 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.76/0.69 % (148869)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=3783260736: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)
% 2.76/0.69 % (148869)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.76/0.69 % (148855)Instruction limit reached!
% 2.76/0.69 % (148855)------------------------------
% 2.76/0.69 % (148855)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.76/0.69 % (148855)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.76/0.69 % (148855)CaDiCaL version: 2.1.3
% 2.76/0.69 % (148855)Termination reason: Instruction limit
% 2.76/0.69 % (148855)Termination phase: Saturation
% 2.76/0.69 % (148855)Time elapsed: 0.149 s
% 2.76/0.69 % (148855)Peak memory usage: 13 MB
% 2.76/0.69 % (148855)Instructions burned: 181 (million)
% 2.76/0.69 % (148874)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=2718543464:i=879:kws=inv_precedence:fsr=off_2996 on theBenchmark for (2996ds/879Mi)
% 2.76/0.69 % (148874)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.76/0.69 % (148854) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-148833-148854"...
% 2.76/0.69 % (148854)...printing done.
% 2.76/0.69 % (148854)Refutation found. Thanks to Tanya!
% 2.76/0.69 % SZS status Theorem for theBenchmark
% 2.76/0.69 % SZS output start Proof for theBenchmark
% 2.76/0.69 thf(type_def_5, type, coindu1593790203_llist: $tType > $tType).
% 2.76/0.69 thf(type_def_6, type, product_prod: ($tType * $tType) > $tType).
% 2.76/0.69 thf(type_def_7, type, set: $tType > $tType).
% 2.76/0.69 thf(type_def_8, type, itself: $tType > $tType).
% 2.76/0.69 thf(type_def_9, type, a: $tType).
% 2.76/0.69 thf(type_def_10, type, sTfun: ($tType * $tType) > $tType).
% 2.76/0.69 thf(func_def_0, type, bounded_lattice: !>[X0: $tType]:((itself @ X0 > $o))).
% 2.76/0.69 thf(func_def_1, type, type: !>[X0: $tType]:((itself @ X0 > $o))).
% 2.76/0.69 thf(func_def_2, type, lattice: !>[X0: $tType]:((itself @ X0 > $o))).
% 2.76/0.69 thf(func_def_3, type, semilattice_sup: !>[X0: $tType]:((itself @ X0 > $o))).
% 2.76/0.69 thf(func_def_4, type, bounded_lattice_bot: !>[X0: $tType]:((itself @ X0 > $o))).
% 2.76/0.69 thf(func_def_5, type, bounde1808546759up_bot: !>[X0: $tType]:((itself @ X0 > $o))).
% 2.76/0.69 thf(func_def_6, type, coindu1928975208n_lset: !>[X0: $tType]:((set @ X0 > coindu1593790203_llist @ X0 > set @ X0))).
% 2.76/0.69 thf(func_def_7, type, coindu268472904append: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 2.76/0.69 thf(func_def_8, type, coindu1213758845finite: !>[X0: $tType]:((coindu1593790203_llist @ X0 > $o))).
% 2.76/0.69 thf(func_def_9, type, coindu1121789889_LCons: !>[X0: $tType]:((X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 2.76/0.69 thf(func_def_10, type, coindu1598213697e_LNil: !>[X0: $tType]:(coindu1593790203_llist @ X0)).
% 2.76/0.69 thf(func_def_11, type, coindu882539134_llist: !>[X0: $tType, X1: $tType]:((X0 > (X1 > coindu1593790203_llist @ X1 > X0) > coindu1593790203_llist @ X1 > X0))).
% 2.76/0.69 thf(func_def_12, type, coindu1244876290_llist: !>[X0: $tType, X1: $tType]:(((X0 > $o) > (X0 > X1) > (X0 > $o) > (X0 > coindu1593790203_llist @ X1) > (X0 > X0) > X0 > coindu1593790203_llist @ X1))).
% 2.76/0.69 thf(func_def_13, type, coindu1046438764le_lhd: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0))).
% 2.76/0.69 thf(func_def_14, type, coindu987187967t_all2: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X1 > $o))).
% 2.76/0.69 thf(func_def_15, type, coindu335574135_lnull: !>[X0: $tType]:((coindu1593790203_llist @ X0 > $o))).
% 2.76/0.69 thf(func_def_16, type, coindu1112613586e_lset: !>[X0: $tType]:((coindu1593790203_llist @ X0 > set @ X0))).
% 2.76/0.69 thf(func_def_17, type, coindu1047225960le_ltl: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 2.76/0.69 thf(func_def_18, type, coindu44415597_llist: !>[X0: $tType]:(((X0 > $o) > coindu1593790203_llist @ X0 > $o))).
% 2.76/0.69 thf(func_def_19, type, coindu567634248member: !>[X0: $tType]:((X0 > coindu1593790203_llist @ X0 > $o))).
% 2.76/0.69 thf(func_def_20, type, coindu1696667936prefix: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o))).
% 2.76/0.69 thf(func_def_21, type, coindu1055736764_lsetp: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0 > $o))).
% 2.76/0.69 thf(func_def_22, type, coindu1599971794_llist: !>[X0: $tType, X1: $tType]:(((X0 > $o) > (X0 > X1) > (X0 > X0) > X0 > coindu1593790203_llist @ X1))).
% 2.76/0.69 thf(func_def_23, type, comple1396247847notone: !>[X0: $tType, X1: $tType]:(((X0 > X0 > $o) > (X1 > X1 > $o) > (X0 > X1) > $o))).
% 2.76/0.69 thf(func_def_24, type, if: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 2.76/0.69 thf(func_def_25, type, sup_sup: !>[X0: $tType]:((X0 > X0 > X0))).
% 2.76/0.69 thf(func_def_26, type, bot_bot: !>[X0: $tType]:(X0)).
% 2.76/0.69 thf(func_def_27, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 2.76/0.69 thf(func_def_28, type, product_Pair: !>[X0: $tType, X1: $tType]:((X0 > X1 > product_prod @ X0 @ X1))).
% 2.76/0.69 thf(func_def_29, type, type2: !>[X0: $tType]:(itself @ X0)).
% 2.76/0.69 thf(func_def_30, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 2.76/0.69 thf(func_def_31, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 2.76/0.69 thf(func_def_32, type, x: a).
% 2.76/0.69 thf(func_def_36, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 2.76/0.69 thf(func_def_37, type, vAND: ($o > $o > $o)).
% 2.76/0.69 thf(func_def_38, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 2.76/0.69 thf(func_def_39, type, db0: !>[X0: $tType]:(X0)).
% 2.76/0.69 thf(func_def_40, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 2.76/0.69 thf(func_def_41, type, vOR: ($o > $o > $o)).
% 2.76/0.69 thf(func_def_42, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 2.76/0.69 thf(func_def_43, type, vIMP: ($o > $o > $o)).
% 2.76/0.69 thf(func_def_44, type, db4: !>[X0: $tType]:(X0)).
% 2.76/0.69 thf(func_def_45, type, db1: !>[X0: $tType]:(X0)).
% 2.76/0.69 thf(func_def_46, type, db3: !>[X0: $tType]:(X0)).
% 2.76/0.69 thf(func_def_47, type, db2: !>[X0: $tType]:(X0)).
% 2.76/0.69 thf(func_def_48, type, vNOT: ($o > $o)).
% 2.76/0.69 thf(func_def_49, type, db5: !>[X0: $tType]:(X0)).
% 2.76/0.69 thf(func_def_50, type, sP0: !>[X0: $tType, X1: $tType]:((X0 > coindu1593790203_llist @ X1 > (coindu1593790203_llist @ X1 > X0) > (coindu1593790203_llist @ X1 > X0) > $o))).
% 2.76/0.69 thf(func_def_51, type, sP1: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o))).
% 2.76/0.69 thf(func_def_52, type, sK2: !>[X0: $tType, X1: $tType]:((X0 > coindu1593790203_llist @ X1 > (coindu1593790203_llist @ X1 > X0) > (coindu1593790203_llist @ X1 > X0) > coindu1593790203_llist @ X1))).
% 2.76/0.69 thf(func_def_53, type, sK3: !>[X0: $tType, X1: $tType]:(((X0 > X0 > $o) > (coindu1593790203_llist @ X1 > X0) > X0 > coindu1593790203_llist @ X1 > coindu1593790203_llist @ X1))).
% 2.76/0.69 thf(func_def_54, type, sK4: !>[X0: $tType, X1: $tType]:(((X0 > X0 > $o) > (coindu1593790203_llist @ X1 > X0) > coindu1593790203_llist @ X1 > coindu1593790203_llist @ X1))).
% 2.76/0.69 thf(func_def_55, type, sK5: !>[X0: $tType, X1: $tType]:(((X0 > X0 > $o) > (coindu1593790203_llist @ X1 > X0) > coindu1593790203_llist @ X1 > coindu1593790203_llist @ X1))).
% 2.76/0.69 thf(func_def_56, type, sK6: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X0 > X0 > $o) > (X1 > X1 > $o) > X1))).
% 2.76/0.69 thf(func_def_57, type, sK7: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X0 > X0 > $o) > (X1 > X1 > $o) > X1))).
% 2.76/0.69 thf(func_def_58, type, sK8: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 2.76/0.69 thf(func_def_59, type, sK9: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 2.76/0.69 thf(func_def_60, type, sK10: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > X0))).
% 2.76/0.69 thf(func_def_61, type, sK11: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 2.76/0.69 thf(func_def_62, type, sK12: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 2.76/0.69 thf(func_def_63, type, sK13: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 2.76/0.69 thf(func_def_64, type, sK14: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0))).
% 2.76/0.69 thf(func_def_65, type, sK15: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 2.76/0.69 thf(func_def_66, type, sK16: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > X0 > $o) > coindu1593790203_llist @ X0))).
% 2.76/0.69 thf(func_def_67, type, sK17: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > X0 > $o) > X0))).
% 2.76/0.69 thf(func_def_68, type, sK18: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > X0 > $o) > X0))).
% 2.76/0.69 thf(func_def_69, type, sK19: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > X0 > $o) > X0))).
% 2.76/0.69 thf(func_def_70, type, sK20: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > X0 > $o) > coindu1593790203_llist @ X0))).
% 2.76/0.69 thf(func_def_71, type, sK21: !>[X0: $tType]:((X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 2.76/0.69 thf(func_def_72, type, sK22: !>[X0: $tType]:((X0 > coindu1593790203_llist @ X0 > X0))).
% 2.76/0.69 thf(func_def_73, type, sK23: !>[X0: $tType]:((X0 > coindu1593790203_llist @ X0 > X0))).
% 2.76/0.69 thf(func_def_74, type, sK24: !>[X0: $tType]:((X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 2.76/0.69 thf(func_def_75, type, sK25: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 2.76/0.69 thf(func_def_76, type, sK26: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > $o) > X0))).
% 2.76/0.69 thf(func_def_77, type, sK27: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 2.76/0.69 thf(func_def_78, type, sK28: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0))).
% 2.76/0.69 thf(func_def_79, type, sK29: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 2.76/0.69 thf(func_def_80, type, sK30: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 2.76/0.69 thf(func_def_81, type, sK31: !>[X0: $tType, X1: $tType]:((coindu1593790203_llist @ X1 > coindu1593790203_llist @ X0 > (X0 > X1 > $o) > X0))).
% 2.76/0.69 thf(func_def_82, type, sK32: !>[X0: $tType, X1: $tType]:((coindu1593790203_llist @ X1 > coindu1593790203_llist @ X0 > (X0 > X1 > $o) > coindu1593790203_llist @ X0))).
% 2.76/0.69 thf(func_def_83, type, sK33: !>[X0: $tType, X1: $tType]:((coindu1593790203_llist @ X1 > coindu1593790203_llist @ X0 > (X0 > X1 > $o) > X1))).
% 2.76/0.69 thf(func_def_84, type, sK34: !>[X0: $tType, X1: $tType]:((coindu1593790203_llist @ X1 > coindu1593790203_llist @ X0 > (X0 > X1 > $o) > coindu1593790203_llist @ X1))).
% 2.76/0.69 thf(func_def_85, type, sK35: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 2.76/0.69 thf(func_def_86, type, sK36: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 2.76/0.69 thf(func_def_87, type, sK37: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 2.76/0.69 thf(func_def_88, type, sK38: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > (coindu1593790203_llist @ X0 > coindu1593790203_llist @ X1 > $o) > coindu1593790203_llist @ X0))).
% 2.76/0.69 thf(func_def_89, type, sK39: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > (coindu1593790203_llist @ X0 > coindu1593790203_llist @ X1 > $o) > coindu1593790203_llist @ X1))).
% 2.76/0.69 thf(func_def_90, type, sK40: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 2.76/0.69 thf(func_def_91, type, sK41: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 2.76/0.69 thf(func_def_92, type, sK42: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0 > coindu1593790203_llist @ X0))).
% 2.76/0.69 thf(func_def_93, type, sK43: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0 > coindu1593790203_llist @ X0))).
% 2.76/0.69 thf(func_def_94, type, sK44: !>[X0: $tType]:(((X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 2.76/0.69 thf(func_def_95, type, sK45: !>[X0: $tType]:(((X0 > coindu1593790203_llist @ X0 > $o) > X0))).
% 2.76/0.69 thf(func_def_96, type, sK46: !>[X0: $tType]:(((X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 2.76/0.69 thf(func_def_97, type, sK47: !>[X0: $tType]:(((X0 > coindu1593790203_llist @ X0 > $o) > X0))).
% 2.76/0.69 thf(func_def_98, type, sK48: !>[X0: $tType]:(((X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 2.76/0.69 thf(func_def_99, type, sK49: !>[X0: $tType]:(((X0 > coindu1593790203_llist @ X0 > $o) > X0))).
% 2.76/0.69 thf(func_def_100, type, sK50: !>[X0: $tType]:(((X0 > coindu1593790203_llist @ X0 > $o) > X0))).
% 2.76/0.69 thf(func_def_101, type, sK51: !>[X0: $tType]:(((X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 2.76/0.69 thf(func_def_102, type, sK52: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0 > X0))).
% 2.76/0.69 thf(func_def_103, type, sK53: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0 > coindu1593790203_llist @ X0))).
% 2.76/0.69 thf(func_def_104, type, sK54: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0 > coindu1593790203_llist @ X0))).
% 2.76/0.69 thf(func_def_105, type, sK55: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > $o) > X0 > X0))).
% 2.76/0.69 thf(func_def_106, type, sK56: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > $o) > X0 > coindu1593790203_llist @ X0))).
% 2.76/0.69 thf(func_def_107, type, sK57: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > $o) > X0 > coindu1593790203_llist @ X0))).
% 2.76/0.69 thf(func_def_108, type, sK58: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > $o) > X0 > X0))).
% 2.76/0.69 thf(func_def_109, type, sK59: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > $o) > X0 > coindu1593790203_llist @ X0))).
% 2.76/0.69 thf(func_def_110, type, sK60: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > $o) > X0 > coindu1593790203_llist @ X0))).
% 2.76/0.69 thf(func_def_111, type, sK61: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0 > X0))).
% 2.76/0.69 thf(func_def_112, type, sK62: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0 > coindu1593790203_llist @ X0))).
% 2.76/0.69 thf(func_def_113, type, sK63: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0 > coindu1593790203_llist @ X0))).
% 2.76/0.69 thf(func_def_114, type, sK64: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > (X0 > X1 > $o) > coindu1593790203_llist @ X1 > coindu1593790203_llist @ X0 > X0))).
% 2.76/0.69 thf(func_def_115, type, sK65: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > (X0 > X1 > $o) > coindu1593790203_llist @ X1 > coindu1593790203_llist @ X0 > X1))).
% 2.76/0.69 thf(func_def_116, type, sK66: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > coindu1593790203_llist @ X1 > coindu1593790203_llist @ X0 > (X0 > X1 > $o) > X0))).
% 2.76/0.69 thf(func_def_117, type, sK67: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > coindu1593790203_llist @ X1 > coindu1593790203_llist @ X0 > (X0 > X1 > $o) > X1))).
% 2.76/0.69 thf(func_def_118, type, sK68: !>[X0: $tType]:(((X0 > X0 > $o) > coindu1593790203_llist @ X0 > X0))).
% 2.76/0.69 thf(func_def_119, type, sK69: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > coindu1593790203_llist @ X0 > X0))).
% 2.76/0.69 thf(func_def_120, type, sK70: !>[X0: $tType]:(((X0 > $o) > coindu1593790203_llist @ X0 > (X0 > $o) > X0))).
% 2.76/0.69 thf(func_def_121, type, sK71: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 2.76/0.69 thf(func_def_122, type, sK72: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 2.76/0.69 thf(func_def_123, type, sK73: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 2.76/0.69 thf(func_def_124, type, sK74: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 2.76/0.69 thf(func_def_125, type, sK75: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0 > coindu1593790203_llist @ X0))).
% 2.76/0.69 thf(func_def_126, type, sK76: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0 > coindu1593790203_llist @ X0))).
% 2.76/0.69 thf(func_def_127, type, sK77: !>[X0: $tType]:((set @ product_prod @ coindu1593790203_llist @ X0 @ coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 2.76/0.69 thf(func_def_128, type, sK78: !>[X0: $tType]:((set @ product_prod @ coindu1593790203_llist @ X0 @ coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 2.76/0.69 thf(func_def_129, type, sK79: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 2.76/0.69 thf(func_def_130, type, sK80: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 2.76/0.69 thf(func_def_131, type, sK81: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 2.76/0.69 thf(func_def_132, type, sK82: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 2.76/0.69 thf(func_def_133, type, sK83: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 2.76/0.69 thf(func_def_134, type, sK84: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 2.76/0.69 thf(func_def_135, type, sK85: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 2.76/0.69 thf(func_def_136, type, sK86: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 2.76/0.69 thf(func_def_137, type, sK87: coindu1593790203_llist @ a).
% 2.76/0.69 thf(func_def_138, type, sK88: coindu1593790203_llist @ a).
% 2.76/0.69 thf(func_def_139, type, sK89: !>[X0: $tType]:(((X0 > $o) > X0))).
% 2.76/0.69 thf(func_def_140, type, sK90: !>[X0: $tType]:(((X0 > $o) > X0))).
% 2.76/0.69 thf(func_def_141, type, sK91: !>[X0: $tType]:((set @ X0 > X0))).
% 2.76/0.69 thf(func_def_142, type, sK92: !>[X0: $tType]:((set @ X0 > set @ X0 > (X0 > $o) > X0))).
% 2.76/0.69 thf(func_def_143, type, sK93: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 2.76/0.69 thf(func_def_144, type, sK94: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 2.76/0.69 thf(func_def_145, type, sK95: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 2.76/0.69 thf(func_def_146, type, sK96: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 2.76/0.69 thf(func_def_147, type, sK97: !>[X0: $tType]:((set @ X0 > (X0 > $o) > set @ X0 > X0))).
% 2.76/0.69 thf(func_def_148, type, sK98: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 2.76/0.69 thf(func_def_149, type, sK99: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0))).
% 2.76/0.69 thf(func_def_150, type, sK100: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 2.76/0.69 thf(func_def_151, type, sK101: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0))).
% 2.76/0.69 thf(func_def_152, type, sK102: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 2.76/0.69 thf(func_def_153, type, sK103: !>[X0: $tType, X1: $tType]:(((X0 > X0 > $o) > (X1 > X0) > (X1 > X1 > $o) > X1))).
% 2.76/0.69 thf(func_def_154, type, sK104: !>[X0: $tType, X1: $tType]:(((X0 > X0 > $o) > (X1 > X0) > (X1 > X1 > $o) > X1))).
% 2.76/0.69 thf(func_def_155, type, sK105: !>[X0: $tType]:((X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 2.76/0.69 thf(f8,axiom,(
% 2.76/0.69 ! [X0 : $tType,X1 : coindu1593790203_llist @ X0,X2 : coindu1593790203_llist @ X0,X3 : X0] : ((coindu1696667936prefix @ X0 @ X1 @ X2) => (coindu1696667936prefix @ X0 @ (coindu1121789889_LCons @ X0 @ X3 @ X1) @ (coindu1121789889_LCons @ X0 @ X3 @ X2)))),
% 2.76/0.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_Le__LCons)).
% 2.76/0.69 thf(f16,axiom,(
% 2.76/0.69 ! [X0 : $tType,X1 : $tType] : (comple1396247847notone @ X1 @ X0 = (^[X2 : (X1 > X1 > $o), X3 : (X0 > X0 > $o), X4 : (X1 > X0)] : (! [X5 : X1,X6 : X1] : ((X2 @ X5 @ X6) => (X3 @ (X4 @ X5) @ (X4 @ X6))))))),
% 2.76/0.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_monotone__def)).
% 2.76/0.69 thf(f273,conjecture,(
% 2.76/0.69 (comple1396247847notone @ coindu1593790203_llist @ a @ coindu1593790203_llist @ a @ coindu1696667936prefix @ a @ coindu1696667936prefix @ a @ (coindu1121789889_LCons @ a @ x))),
% 2.76/0.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 2.76/0.69 thf(f274,negated_conjecture,(
% 2.76/0.69 ~(comple1396247847notone @ coindu1593790203_llist @ a @ coindu1593790203_llist @ a @ coindu1696667936prefix @ a @ coindu1696667936prefix @ a @ (coindu1121789889_LCons @ a @ x))),
% 2.76/0.69 inference(negated_conjecture,[status(cth)],[f273])).
% 2.76/0.69 thf(f288,plain,(
% 2.76/0.69 ! [X0 : $tType,X1 : coindu1593790203_llist @ X0,X2 : coindu1593790203_llist @ X0,X3 : X0] : ((coindu1696667936prefix @ X0 @ X1 @ X2) => (coindu1696667936prefix @ X0 @ (coindu1121789889_LCons @ X0 @ X3 @ X1) @ (coindu1121789889_LCons @ X0 @ X3 @ X2)))),
% 2.76/0.69 inference(rectify,[],[f8])).
% 2.76/0.69 thf(f289,plain,(
% 2.76/0.69 ! [X0 : $tType,X1 : coindu1593790203_llist @ X0,X2 : coindu1593790203_llist @ X0,X3 : X0] : ((((coindu1696667936prefix @ X0 @ X1 @ X2)) = $true) => (((coindu1696667936prefix @ X0 @ (coindu1121789889_LCons @ X0 @ X3 @ X1) @ (coindu1121789889_LCons @ X0 @ X3 @ X2))) = $true))),
% 2.76/0.69 inference(fool_elimination,[],[f288])).
% 2.76/0.69 thf(f304,plain,(
% 2.76/0.69 ! [X0 : $tType,X1 : $tType] : (comple1396247847notone @ X1 @ X0 = (^[X2 : (X1 > X1 > $o), X3 : (X0 > X0 > $o), X4 : (X1 > X0)] : (! [X5 : X1,X6 : X1] : ((X2 @ X5 @ X6) => (X3 @ (X4 @ X5) @ (X4 @ X6))))))),
% 2.76/0.69 inference(rectify,[],[f16])).
% 2.76/0.69 thf(f305,plain,(
% 2.76/0.69 ! [X0 : $tType,X1 : $tType] : (comple1396247847notone @ X1 @ X0 = (^[Y0 : X1 > X1 > $o]: ((^[Y1 : X0 > X0 > $o]: ((^[Y2 : X1 > X0]: (!! @ X1 @ (^[Y3 : X1]: (!! @ X1 @ (^[Y4 : X1]: ((Y0 @ Y4 @ Y3) => (Y1 @ (Y2 @ Y4) @ (Y2 @ Y3)))))))))))))),
% 2.76/0.69 inference(fool_elimination,[],[f304])).
% 2.76/0.69 thf(f738,plain,(
% 2.76/0.69 ~(comple1396247847notone @ coindu1593790203_llist @ a @ coindu1593790203_llist @ a @ coindu1696667936prefix @ a @ coindu1696667936prefix @ a @ (coindu1121789889_LCons @ a @ x))),
% 2.76/0.69 inference(rectify,[],[f274])).
% 2.76/0.69 thf(f739,plain,(
% 2.76/0.69 ~ (((comple1396247847notone @ coindu1593790203_llist @ a @ coindu1593790203_llist @ a @ coindu1696667936prefix @ a @ coindu1696667936prefix @ a @ (coindu1121789889_LCons @ a @ x))) = $true)),
% 2.76/0.69 inference(fool_elimination,[],[f738])).
% 2.76/0.69 thf(f790,plain,(
% 2.76/0.69 (((comple1396247847notone @ coindu1593790203_llist @ a @ coindu1593790203_llist @ a @ coindu1696667936prefix @ a @ coindu1696667936prefix @ a @ (coindu1121789889_LCons @ a @ x))) != $true)),
% 2.76/0.69 inference(flattening,[],[f739])).
% 2.76/0.69 thf(f797,plain,(
% 2.76/0.69 ! [X0 : $tType,X1 : coindu1593790203_llist @ X0,X2 : coindu1593790203_llist @ X0,X3 : X0] : ((((coindu1696667936prefix @ X0 @ (coindu1121789889_LCons @ X0 @ X3 @ X1) @ (coindu1121789889_LCons @ X0 @ X3 @ X2))) = $true) | (((coindu1696667936prefix @ X0 @ X1 @ X2)) != $true))),
% 2.76/0.69 inference(ennf_transformation,[],[f289])).
% 2.76/0.69 thf(f1066,plain,(
% 2.76/0.69 ( ! [X0 : $tType,X2 : coindu1593790203_llist @ X0,X3 : X0,X1 : coindu1593790203_llist @ X0] : ((((coindu1696667936prefix @ X0 @ X1 @ X2)) != $true) | (((coindu1696667936prefix @ X0 @ (coindu1121789889_LCons @ X0 @ X3 @ X1) @ (coindu1121789889_LCons @ X0 @ X3 @ X2))) = $true)) )),
% 2.76/0.69 inference(cnf_transformation,[],[f797])).
% 2.76/0.69 thf(f1084,plain,(
% 2.76/0.69 ( ! [X1 : $tType,X0 : $tType] : ((comple1396247847notone @ X1 @ X0 = (^[Y0 : X1 > X1 > $o]: ((^[Y1 : X0 > X0 > $o]: ((^[Y2 : X1 > X0]: (!! @ X1 @ (^[Y3 : X1]: (!! @ X1 @ (^[Y4 : X1]: ((Y0 @ Y4 @ Y3) => (Y1 @ (Y2 @ Y4) @ (Y2 @ Y3)))))))))))))) )),
% 2.76/0.69 inference(cnf_transformation,[],[f305])).
% 2.76/0.69 thf(f1439,plain,(
% 2.76/0.69 (((comple1396247847notone @ coindu1593790203_llist @ a @ coindu1593790203_llist @ a @ coindu1696667936prefix @ a @ coindu1696667936prefix @ a @ (coindu1121789889_LCons @ a @ x))) != $true)),
% 2.76/0.69 inference(cnf_transformation,[],[f790])).
% 2.76/0.69 thf(f1534,plain,(
% 2.76/0.69 ($true != (((^[Y0 : coindu1593790203_llist @ a > coindu1593790203_llist @ a > $o]: ((^[Y1 : coindu1593790203_llist @ a > coindu1593790203_llist @ a > $o]: ((^[Y2 : coindu1593790203_llist @ a > coindu1593790203_llist @ a]: (!! @ coindu1593790203_llist @ a @ (^[Y3 : coindu1593790203_llist @ a]: (!! @ coindu1593790203_llist @ a @ (^[Y4 : coindu1593790203_llist @ a]: ((Y0 @ Y4 @ Y3) => (Y1 @ (Y2 @ Y4) @ (Y2 @ Y3)))))))))))) @ coindu1696667936prefix @ a @ coindu1696667936prefix @ a @ (coindu1121789889_LCons @ a @ x))))),
% 2.76/0.69 inference(definition_unfolding,[],[f1439,f1084])).
% 2.76/0.69 thf(f1549,plain,(
% 2.76/0.69 ($true != ((!! @ coindu1593790203_llist @ a @ (^[Y0 : coindu1593790203_llist @ a]: (!! @ coindu1593790203_llist @ a @ (^[Y1 : coindu1593790203_llist @ a]: ((coindu1696667936prefix @ a @ Y1 @ Y0) => (coindu1696667936prefix @ a @ (coindu1121789889_LCons @ a @ x @ Y1) @ (coindu1121789889_LCons @ a @ x @ Y0)))))))))),
% 2.76/0.69 inference(beta-eta_normalization,[],[f1534])).
% 2.76/0.69 thf(f1550,plain,(
% 2.76/0.69 ($false = (((^[Y0 : coindu1593790203_llist @ a]: (!! @ coindu1593790203_llist @ a @ (^[Y1 : coindu1593790203_llist @ a]: ((coindu1696667936prefix @ a @ Y1 @ Y0) => (coindu1696667936prefix @ a @ (coindu1121789889_LCons @ a @ x @ Y1) @ (coindu1121789889_LCons @ a @ x @ Y0)))))) @ sK87)))),
% 2.76/0.69 inference(sigma_proxy_clausification,[],[f1549])).
% 2.76/0.69 thf(f1551,plain,(
% 2.76/0.69 ($false = ((!! @ coindu1593790203_llist @ a @ (^[Y0 : coindu1593790203_llist @ a]: ((coindu1696667936prefix @ a @ Y0 @ sK87) => (coindu1696667936prefix @ a @ (coindu1121789889_LCons @ a @ x @ Y0) @ (coindu1121789889_LCons @ a @ x @ sK87)))))))),
% 2.76/0.69 inference(beta-eta_normalization,[],[f1550])).
% 2.76/0.69 thf(f1552,plain,(
% 2.76/0.69 ($false = (((^[Y0 : coindu1593790203_llist @ a]: ((coindu1696667936prefix @ a @ Y0 @ sK87) => (coindu1696667936prefix @ a @ (coindu1121789889_LCons @ a @ x @ Y0) @ (coindu1121789889_LCons @ a @ x @ sK87)))) @ sK88)))),
% 2.76/0.69 inference(sigma_proxy_clausification,[],[f1551])).
% 2.76/0.69 thf(f1553,plain,(
% 2.76/0.69 ($false = (((coindu1696667936prefix @ a @ sK88 @ sK87) => (coindu1696667936prefix @ a @ (coindu1121789889_LCons @ a @ x @ sK88) @ (coindu1121789889_LCons @ a @ x @ sK87)))))),
% 2.76/0.69 inference(beta-eta_normalization,[],[f1552])).
% 2.76/0.69 thf(f1554,plain,(
% 2.76/0.69 ($false = ((coindu1696667936prefix @ a @ (coindu1121789889_LCons @ a @ x @ sK88) @ (coindu1121789889_LCons @ a @ x @ sK87))))),
% 2.76/0.69 inference(imp_proxy_clausification,[],[f1553])).
% 2.76/0.69 thf(f1555,plain,(
% 2.76/0.69 ($true = ((coindu1696667936prefix @ a @ sK88 @ sK87)))),
% 2.76/0.69 inference(imp_proxy_clausification,[],[f1553])).
% 2.76/0.69 thf(f3611,plain,(
% 2.76/0.69 ( ! [X0 : a] : (($true != $true) | ($true = ((coindu1696667936prefix @ a @ (coindu1121789889_LCons @ a @ X0 @ sK88) @ (coindu1121789889_LCons @ a @ X0 @ sK87))))) )),
% 2.76/0.69 inference(constrained_superposition,[],[f1066,f1555])).
% 2.76/0.69 thf(f3626,plain,(
% 2.76/0.69 ( ! [X0 : a] : (($true = ((coindu1696667936prefix @ a @ (coindu1121789889_LCons @ a @ X0 @ sK88) @ (coindu1121789889_LCons @ a @ X0 @ sK87))))) )),
% 2.76/0.69 inference(trivial_inequality_removal,[],[f3611])).
% 2.76/0.69 thf(f3964,plain,(
% 2.76/0.69 ($true = $false)),
% 2.76/0.69 inference(constrained_superposition,[],[f1554,f3626])).
% 2.76/0.69 thf(f3993,plain,(
% 2.76/0.69 $false),
% 2.76/0.69 inference(trivial_inequality_removal,[],[f3964])).
% 2.76/0.69 % SZS output end Proof for theBenchmark
% 2.76/0.69 % (148854)------------------------------
% 2.76/0.69 % (148854)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.76/0.69 % (148854)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.76/0.69 % (148854)CaDiCaL version: 2.1.3
% 2.76/0.69 % (148854)Termination reason: Refutation
% 2.76/0.69 % (148854)Time elapsed: 0.257 s
% 2.76/0.69 % (148854)Peak memory usage: 14 MB
% 2.76/0.69 % (148854)Instructions burned: 292 (million)
% 2.76/0.69 % (148833)Success in time 0.432 s
% 2.76/0.69 % Vampire exiting
%------------------------------------------------------------------------------