%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT121^1 : 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 : n020.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 07:48:55 AM UTC 2026
% Result : Theorem 0.97s 0.36s
% Output : Refutation 0.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT121^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n020.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 17:59:20 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.21 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
% 0.97/0.36 % (1399598)Will run a generic schedule for satisfiability detection.
% 0.97/0.36 % (1399609)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3088650722:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.97/0.36 % (1399604)% WARNING: option uhcvi not known.
% 0.97/0.36 % (1399605)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1100086292:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.97/0.36 % (1399603)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1167698723_2999 on theBenchmark for (2999ds/0Mi)
% 0.97/0.36 % (1399606)dis+10_1_sil=32000:sp=arity:random_seed=2149205614:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.97/0.36 % (1399604)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1441499009:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.97/0.36 % (1399607)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3422072392:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.97/0.36 % (1399608)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3449627520:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.97/0.36 % (1399604)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.97/0.36 % (1399607)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.97/0.36 % Exception at run slice level
% 0.97/0.36 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.97/0.36 % (1399604)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.97/0.36 % (1399609)Instruction limit reached!
% 0.97/0.36 % (1399609)------------------------------
% 0.97/0.36 % (1399609)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.97/0.36 % (1399609)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.97/0.36 % (1399609)CaDiCaL version: 2.1.3
% 0.97/0.36 % (1399609)Termination reason: Instruction limit
% 0.97/0.36 % (1399609)Termination phase: Saturation
% 0.97/0.36 % (1399609)Time elapsed: 0.040 s
% 0.97/0.36 % (1399609)Peak memory usage: 13 MB
% 0.97/0.36 % (1399609)Instructions burned: 160 (million)
% 0.97/0.36 % (1399618)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=41062846:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.97/0.36 % (1399606)Instruction limit reached!
% 0.97/0.36 % (1399606)------------------------------
% 0.97/0.36 % (1399606)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.97/0.36 % (1399606)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.97/0.36 % (1399606)CaDiCaL version: 2.1.3
% 0.97/0.36 % (1399606)Termination reason: Instruction limit
% 0.97/0.36 % (1399606)Termination phase: Saturation
% 0.97/0.36 % (1399606)Time elapsed: 0.046 s
% 0.97/0.36 % (1399606)Peak memory usage: 12 MB
% 0.97/0.36 % (1399606)Instructions burned: 105 (million)
% 0.97/0.36 % (1399617)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1117232846:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.97/0.36 % (1399607)Instruction limit reached!
% 0.97/0.36 % (1399607)------------------------------
% 0.97/0.36 % (1399607)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.97/0.36 % (1399607)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.97/0.36 % (1399607)CaDiCaL version: 2.1.3
% 0.97/0.36 % (1399607)Termination reason: Instruction limit
% 0.97/0.36 % (1399607)Termination phase: Saturation
% 0.97/0.36 % (1399607)Time elapsed: 0.053 s
% 0.97/0.36 % (1399607)Peak memory usage: 13 MB
% 0.97/0.36 % (1399607)Instructions burned: 117 (million)
% 0.97/0.36 % (1399608)Instruction limit reached!
% 0.97/0.36 % (1399608)------------------------------
% 0.97/0.36 % (1399608)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.97/0.36 % (1399608)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.97/0.36 % (1399608)CaDiCaL version: 2.1.3
% 0.97/0.36 % (1399608)Termination reason: Instruction limit
% 0.97/0.36 % (1399608)Termination phase: Saturation
% 0.97/0.36 % (1399608)Time elapsed: 0.059 s
% 0.97/0.36 % (1399608)Peak memory usage: 13 MB
% 0.97/0.36 % (1399608)Instructions burned: 133 (million)
% 0.97/0.36 % (1399621)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=1418838932:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.97/0.36 % (1399622)ott-21_1_sil=16000:fs=off:random_seed=3489557373:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 0.97/0.36 % Exception at run slice level
% 0.97/0.36 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.97/0.36 % (1399623)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1101388179:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 0.97/0.36 % (1399618)Instruction limit reached!
% 0.97/0.36 % (1399618)------------------------------
% 0.97/0.36 % (1399618)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.97/0.36 % (1399618)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.97/0.36 % (1399618)CaDiCaL version: 2.1.3
% 0.97/0.36 % (1399618)Termination reason: Instruction limit
% 0.97/0.36 % (1399618)Termination phase: Saturation
% 0.97/0.36 % (1399618)Time elapsed: 0.036 s
% 0.97/0.36 % (1399618)Peak memory usage: 13 MB
% 0.97/0.36 % (1399618)Instructions burned: 140 (million)
% 0.97/0.36 % (1399621)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.97/0.36 % (1399628)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=1456858090:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 0.97/0.36 % (1399626)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1614545419:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 0.97/0.36 % (1399621)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.97/0.36 % (1399621) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1399598-1399621"...
% 0.97/0.36 % (1399621)...printing done.
% 0.97/0.36 % (1399621)Refutation found. Thanks to Tanya!
% 0.97/0.36 % SZS status Theorem for theBenchmark
% 0.97/0.36 % SZS output start Proof for theBenchmark
% 0.97/0.36 thf(type_def_5, type, coindu1593790203_llist: $tType > $tType).
% 0.97/0.36 thf(type_def_6, type, code_natural: $tType).
% 0.97/0.36 thf(type_def_7, type, extended_enat: $tType).
% 0.97/0.36 thf(type_def_8, type, real: $tType).
% 0.97/0.36 thf(type_def_9, type, num: $tType).
% 0.97/0.36 thf(type_def_10, type, nat: $tType).
% 0.97/0.36 thf(type_def_11, type, int: $tType).
% 0.97/0.36 thf(type_def_12, type, itself: $tType > $tType).
% 0.97/0.36 thf(type_def_13, type, a: $tType).
% 0.97/0.36 thf(type_def_14, type, sTfun: ($tType * $tType) > $tType).
% 0.97/0.36 thf(func_def_0, type, type: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.97/0.36 thf(func_def_1, type, zero: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.97/0.36 thf(func_def_2, type, numeral: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.97/0.36 thf(func_def_3, type, minus: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.97/0.36 thf(func_def_4, type, ring_1: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.97/0.36 thf(func_def_5, type, ord: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.97/0.36 thf(func_def_6, type, ring_char_0: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.97/0.36 thf(func_def_7, type, neg_numeral: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.97/0.36 thf(func_def_8, type, order: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.97/0.36 thf(func_def_9, type, group_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.97/0.36 thf(func_def_10, type, semiring_1: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.97/0.36 thf(func_def_11, type, linorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.97/0.36 thf(func_def_12, type, preorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.97/0.36 thf(func_def_13, type, semiring_char_0: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.97/0.36 thf(func_def_14, type, linordered_idom: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.97/0.36 thf(func_def_15, type, comm_monoid_diff: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.97/0.36 thf(func_def_16, type, linordered_semidom: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.97/0.36 thf(func_def_17, type, ordered_ab_group_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.97/0.36 thf(func_def_18, type, cancel1352612707id_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.97/0.36 thf(func_def_19, type, cancel146912293up_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.97/0.36 thf(func_def_20, type, archim1727834104eiling: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.97/0.36 thf(func_def_21, type, ordere142940540dd_abs: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.97/0.36 thf(func_def_22, type, comple187826305attice: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.97/0.36 thf(func_def_23, type, archim1804426504_field: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.97/0.36 thf(func_def_24, type, canoni770627133id_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.97/0.36 thf(func_def_25, type, archimedean_ceiling: !>[X0: $tType]:((X0 > int))).
% 0.97/0.36 thf(func_def_26, type, archimedean_round: !>[X0: $tType]:((X0 > int))).
% 0.97/0.36 thf(func_def_27, type, code_Suc: (code_natural > code_natural)).
% 0.97/0.36 thf(func_def_28, type, code_case_natural: !>[X0: $tType]:((X0 > (code_natural > X0) > code_natural > X0))).
% 0.97/0.36 thf(func_def_29, type, code_rec_natural: !>[X0: $tType]:((X0 > (code_natural > X0 > X0) > code_natural > X0))).
% 0.97/0.36 thf(func_def_30, type, code_size_natural: (code_natural > nat)).
% 0.97/0.36 thf(func_def_31, type, coindu493225792length: !>[X0: $tType]:((nat > coindu1593790203_llist @ X0 > extended_enat))).
% 0.97/0.36 thf(func_def_32, type, coindu268472904append: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.97/0.36 thf(func_def_33, type, coindu191418589_ldrop: !>[X0: $tType]:((extended_enat > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.97/0.36 thf(func_def_34, type, coindu1018505716length: !>[X0: $tType]:((coindu1593790203_llist @ X0 > extended_enat))).
% 0.97/0.36 thf(func_def_35, type, coindu1598213697e_LNil: !>[X0: $tType]:(coindu1593790203_llist @ X0)).
% 0.97/0.36 thf(func_def_36, type, coindu1046438764le_lhd: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0))).
% 0.97/0.36 thf(func_def_37, type, coindu335574135_lnull: !>[X0: $tType]:((coindu1593790203_llist @ X0 > $o))).
% 0.97/0.36 thf(func_def_38, type, coindu567634248member: !>[X0: $tType]:((X0 > coindu1593790203_llist @ X0 > $o))).
% 0.97/0.36 thf(func_def_39, type, coindu1696667936prefix: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o))).
% 0.97/0.36 thf(func_def_40, type, coindu574146665prefix: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o))).
% 0.97/0.36 thf(func_def_41, type, coindu1802687541_ltake: !>[X0: $tType]:((extended_enat > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.97/0.36 thf(func_def_42, type, coindu721411036eWhile: !>[X0: $tType]:(((X0 > $o) > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.97/0.36 thf(func_def_43, type, extended_case_enat: !>[X0: $tType]:(((nat > X0) > X0 > extended_enat > X0))).
% 0.97/0.36 thf(func_def_44, type, extended_the_enat: (extended_enat > nat)).
% 0.97/0.36 thf(func_def_45, type, abs_abs: !>[X0: $tType]:((X0 > X0))).
% 0.97/0.36 thf(func_def_46, type, minus_minus: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.97/0.36 thf(func_def_47, type, zero_zero: !>[X0: $tType]:(X0)).
% 0.97/0.36 thf(func_def_48, type, hilbert_LeastM: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > $o) > X0))).
% 0.97/0.36 thf(func_def_49, type, if: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 0.97/0.36 thf(func_def_50, type, nat2: (int > nat)).
% 0.97/0.36 thf(func_def_51, type, ring_1_of_int: !>[X0: $tType]:((int > X0))).
% 0.97/0.36 thf(func_def_52, type, semiring_1_of_nat: !>[X0: $tType]:((nat > X0))).
% 0.97/0.36 thf(func_def_53, type, size_size: !>[X0: $tType]:((X0 > nat))).
% 0.97/0.36 thf(func_def_54, type, nat_tsub: (int > int > int)).
% 0.97/0.36 thf(func_def_55, type, neg_numeral_dbl: !>[X0: $tType]:((X0 > X0))).
% 0.97/0.36 thf(func_def_56, type, numeral_numeral: !>[X0: $tType]:((num > X0))).
% 0.97/0.36 thf(func_def_57, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.97/0.36 thf(func_def_58, type, type2: !>[X0: $tType]:(itself @ X0)).
% 0.97/0.36 thf(func_def_59, type, m: extended_enat).
% 0.97/0.36 thf(func_def_60, type, xs: coindu1593790203_llist @ a).
% 0.97/0.36 thf(func_def_62, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.97/0.36 thf(func_def_65, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.97/0.36 thf(func_def_66, type, db2: !>[X0: $tType]:(X0)).
% 0.97/0.36 thf(func_def_67, type, db0: !>[X0: $tType]:(X0)).
% 0.97/0.36 thf(func_def_68, type, db1: !>[X0: $tType]:(X0)).
% 0.97/0.36 thf(func_def_69, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.97/0.36 thf(func_def_70, type, vAND: ($o > $o > $o)).
% 0.97/0.36 thf(func_def_71, type, vOR: ($o > $o > $o)).
% 0.97/0.36 thf(func_def_72, type, vNOT: ($o > $o)).
% 0.97/0.36 thf(func_def_73, type, vIMP: ($o > $o > $o)).
% 0.97/0.36 thf(func_def_74, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.97/0.36 thf(func_def_75, type, sP0: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.97/0.36 thf(func_def_76, type, sP1: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.97/0.36 thf(func_def_77, type, sP2: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.97/0.36 thf(func_def_78, type, sK3: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.97/0.36 thf(func_def_79, type, sK4: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.97/0.36 thf(func_def_80, type, sK5: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.97/0.36 thf(func_def_81, type, sK6: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.97/0.36 thf(func_def_82, type, sK7: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.97/0.36 thf(func_def_83, type, sK8: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.97/0.36 thf(func_def_84, type, sK9: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.97/0.36 thf(func_def_85, type, sK10: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.97/0.36 thf(func_def_86, type, sK11: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.97/0.36 thf(func_def_87, type, sK12: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.97/0.36 thf(func_def_88, type, sK13: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.97/0.36 thf(func_def_89, type, sK14: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.97/0.36 thf(func_def_90, type, sK15: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.97/0.36 thf(func_def_91, type, sK16: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.97/0.36 thf(func_def_92, type, sK17: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.97/0.36 thf(func_def_93, type, sK18: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.97/0.36 thf(func_def_94, type, sK19: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > X0))).
% 0.97/0.36 thf(func_def_95, type, sK20: !>[X0: $tType]:((X0 > nat))).
% 0.97/0.36 thf(func_def_96, type, sK21: !>[X0: $tType, X1: $tType]:(((X1 > $o) > (X1 > X0) > (X1 > $o) > X1))).
% 0.97/0.36 thf(func_def_97, type, sK22: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1 > (X1 > $o) > X1))).
% 0.97/0.36 thf(func_def_98, type, sK23: (code_natural > code_natural)).
% 0.97/0.36 thf(func_def_99, type, sK24: ((code_natural > $o) > code_natural)).
% 0.97/0.36 thf(func_def_100, type, sK25: (int > nat)).
% 0.97/0.36 thf(func_def_101, type, sK26: (int > nat)).
% 0.97/0.36 thf(func_def_102, type, sK27: (int > nat)).
% 0.97/0.36 thf(func_def_103, type, sK28: (int > nat)).
% 0.97/0.36 thf(func_def_104, type, sK29: (int > nat)).
% 0.97/0.36 thf(func_def_105, type, sK30: !>[X0: $tType]:((X0 > int))).
% 0.97/0.36 thf(func_def_106, type, sK31: ((int > $o) > nat)).
% 0.97/0.36 thf(func_def_107, type, sK32: ((int > $o) > int)).
% 0.97/0.36 thf(func_def_108, type, sK33: ((int > $o) > int)).
% 0.97/0.36 thf(func_def_109, type, sK34: ((int > $o) > nat)).
% 0.97/0.36 thf(f5,axiom,(
% 0.97/0.36 ! [X0 : $tType,X1 : extended_enat,X2 : coindu1593790203_llist @ X0] : (((coindu335574135_lnull @ X0 @ (coindu191418589_ldrop @ X0 @ X1 @ X2))) = ((ord_less_eq @ extended_enat @ (coindu1018505716length @ X0 @ X2) @ X1)))),
% 0.97/0.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_lnull__ldrop)).
% 0.97/0.36 thf(f22,axiom,(
% 0.97/0.36 ! [X0 : $tType] : (coindu335574135_lnull @ X0 = (^[X1 : coindu1593790203_llist @ X0] : ((X1 = coindu1598213697e_LNil @ X0))))),
% 0.97/0.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_lnull__def)).
% 0.97/0.36 thf(f71,axiom,(
% 0.97/0.36 ! [X0 : $tType] : (coindu1018505716length @ X0 = ((coindu493225792length @ X0 @ zero_zero @ nat)))),
% 0.97/0.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_llength__code)).
% 0.97/0.36 thf(f345,axiom,(
% 0.97/0.36 (ord_less_eq @ extended_enat @ (coindu1018505716length @ a @ xs) @ m)),
% 0.97/0.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 0.97/0.36 thf(f346,conjecture,(
% 0.97/0.36 (((coindu191418589_ldrop @ a @ m @ xs)) = coindu1598213697e_LNil @ a)),
% 0.97/0.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1)).
% 0.97/0.36 thf(f347,negated_conjecture,(
% 0.97/0.36 ~ (((coindu191418589_ldrop @ a @ m @ xs)) = coindu1598213697e_LNil @ a)),
% 0.97/0.37 inference(negated_conjecture,[status(cth)],[f346])).
% 0.97/0.37 thf(f380,plain,(
% 0.97/0.37 ! [X0 : $tType] : (coindu335574135_lnull @ X0 = (^[Y0 : coindu1593790203_llist @ X0]: (coindu1598213697e_LNil @ X0 = Y0)))),
% 0.97/0.37 inference(fool_elimination,[],[f22])).
% 0.97/0.37 thf(f930,plain,(
% 0.97/0.37 (ord_less_eq @ extended_enat @ (coindu1018505716length @ a @ xs) @ m)),
% 0.97/0.37 inference(rectify,[],[f345])).
% 0.97/0.37 thf(f931,plain,(
% 0.97/0.37 (((ord_less_eq @ extended_enat @ (coindu1018505716length @ a @ xs) @ m)) = $true)),
% 0.97/0.37 inference(fool_elimination,[],[f930])).
% 0.97/0.37 thf(f952,plain,(
% 0.97/0.37 (((coindu191418589_ldrop @ a @ m @ xs)) != coindu1598213697e_LNil @ a)),
% 0.97/0.37 inference(flattening,[],[f347])).
% 0.97/0.37 thf(f1212,plain,(
% 0.97/0.37 ( ! [X0 : $tType,X2 : coindu1593790203_llist @ X0,X1 : extended_enat] : ((((ord_less_eq @ extended_enat @ (coindu1018505716length @ X0 @ X2) @ X1)) = ((coindu335574135_lnull @ X0 @ (coindu191418589_ldrop @ X0 @ X1 @ X2))))) )),
% 0.97/0.37 inference(cnf_transformation,[],[f5])).
% 0.97/0.37 thf(f1236,plain,(
% 0.97/0.37 ( ! [X0 : $tType] : ((coindu335574135_lnull @ X0 = (^[Y0 : coindu1593790203_llist @ X0]: (coindu1598213697e_LNil @ X0 = Y0)))) )),
% 0.97/0.37 inference(cnf_transformation,[],[f380])).
% 0.97/0.37 thf(f1303,plain,(
% 0.97/0.37 ( ! [X0 : $tType] : ((coindu1018505716length @ X0 = ((coindu493225792length @ X0 @ zero_zero @ nat)))) )),
% 0.97/0.37 inference(cnf_transformation,[],[f71])).
% 0.97/0.37 thf(f1593,plain,(
% 0.97/0.37 (((ord_less_eq @ extended_enat @ (coindu1018505716length @ a @ xs) @ m)) = $true)),
% 0.97/0.37 inference(cnf_transformation,[],[f931])).
% 0.97/0.37 thf(f1594,plain,(
% 0.97/0.37 (((coindu191418589_ldrop @ a @ m @ xs)) != coindu1598213697e_LNil @ a)),
% 0.97/0.37 inference(cnf_transformation,[],[f952])).
% 0.97/0.37 thf(f1598,plain,(
% 0.97/0.37 ( ! [X0 : $tType,X2 : coindu1593790203_llist @ X0,X1 : extended_enat] : ((((ord_less_eq @ extended_enat @ (coindu493225792length @ X0 @ zero_zero @ nat @ X2) @ X1)) = (((^[Y0 : coindu1593790203_llist @ X0]: (coindu1598213697e_LNil @ X0 = Y0)) @ (coindu191418589_ldrop @ X0 @ X1 @ X2))))) )),
% 0.97/0.37 inference(definition_unfolding,[],[f1212,f1303,f1236])).
% 0.97/0.37 thf(f1653,plain,(
% 0.97/0.37 ($true = ((ord_less_eq @ extended_enat @ (coindu493225792length @ a @ zero_zero @ nat @ xs) @ m)))),
% 0.97/0.37 inference(definition_unfolding,[],[f1593,f1303])).
% 0.97/0.37 thf(f2166,plain,(
% 0.97/0.37 ( ! [X0 : $tType,X2 : coindu1593790203_llist @ X0,X1 : extended_enat] : (($false = ((ord_less_eq @ extended_enat @ (coindu493225792length @ X0 @ zero_zero @ nat @ X2) @ X1))) | ($true = (((^[Y0 : coindu1593790203_llist @ X0]: (coindu1598213697e_LNil @ X0 = Y0)) @ (coindu191418589_ldrop @ X0 @ X1 @ X2))))) )),
% 0.97/0.37 inference(iff_proxy_clausification,[],[f1598])).
% 0.97/0.37 thf(f2167,plain,(
% 0.97/0.37 ( ! [X0 : $tType,X2 : coindu1593790203_llist @ X0,X1 : extended_enat] : (($false = ((ord_less_eq @ extended_enat @ (coindu493225792length @ X0 @ zero_zero @ nat @ X2) @ X1))) | (((coindu1598213697e_LNil @ X0 = (coindu191418589_ldrop @ X0 @ X1 @ X2))) = $true)) )),
% 0.97/0.37 inference(beta-eta_normalization,[],[f2166])).
% 0.97/0.37 thf(f2168,plain,(
% 0.97/0.37 ( ! [X0 : $tType,X2 : coindu1593790203_llist @ X0,X1 : extended_enat] : (($false = ((ord_less_eq @ extended_enat @ (coindu493225792length @ X0 @ zero_zero @ nat @ X2) @ X1))) | (coindu1598213697e_LNil @ X0 = ((coindu191418589_ldrop @ X0 @ X1 @ X2)))) )),
% 0.97/0.37 inference(equality_proxy_clausification,[],[f2167])).
% 0.97/0.37 thf(f2203,plain,(
% 0.97/0.37 ($true = $false) | (((coindu191418589_ldrop @ a @ m @ xs)) = coindu1598213697e_LNil @ a)),
% 0.97/0.37 inference(constrained_superposition,[],[f1653,f2168])).
% 0.97/0.37 thf(f2208,plain,(
% 0.97/0.37 (((coindu191418589_ldrop @ a @ m @ xs)) = coindu1598213697e_LNil @ a)),
% 0.97/0.37 inference(trivial_inequality_removal,[],[f2203])).
% 0.97/0.37 thf(f2211,plain,(
% 0.97/0.37 $false),
% 0.97/0.37 inference(forward_subsumption_resolution,[],[f2208,f1594])).
% 0.97/0.37 % SZS output end Proof for theBenchmark
% 0.97/0.37 % (1399621)------------------------------
% 0.97/0.37 % (1399621)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.97/0.37 % (1399621)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.97/0.37 % (1399621)CaDiCaL version: 2.1.3
% 0.97/0.37 % (1399621)Termination reason: Refutation
% 0.97/0.37 % (1399621)Time elapsed: 0.041 s
% 0.97/0.37 % (1399621)Peak memory usage: 13 MB
% 0.97/0.37 % (1399621)Instructions burned: 88 (million)
% 0.97/0.37 % (1399598)Success in time 0.15 s
% 0.97/0.37 % Vampire exiting
%------------------------------------------------------------------------------