%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT130^1 : 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 : n006.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 0.20s 0.34s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT130^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.20 % Computer : n006.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 17:58:24 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.23 Running first-order model finding
% 0.08/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.34 % (1102397)Will run a generic schedule for satisfiability detection.
% 0.20/0.34 % (1102403)% WARNING: option uhcvi not known.
% 0.20/0.34 % (1102403)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1793522041:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.34 % (1102402)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3647680448_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.34 % (1102405)dis+10_1_sil=32000:sp=arity:random_seed=2281400248:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.34 % (1102408)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1308987008:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.34 % (1102404)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=851271532:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.34 % (1102406)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1888926627:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.34 % (1102407)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=75526269:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.34 % (1102403)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.34 % (1102403)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.34 % (1102406)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.34 % Exception at run slice level
% 0.20/0.34 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.34 % (1102405)Instruction limit reached!
% 0.20/0.34 % (1102405)------------------------------
% 0.20/0.34 % (1102405)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.34 % (1102405)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.34 % (1102405)CaDiCaL version: 2.1.3
% 0.20/0.34 % (1102405)Termination reason: Instruction limit
% 0.20/0.34 % (1102405)Termination phase: Saturation
% 0.20/0.34 % (1102405)Time elapsed: 0.045 s
% 0.20/0.34 % (1102405)Peak memory usage: 12 MB
% 0.20/0.34 % (1102405)Instructions burned: 103 (million)
% 0.20/0.34 % (1102403) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1102397-1102403"...
% 0.20/0.34 % (1102403)...printing done.
% 0.20/0.34 % (1102403)Refutation found. Thanks to Tanya!
% 0.20/0.34 % SZS status Theorem for theBenchmark
% 0.20/0.34 % SZS output start Proof for theBenchmark
% 0.20/0.34 thf(type_def_5, type, coindu1593790203_llist: $tType > $tType).
% 0.20/0.34 thf(type_def_6, type, set: $tType > $tType).
% 0.20/0.34 thf(type_def_7, type, itself: $tType > $tType).
% 0.20/0.34 thf(type_def_8, type, a: $tType).
% 0.20/0.34 thf(type_def_9, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.34 thf(func_def_0, type, type: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.20/0.34 thf(func_def_1, type, lattice: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.20/0.34 thf(func_def_2, type, semilattice_inf: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.20/0.34 thf(func_def_3, type, coindu1571841457prefix: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o))).
% 0.20/0.34 thf(func_def_4, type, coindu526335360e_lSup: !>[X0: $tType]:((set @ coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.20/0.34 thf(func_def_5, type, coindu268472904append: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.20/0.34 thf(func_def_6, type, coindu6345450stinct: !>[X0: $tType]:((coindu1593790203_llist @ X0 > $o))).
% 0.20/0.34 thf(func_def_7, type, coindu1213758845finite: !>[X0: $tType]:((coindu1593790203_llist @ X0 > $o))).
% 0.20/0.34 thf(func_def_8, type, coindu2000965700_llast: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0))).
% 0.20/0.34 thf(func_def_9, type, coindu300403952lexord: !>[X0: $tType]:(((X0 > X0 > $o) > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o))).
% 0.20/0.34 thf(func_def_10, type, coindu1121789889_LCons: !>[X0: $tType]:((X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.20/0.34 thf(func_def_11, type, coindu1598213697e_LNil: !>[X0: $tType]:(coindu1593790203_llist @ X0)).
% 0.20/0.34 thf(func_def_12, type, coindu882539134_llist: !>[X0: $tType, X1: $tType]:((X0 > (X1 > coindu1593790203_llist @ X1 > X0) > coindu1593790203_llist @ X1 > X0))).
% 0.20/0.34 thf(func_def_13, type, coindu1046438764le_lhd: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0))).
% 0.20/0.34 thf(func_def_14, type, coindu335574135_lnull: !>[X0: $tType]:((coindu1593790203_llist @ X0 > $o))).
% 0.20/0.34 thf(func_def_15, type, coindu1112613586e_lset: !>[X0: $tType]:((coindu1593790203_llist @ X0 > set @ X0))).
% 0.20/0.34 thf(func_def_16, type, coindu1047225960le_ltl: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.20/0.34 thf(func_def_17, type, coindu1696667936prefix: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o))).
% 0.20/0.34 thf(func_def_18, type, coindu574146665prefix: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o))).
% 0.20/0.34 thf(func_def_19, type, coindu721411036eWhile: !>[X0: $tType]:(((X0 > $o) > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.20/0.34 thf(func_def_20, type, coindu543932918sorted: !>[X0: $tType]:(((X0 > X0 > $o) > coindu1593790203_llist @ X0 > $o))).
% 0.20/0.34 thf(func_def_21, type, coindu1599971794_llist: !>[X0: $tType, X1: $tType]:(((X0 > $o) > (X0 > X1) > (X0 > X0) > X0 > coindu1593790203_llist @ X1))).
% 0.20/0.34 thf(func_def_22, type, comple2143767107ompact: !>[X0: $tType]:(((set @ X0 > X0) > (X0 > X0 > $o) > X0 > $o))).
% 0.20/0.34 thf(func_def_23, type, comple1412571634l_cont: !>[X0: $tType, X1: $tType]:(((set @ X0 > X0) > (X0 > X0 > $o) > (set @ X1 > X1) > (X1 > X1 > $o) > (X0 > X1) > $o))).
% 0.20/0.34 thf(func_def_24, type, comple1986059218ssible: !>[X0: $tType]:(((set @ X0 > X0) > (X0 > X0 > $o) > (X0 > $o) > $o))).
% 0.20/0.34 thf(func_def_25, type, comple1193779247_chain: !>[X0: $tType]:(((X0 > X0 > $o) > set @ X0 > $o))).
% 0.20/0.34 thf(func_def_26, type, finite_finite: !>[X0: $tType]:((set @ X0 > $o))).
% 0.20/0.34 thf(func_def_27, type, if: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 0.20/0.34 thf(func_def_28, type, inf_inf: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.20/0.34 thf(func_def_29, type, max: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > X0 > X0))).
% 0.20/0.34 thf(func_def_30, type, min: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > X0 > X0))).
% 0.20/0.34 thf(func_def_31, type, type2: !>[X0: $tType]:(itself @ X0)).
% 0.20/0.34 thf(func_def_32, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.20/0.34 thf(func_def_33, type, set_atLeast: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > set @ X0))).
% 0.20/0.34 thf(func_def_34, type, set_atLeastAtMost: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > X0 > set @ X0))).
% 0.20/0.34 thf(func_def_35, type, set_atMost: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > set @ X0))).
% 0.20/0.34 thf(func_def_36, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.20/0.34 thf(func_def_37, type, ya: set @ coindu1593790203_llist @ a).
% 0.20/0.34 thf(func_def_38, type, less_eq: (a > a > $o)).
% 0.20/0.34 thf(func_def_39, type, xs: coindu1593790203_llist @ a).
% 0.20/0.34 thf(func_def_43, type, vAND: ($o > $o > $o)).
% 0.20/0.34 thf(func_def_44, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.20/0.34 thf(func_def_45, type, vIMP: ($o > $o > $o)).
% 0.20/0.34 thf(func_def_46, type, db0: !>[X0: $tType]:(X0)).
% 0.20/0.34 thf(func_def_47, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.20/0.34 thf(func_def_48, type, vNOT: ($o > $o)).
% 0.20/0.34 thf(func_def_49, type, db2: !>[X0: $tType]:(X0)).
% 0.20/0.34 thf(func_def_50, type, db1: !>[X0: $tType]:(X0)).
% 0.20/0.34 thf(func_def_51, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.20/0.34 thf(func_def_52, type, vOR: ($o > $o > $o)).
% 0.20/0.34 thf(func_def_53, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.20/0.34 thf(func_def_54, type, db4: !>[X0: $tType]:(X0)).
% 0.20/0.34 thf(func_def_55, type, db3: !>[X0: $tType]:(X0)).
% 0.20/0.34 thf(func_def_56, type, db5: !>[X0: $tType]:(X0)).
% 0.20/0.34 thf(func_def_57, type, db6: !>[X0: $tType]:(X0)).
% 0.20/0.34 thf(func_def_58, type, sP0: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o))).
% 0.20/0.34 thf(func_def_59, type, sP1: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > (X0 > X0 > $o) > $o))).
% 0.20/0.34 thf(func_def_60, type, sK2: coindu1593790203_llist @ a).
% 0.20/0.34 thf(func_def_61, type, sK3: ((coindu1593790203_llist @ a > $o) > coindu1593790203_llist @ a)).
% 0.20/0.34 thf(func_def_62, type, sK4: !>[X0: $tType]:((coindu1593790203_llist @ X0 > set @ coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.20/0.34 thf(func_def_63, type, sK5: !>[X0: $tType]:((coindu1593790203_llist @ X0 > set @ coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.20/0.34 thf(func_def_64, type, sK6: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.20/0.34 thf(func_def_65, type, sK7: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.20/0.34 thf(func_def_66, type, sK8: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.20/0.34 thf(func_def_67, type, sK9: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.20/0.34 thf(func_def_68, type, sK10: !>[X0: $tType]:((set @ coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.20/0.34 thf(func_def_69, type, sK11: !>[X0: $tType]:(((X0 > X0 > $o) > (coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.20/0.34 thf(func_def_70, type, sK12: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.20/0.34 thf(func_def_71, type, sK13: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.20/0.34 thf(func_def_72, type, sK14: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.20/0.34 thf(func_def_73, type, sK15: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.20/0.34 thf(func_def_74, type, sK16: (coindu1593790203_llist @ a > a)).
% 0.20/0.34 thf(func_def_75, type, sK17: (coindu1593790203_llist @ a > a)).
% 0.20/0.34 thf(func_def_76, type, sK18: (coindu1593790203_llist @ a > coindu1593790203_llist @ a)).
% 0.20/0.34 thf(func_def_77, type, sK19: (coindu1593790203_llist @ a > a)).
% 0.20/0.34 thf(func_def_78, type, sK20: ((coindu1593790203_llist @ a > $o) > coindu1593790203_llist @ a)).
% 0.20/0.34 thf(func_def_79, type, sK21: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.20/0.34 thf(func_def_80, type, sK22: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.20/0.34 thf(func_def_81, type, sK23: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > X0))).
% 0.20/0.34 thf(func_def_82, type, sK24: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.20/0.34 thf(func_def_83, type, sK25: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.20/0.34 thf(func_def_84, type, sK26: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.20/0.34 thf(func_def_85, type, sK27: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0))).
% 0.20/0.34 thf(func_def_86, type, sK28: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.20/0.34 thf(func_def_87, type, sK29: !>[X0: $tType]:(((X0 > X0 > $o) > (coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.20/0.34 thf(func_def_88, type, sK30: !>[X0: $tType]:((coindu1593790203_llist @ X0 > (X0 > X0 > $o) > X0))).
% 0.20/0.34 thf(func_def_89, type, sK31: !>[X0: $tType]:((coindu1593790203_llist @ X0 > (X0 > X0 > $o) > X0))).
% 0.20/0.34 thf(func_def_90, type, sK32: !>[X0: $tType]:((coindu1593790203_llist @ X0 > (X0 > X0 > $o) > coindu1593790203_llist @ X0))).
% 0.20/0.34 thf(func_def_91, type, sK33: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0))).
% 0.20/0.34 thf(func_def_92, type, sK34: !>[X0: $tType]:((set @ coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.20/0.34 thf(func_def_93, type, sK35: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.20/0.34 thf(func_def_94, type, sK36: !>[X0: $tType]:((set @ coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.20/0.34 thf(func_def_95, type, sK37: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.20/0.34 thf(func_def_96, type, sK38: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0 > X0))).
% 0.20/0.34 thf(func_def_97, type, sK39: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0 > coindu1593790203_llist @ X0))).
% 0.20/0.34 thf(func_def_98, type, sK40: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0 > coindu1593790203_llist @ X0))).
% 0.20/0.34 thf(func_def_99, type, sK41: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > $o) > X0 > X0))).
% 0.20/0.34 thf(func_def_100, type, sK42: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > $o) > X0 > coindu1593790203_llist @ X0))).
% 0.20/0.35 thf(func_def_101, type, sK43: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > $o) > X0 > coindu1593790203_llist @ X0))).
% 0.20/0.35 thf(func_def_102, type, sK44: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > $o) > X0 > X0))).
% 0.20/0.35 thf(func_def_103, type, sK45: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > $o) > X0 > coindu1593790203_llist @ X0))).
% 0.20/0.35 thf(func_def_104, type, sK46: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > $o) > X0 > coindu1593790203_llist @ X0))).
% 0.20/0.35 thf(func_def_105, type, sK47: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0 > X0))).
% 0.20/0.35 thf(func_def_106, type, sK48: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0 > coindu1593790203_llist @ X0))).
% 0.20/0.35 thf(func_def_107, type, sK49: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0 > coindu1593790203_llist @ X0))).
% 0.20/0.35 thf(func_def_108, type, sK50: !>[X0: $tType]:(((X0 > coindu1593790203_llist @ X0 > $o) > X0))).
% 0.20/0.35 thf(func_def_109, type, sK51: !>[X0: $tType]:(((X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.20/0.35 thf(func_def_110, type, sK52: !>[X0: $tType]:(((X0 > coindu1593790203_llist @ X0 > $o) > X0))).
% 0.20/0.35 thf(func_def_111, type, sK53: !>[X0: $tType]:(((X0 > coindu1593790203_llist @ X0 > $o) > X0))).
% 0.20/0.35 thf(func_def_112, type, sK54: !>[X0: $tType]:(((X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.20/0.35 thf(func_def_113, type, sK55: !>[X0: $tType]:(((X0 > $o) > coindu1593790203_llist @ X0 > X0))).
% 0.20/0.35 thf(func_def_114, type, sK56: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > coindu1593790203_llist @ X0 > X0))).
% 0.20/0.35 thf(func_def_115, type, sK57: !>[X0: $tType]:(((X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.20/0.35 thf(func_def_116, type, sK58: !>[X0: $tType]:(((X0 > coindu1593790203_llist @ X0 > $o) > X0))).
% 0.20/0.35 thf(func_def_117, type, sK59: !>[X0: $tType]:(((X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.20/0.35 thf(func_def_118, type, sK60: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0))).
% 0.20/0.35 thf(func_def_119, type, sK61: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.20/0.35 thf(func_def_120, type, sK62: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.20/0.35 thf(func_def_121, type, sK63: !>[X0: $tType]:(((X0 > X0 > $o) > (coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.20/0.35 thf(func_def_122, type, sK64: !>[X0: $tType]:(((X0 > X0 > $o) > (coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.20/0.35 thf(func_def_123, type, sK65: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.20/0.35 thf(func_def_124, type, sK66: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.20/0.35 thf(func_def_125, type, sK67: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.20/0.35 thf(func_def_126, type, sK68: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > $o) > X0))).
% 0.20/0.35 thf(func_def_127, type, sK69: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.20/0.35 thf(func_def_128, type, sK70: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0))).
% 0.20/0.35 thf(func_def_129, type, sK71: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > $o) > X0))).
% 0.20/0.35 thf(func_def_130, type, sK72: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.20/0.35 thf(func_def_131, type, sK73: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > (X0 > X0 > $o) > coindu1593790203_llist @ X0))).
% 0.20/0.35 thf(func_def_132, type, sK74: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > (X0 > X0 > $o) > coindu1593790203_llist @ X0))).
% 0.20/0.35 thf(func_def_133, type, sK75: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > (X0 > X0 > $o) > X0))).
% 0.20/0.35 thf(func_def_134, type, sK76: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.20/0.35 thf(func_def_135, type, sK77: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > (X0 > X0 > $o) > X0))).
% 0.20/0.35 thf(func_def_136, type, sK78: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > (X0 > X0 > $o) > X0))).
% 0.20/0.35 thf(func_def_137, type, sK79: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > (X0 > X0 > $o) > coindu1593790203_llist @ X0))).
% 0.20/0.35 thf(func_def_138, type, sK80: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > (X0 > X0 > $o) > coindu1593790203_llist @ X0))).
% 0.20/0.35 thf(func_def_139, type, sK81: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > $o) > X0))).
% 0.20/0.35 thf(func_def_140, type, sK82: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.20/0.35 thf(func_def_141, type, sK83: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > (coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.20/0.35 thf(func_def_142, type, sK84: !>[X0: $tType]:((set @ coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.20/0.35 thf(func_def_143, type, sK85: !>[X0: $tType]:(((X0 > $o) > coindu1593790203_llist @ X0 > X0))).
% 0.20/0.35 thf(func_def_144, type, sK86: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > X0 > coindu1593790203_llist @ X0))).
% 0.20/0.35 thf(func_def_145, type, sK87: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.20/0.35 thf(func_def_146, type, sK88: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0))).
% 0.20/0.35 thf(func_def_147, type, sK89: !>[X0: $tType]:((X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.20/0.35 thf(func_def_148, type, sK90: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.20/0.35 thf(func_def_149, type, sK91: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0))).
% 0.20/0.35 thf(func_def_150, type, sK92: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.20/0.35 thf(func_def_151, type, sK93: (coindu1593790203_llist @ a > coindu1593790203_llist @ a)).
% 0.20/0.35 thf(func_def_152, type, sK94: (coindu1593790203_llist @ a > a)).
% 0.20/0.35 thf(func_def_153, type, sK95: (coindu1593790203_llist @ a > a)).
% 0.20/0.35 thf(func_def_154, type, sK96: (coindu1593790203_llist @ a > a)).
% 0.20/0.35 thf(func_def_155, type, sK97: !>[X0: $tType]:((set @ coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.20/0.35 thf(func_def_156, type, sK98: !>[X0: $tType]:((set @ coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.20/0.35 thf(f2,axiom,(
% 0.20/0.35 (less_eq @ (coindu1046438764le_lhd @ a @ xs) @ (coindu1046438764le_lhd @ a @ (coindu1047225960le_ltl @ a @ xs)))),
% 0.20/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__092_060open_062lhd_Axs_A_092_060le_062_Alhd_A_Iltl_Axs_J_092_060close_062)).
% 0.20/0.35 thf(f5,axiom,(
% 0.20/0.35 (((coindu1046438764le_lhd @ a @ (coindu526335360e_lSup @ a @ ya))) = ((coindu1046438764le_lhd @ a @ xs)))),
% 0.20/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4__092_060open_062lhd_A_IlSup_AY_J_A_061_Alhd_Axs_092_060close_062)).
% 0.20/0.35 thf(f6,axiom,(
% 0.20/0.35 (((coindu1046438764le_lhd @ a @ (coindu1047225960le_ltl @ a @ (coindu526335360e_lSup @ a @ ya)))) = ((coindu1046438764le_lhd @ a @ (coindu1047225960le_ltl @ a @ xs))))),
% 0.20/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5__092_060open_062lhd_A_Iltl_A_IlSup_AY_J_J_A_061_Alhd_A_Iltl_Axs_J_092_060close_062)).
% 0.20/0.35 thf(f264,conjecture,(
% 0.20/0.35 (less_eq @ (coindu1046438764le_lhd @ a @ (coindu526335360e_lSup @ a @ ya)) @ (coindu1046438764le_lhd @ a @ (coindu1047225960le_ltl @ a @ (coindu526335360e_lSup @ a @ ya))))),
% 0.20/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 0.20/0.35 thf(f265,negated_conjecture,(
% 0.20/0.35 ~(less_eq @ (coindu1046438764le_lhd @ a @ (coindu526335360e_lSup @ a @ ya)) @ (coindu1046438764le_lhd @ a @ (coindu1047225960le_ltl @ a @ (coindu526335360e_lSup @ a @ ya))))),
% 0.20/0.35 inference(negated_conjecture,[status(cth)],[f264])).
% 0.20/0.35 thf(f268,plain,(
% 0.20/0.35 (less_eq @ (coindu1046438764le_lhd @ a @ xs) @ (coindu1046438764le_lhd @ a @ (coindu1047225960le_ltl @ a @ xs)))),
% 0.20/0.35 inference(rectify,[],[f2])).
% 0.20/0.35 thf(f269,plain,(
% 0.20/0.35 (((less_eq @ (coindu1046438764le_lhd @ a @ xs) @ (coindu1046438764le_lhd @ a @ (coindu1047225960le_ltl @ a @ xs)))) = $true)),
% 0.20/0.35 inference(fool_elimination,[],[f268])).
% 0.20/0.35 thf(f711,plain,(
% 0.20/0.35 ~(less_eq @ (coindu1046438764le_lhd @ a @ (coindu526335360e_lSup @ a @ ya)) @ (coindu1046438764le_lhd @ a @ (coindu1047225960le_ltl @ a @ (coindu526335360e_lSup @ a @ ya))))),
% 0.20/0.35 inference(rectify,[],[f265])).
% 0.20/0.35 thf(f712,plain,(
% 0.20/0.35 ~ (((less_eq @ (coindu1046438764le_lhd @ a @ (coindu526335360e_lSup @ a @ ya)) @ (coindu1046438764le_lhd @ a @ (coindu1047225960le_ltl @ a @ (coindu526335360e_lSup @ a @ ya))))) = $true)),
% 0.20/0.35 inference(fool_elimination,[],[f711])).
% 0.20/0.35 thf(f774,plain,(
% 0.20/0.35 (((less_eq @ (coindu1046438764le_lhd @ a @ (coindu526335360e_lSup @ a @ ya)) @ (coindu1046438764le_lhd @ a @ (coindu1047225960le_ltl @ a @ (coindu526335360e_lSup @ a @ ya))))) != $true)),
% 0.20/0.35 inference(flattening,[],[f712])).
% 0.20/0.35 thf(f1047,plain,(
% 0.20/0.35 (((less_eq @ (coindu1046438764le_lhd @ a @ xs) @ (coindu1046438764le_lhd @ a @ (coindu1047225960le_ltl @ a @ xs)))) = $true)),
% 0.20/0.35 inference(cnf_transformation,[],[f269])).
% 0.20/0.35 thf(f1050,plain,(
% 0.20/0.35 (((coindu1046438764le_lhd @ a @ xs)) = ((coindu1046438764le_lhd @ a @ (coindu526335360e_lSup @ a @ ya))))),
% 0.20/0.35 inference(cnf_transformation,[],[f5])).
% 0.20/0.35 thf(f1051,plain,(
% 0.20/0.35 (((coindu1046438764le_lhd @ a @ (coindu1047225960le_ltl @ a @ xs))) = ((coindu1046438764le_lhd @ a @ (coindu1047225960le_ltl @ a @ (coindu526335360e_lSup @ a @ ya)))))),
% 0.20/0.35 inference(cnf_transformation,[],[f6])).
% 0.20/0.35 thf(f1438,plain,(
% 0.20/0.35 (((less_eq @ (coindu1046438764le_lhd @ a @ (coindu526335360e_lSup @ a @ ya)) @ (coindu1046438764le_lhd @ a @ (coindu1047225960le_ltl @ a @ (coindu526335360e_lSup @ a @ ya))))) != $true)),
% 0.20/0.35 inference(cnf_transformation,[],[f774])).
% 0.20/0.35 thf(f2396,plain,(
% 0.20/0.35 ($true != ((less_eq @ (coindu1046438764le_lhd @ a @ xs) @ (coindu1046438764le_lhd @ a @ (coindu1047225960le_ltl @ a @ (coindu526335360e_lSup @ a @ ya))))))),
% 0.20/0.35 inference(constrained_superposition,[],[f1438,f1050])).
% 0.20/0.35 thf(f3323,plain,(
% 0.20/0.35 (((less_eq @ (coindu1046438764le_lhd @ a @ xs) @ (coindu1046438764le_lhd @ a @ (coindu1047225960le_ltl @ a @ xs)))) != $true)),
% 0.20/0.35 inference(constrained_superposition,[],[f2396,f1051])).
% 0.20/0.35 thf(f3326,plain,(
% 0.20/0.35 $false),
% 0.20/0.35 inference(forward_subsumption_resolution,[],[f3323,f1047])).
% 0.20/0.35 % SZS output end Proof for theBenchmark
% 0.20/0.35 % (1102403)------------------------------
% 0.20/0.35 % (1102403)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (1102403)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (1102403)CaDiCaL version: 2.1.3
% 0.20/0.35 % (1102403)Termination reason: Refutation
% 0.20/0.35 % (1102403)Time elapsed: 0.061 s
% 0.20/0.35 % (1102403)Peak memory usage: 14 MB
% 0.20/0.35 % (1102403)Instructions burned: 226 (million)
% 0.20/0.35 % (1102397)Success in time 0.104 s
% 0.20/0.35 % Vampire exiting
%------------------------------------------------------------------------------