%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : COM179^1 : 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 : n013.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 07:46:30 AM UTC 2026
% Result : Theorem 0.38s 0.30s
% Output : Refutation 0.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COM179^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.17 % Computer : n013.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 17:48:51 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.20 Running first-order model finding
% 0.07/0.20 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
% 0.38/0.30 % (2435977)Will run a generic schedule for satisfiability detection.
% 0.38/0.30 % (2435988)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3875512936:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.38/0.30 % (2435983)% WARNING: option uhcvi not known.
% 0.38/0.30 % (2435982)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2155189373_2999 on theBenchmark for (2999ds/0Mi)
% 0.38/0.30 % (2435983)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3428877730:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.38/0.30 % (2435984)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2445365266:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.38/0.30 % (2435987)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1574156213:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.38/0.30 % (2435986)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3839384429:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.38/0.30 % (2435985)dis+10_1_sil=32000:sp=arity:random_seed=1824399224:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.38/0.30 % (2435983)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.38/0.30 % (2435986)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.38/0.30 % (2435985)Instruction limit reached!
% 0.38/0.30 % (2435985)------------------------------
% 0.38/0.30 % (2435985)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.38/0.30 % (2435985)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.38/0.30 % (2435985)CaDiCaL version: 2.1.3
% 0.38/0.30 % (2435985)Termination reason: Instruction limit
% 0.38/0.30 % (2435985)Termination phase: Saturation
% 0.38/0.30 % (2435985)Time elapsed: 0.026 s
% 0.38/0.30 % (2435985)Peak memory usage: 13 MB
% 0.38/0.30 % (2435985)Instructions burned: 106 (million)
% 0.38/0.30 % Exception at run slice level
% 0.38/0.30 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.38/0.30 % (2435983)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.38/0.30 % (2435996)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1628723535:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.38/0.30 % (2435997)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2245727334:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.38/0.30 % (2435984) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2435977-2435984"...
% 0.38/0.30 % (2435986)Instruction limit reached!
% 0.38/0.30 % (2435986)------------------------------
% 0.38/0.30 % (2435986)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.38/0.30 % (2435986)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.38/0.30 % (2435986)CaDiCaL version: 2.1.3
% 0.38/0.30 % (2435986)Termination reason: Instruction limit
% 0.38/0.30 % (2435986)Termination phase: Saturation
% 0.38/0.30 % (2435986)Time elapsed: 0.054 s
% 0.38/0.30 % (2435986)Peak memory usage: 13 MB
% 0.38/0.30 % (2435986)Instructions burned: 117 (million)
% 0.38/0.30 % Exception at run slice level
% 0.38/0.30 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.38/0.30 % (2435984)...printing done.
% 0.38/0.30 % (2435984)Refutation found. Thanks to Tanya!
% 0.38/0.30 % SZS status Theorem for theBenchmark
% 0.38/0.30 % SZS output start Proof for theBenchmark
% 0.38/0.30 thf(type_def_5, type, coinductive_llist: $tType > $tType).
% 0.38/0.30 thf(type_def_6, type, product_prod: ($tType * $tType) > $tType).
% 0.38/0.30 thf(type_def_7, type, sum_sum: ($tType * $tType) > $tType).
% 0.38/0.30 thf(type_def_8, type, option: $tType > $tType).
% 0.38/0.30 thf(type_def_9, type, set: $tType > $tType).
% 0.38/0.30 thf(type_def_10, type, itself: $tType > $tType).
% 0.38/0.30 thf(type_def_11, type, node: $tType).
% 0.38/0.30 thf(type_def_12, type, sTfun: ($tType * $tType) > $tType).
% 0.38/0.30 thf(func_def_0, type, type: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.38/0.30 thf(func_def_1, type, minus: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.38/0.30 thf(func_def_2, type, uminus: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.38/0.30 thf(func_def_3, type, bot: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.38/0.30 thf(func_def_4, type, ord: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.38/0.30 thf(func_def_5, type, top: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.38/0.30 thf(func_def_6, type, order: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.38/0.30 thf(func_def_7, type, group_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.38/0.30 thf(func_def_8, type, finite_finite: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.38/0.30 thf(func_def_9, type, linorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.38/0.30 thf(func_def_10, type, preorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.38/0.30 thf(func_def_11, type, semiring_char_0: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.38/0.30 thf(func_def_12, type, order_bot: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.38/0.30 thf(func_def_13, type, order_top: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.38/0.30 thf(func_def_14, type, boolean_algebra: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.38/0.30 thf(func_def_15, type, ordered_ab_group_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.38/0.30 thf(func_def_16, type, cancel146912293up_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.38/0.30 thf(func_def_17, type, topolo890362671_space: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.38/0.30 thf(func_def_18, type, basic_fsts: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > set @ X0))).
% 0.38/0.30 thf(func_def_19, type, basic_snds: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > set @ X1))).
% 0.38/0.30 thf(func_def_20, type, coinductive_gen_lset: !>[X0: $tType]:((set @ X0 > coinductive_llist @ X0 > set @ X0))).
% 0.38/0.30 thf(func_def_21, type, coinductive_lfinite: !>[X0: $tType]:((coinductive_llist @ X0 > $o))).
% 0.38/0.30 thf(func_def_22, type, coinductive_lnull: !>[X0: $tType]:((coinductive_llist @ X0 > $o))).
% 0.38/0.30 thf(func_def_23, type, coinductive_lset: !>[X0: $tType]:((coinductive_llist @ X0 > set @ X0))).
% 0.38/0.30 thf(func_def_24, type, finite_finite2: !>[X0: $tType]:((set @ X0 > $o))).
% 0.38/0.30 thf(func_def_25, type, minus_minus: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.38/0.30 thf(func_def_26, type, uminus_uminus: !>[X0: $tType]:((X0 > X0))).
% 0.38/0.30 thf(func_def_27, type, koenig793108494nected: !>[X0: $tType]:(((X0 > X0 > $o) > $o))).
% 0.38/0.30 thf(func_def_28, type, koenig317145564le_via: !>[X0: $tType]:(((X0 > X0 > $o) > set @ X0 > X0 > set @ X0))).
% 0.38/0.30 thf(func_def_29, type, bot_bot: !>[X0: $tType]:(X0)).
% 0.38/0.30 thf(func_def_30, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.38/0.30 thf(func_def_31, type, top_top: !>[X0: $tType]:(X0)).
% 0.38/0.30 thf(func_def_32, type, product_Pair: !>[X0: $tType, X1: $tType]:((X0 > X1 > product_prod @ X0 @ X1))).
% 0.38/0.30 thf(func_def_33, type, produc2004651681e_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 0.38/0.30 thf(func_def_34, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 0.38/0.30 thf(func_def_35, type, type2: !>[X0: $tType]:(itself @ X0)).
% 0.38/0.30 thf(func_def_36, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.38/0.30 thf(func_def_37, type, insert: !>[X0: $tType]:((X0 > set @ X0 > set @ X0))).
% 0.38/0.30 thf(func_def_38, type, is_empty: !>[X0: $tType]:((set @ X0 > $o))).
% 0.38/0.30 thf(func_def_39, type, is_singleton: !>[X0: $tType]:((set @ X0 > $o))).
% 0.38/0.30 thf(func_def_40, type, the_elem: !>[X0: $tType]:((set @ X0 > X0))).
% 0.38/0.30 thf(func_def_41, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.38/0.30 thf(func_def_42, type, f: (product_prod @ node @ set @ node > coinductive_llist @ node)).
% 0.38/0.30 thf(func_def_43, type, graph: (node > node > $o)).
% 0.38/0.30 thf(func_def_44, type, n: node).
% 0.38/0.30 thf(func_def_45, type, ns: set @ node).
% 0.38/0.30 thf(func_def_49, type, vOR: ($o > $o > $o)).
% 0.38/0.30 thf(func_def_50, type, db0: !>[X0: $tType]:(X0)).
% 0.38/0.30 thf(func_def_51, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.38/0.30 thf(func_def_52, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.38/0.30 thf(func_def_53, type, vAND: ($o > $o > $o)).
% 0.38/0.30 thf(func_def_54, type, db1: !>[X0: $tType]:(X0)).
% 0.38/0.30 thf(func_def_55, type, db2: !>[X0: $tType]:(X0)).
% 0.38/0.30 thf(func_def_56, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.38/0.30 thf(func_def_57, type, vNOT: ($o > $o)).
% 0.38/0.30 thf(func_def_58, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.38/0.30 thf(func_def_59, type, vIMP: ($o > $o > $o)).
% 0.38/0.30 thf(func_def_60, type, sP0: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.38/0.30 thf(func_def_61, type, sP1: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.38/0.30 thf(func_def_62, type, sP2: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.38/0.30 thf(func_def_63, type, sP3: !>[X0: $tType]:((set @ X0 > (set @ X0 > $o) > $o))).
% 0.38/0.30 thf(func_def_64, type, sK4: !>[X0: $tType]:((set @ X0 > set @ X0))).
% 0.38/0.30 thf(func_def_65, type, sK5: !>[X0: $tType]:((set @ X0 > X0))).
% 0.38/0.30 thf(func_def_66, type, sK6: !>[X0: $tType]:(((set @ X0 > $o) > X0))).
% 0.38/0.30 thf(func_def_67, type, sK7: !>[X0: $tType]:(((set @ X0 > $o) > set @ X0))).
% 0.38/0.30 thf(func_def_68, type, sK8: !>[X0: $tType]:(((set @ X0 > $o) > set @ X0))).
% 0.38/0.30 thf(func_def_69, type, sK9: !>[X0: $tType]:(((set @ X0 > $o) > X0))).
% 0.38/0.30 thf(func_def_70, type, sK10: !>[X0: $tType]:(((set @ X0 > $o) > X0))).
% 0.38/0.30 thf(func_def_71, type, sK11: !>[X0: $tType]:(((set @ X0 > $o) > set @ X0))).
% 0.38/0.30 thf(func_def_72, type, sK12: !>[X0: $tType]:(((set @ X0 > $o) > X0))).
% 0.38/0.30 thf(func_def_73, type, sK13: !>[X0: $tType]:(((set @ X0 > $o) > X0))).
% 0.38/0.30 thf(func_def_74, type, sK14: !>[X0: $tType]:(((set @ X0 > $o) > set @ X0))).
% 0.38/0.30 thf(func_def_75, type, sK15: !>[X0: $tType]:(((set @ X0 > $o) > set @ X0))).
% 0.38/0.30 thf(func_def_76, type, sK16: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.38/0.30 thf(func_def_77, type, sK17: !>[X0: $tType]:((set @ X0 > X0))).
% 0.38/0.30 thf(func_def_78, type, sK18: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.38/0.30 thf(func_def_79, type, sK19: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.38/0.30 thf(func_def_80, type, sK20: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.38/0.30 thf(func_def_81, type, sK21: !>[X0: $tType]:(X0)).
% 0.38/0.30 thf(func_def_82, type, sK22: !>[X0: $tType]:((set @ X0 > X0))).
% 0.38/0.30 thf(func_def_83, type, sK23: !>[X0: $tType]:(((set @ X0 > $o) > set @ X0 > X0))).
% 0.38/0.30 thf(func_def_84, type, sK24: !>[X0: $tType]:(((set @ X0 > $o) > set @ X0 > set @ X0))).
% 0.38/0.30 thf(func_def_85, type, sK25: !>[X0: $tType]:((set @ X0 > X0))).
% 0.38/0.30 thf(func_def_86, type, sK26: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > set @ X1 > X1 > X0))).
% 0.38/0.30 thf(func_def_87, type, sK27: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > set @ X1 > X1))).
% 0.38/0.30 thf(func_def_88, type, sK28: !>[X0: $tType]:((set @ X0 > X0 > set @ X0))).
% 0.38/0.30 thf(func_def_89, type, sK29: !>[X0: $tType]:((set @ X0 > X0 > set @ X0))).
% 0.38/0.30 thf(func_def_90, type, sK30: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.38/0.30 thf(func_def_91, type, sK31: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.38/0.30 thf(func_def_92, type, sK32: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.38/0.30 thf(func_def_93, type, sK33: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.38/0.30 thf(func_def_94, type, sK34: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.38/0.30 thf(func_def_95, type, sK35: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.38/0.30 thf(func_def_96, type, sK36: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.38/0.30 thf(func_def_97, type, sK37: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.38/0.30 thf(func_def_98, type, sK38: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.38/0.30 thf(func_def_99, type, sK39: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.38/0.30 thf(func_def_100, type, sK40: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.38/0.30 thf(func_def_101, type, sK41: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.38/0.30 thf(func_def_102, type, sK42: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.38/0.30 thf(func_def_103, type, sK43: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.38/0.30 thf(func_def_104, type, sK44: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.38/0.30 thf(func_def_105, type, sK45: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > set @ product_prod @ X1 @ X0 > X1))).
% 0.38/0.30 thf(func_def_106, type, sK46: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > set @ product_prod @ X1 @ X0 > X0))).
% 0.38/0.30 thf(func_def_107, type, sK47: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 0.38/0.30 thf(func_def_108, type, sK48: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 0.38/0.30 thf(func_def_109, type, sK49: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 0.38/0.30 thf(func_def_110, type, sK50: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 0.38/0.30 thf(func_def_111, type, sK51: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X0))).
% 0.38/0.30 thf(func_def_112, type, sK52: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X1))).
% 0.38/0.30 thf(func_def_113, type, sK53: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X2))).
% 0.38/0.30 thf(func_def_114, type, sK54: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X0))).
% 0.38/0.30 thf(func_def_115, type, sK55: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X1))).
% 0.38/0.30 thf(func_def_116, type, sK56: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X2))).
% 0.38/0.30 thf(func_def_117, type, sK57: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X3))).
% 0.38/0.30 thf(func_def_118, type, sK58: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X0))).
% 0.38/0.30 thf(func_def_119, type, sK59: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X1))).
% 0.38/0.30 thf(func_def_120, type, sK60: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X2))).
% 0.38/0.30 thf(func_def_121, type, sK61: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X3))).
% 0.38/0.30 thf(func_def_122, type, sK62: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X4))).
% 0.38/0.30 thf(func_def_123, type, sK63: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X0))).
% 0.38/0.30 thf(func_def_124, type, sK64: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X1))).
% 0.38/0.30 thf(func_def_125, type, sK65: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X2))).
% 0.38/0.30 thf(func_def_126, type, sK66: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X3))).
% 0.38/0.30 thf(func_def_127, type, sK67: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X4))).
% 0.38/0.30 thf(func_def_128, type, sK68: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X5))).
% 0.38/0.30 thf(func_def_129, type, sK69: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X0))).
% 0.38/0.30 thf(func_def_130, type, sK70: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X1))).
% 0.38/0.30 thf(func_def_131, type, sK71: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X2))).
% 0.38/0.30 thf(func_def_132, type, sK72: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X3))).
% 0.38/0.30 thf(func_def_133, type, sK73: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X4))).
% 0.38/0.30 thf(func_def_134, type, sK74: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X5))).
% 0.38/0.30 thf(func_def_135, type, sK75: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X6))).
% 0.38/0.30 thf(func_def_136, type, sK76: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 0.38/0.30 thf(func_def_137, type, sK77: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 0.38/0.30 thf(func_def_138, type, sK78: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 0.38/0.30 thf(func_def_139, type, sK79: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3))).
% 0.38/0.30 thf(func_def_140, type, sK80: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 0.38/0.30 thf(func_def_141, type, sK81: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 0.38/0.30 thf(func_def_142, type, sK82: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 0.38/0.30 thf(func_def_143, type, sK83: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4))).
% 0.38/0.30 thf(func_def_144, type, sK84: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3))).
% 0.38/0.30 thf(func_def_145, type, sK85: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 0.38/0.30 thf(func_def_146, type, sK86: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 0.38/0.30 thf(func_def_147, type, sK87: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 0.38/0.30 thf(func_def_148, type, sK88: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X5))).
% 0.38/0.30 thf(func_def_149, type, sK89: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4))).
% 0.38/0.30 thf(func_def_150, type, sK90: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3))).
% 0.38/0.30 thf(func_def_151, type, sK91: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 0.38/0.30 thf(func_def_152, type, sK92: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 0.38/0.30 thf(func_def_153, type, sK93: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 0.38/0.30 thf(func_def_154, type, sK94: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X6))).
% 0.38/0.30 thf(func_def_155, type, sK95: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X5))).
% 0.38/0.30 thf(func_def_156, type, sK96: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4))).
% 0.38/0.30 thf(func_def_157, type, sK97: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3))).
% 0.38/0.30 thf(func_def_158, type, sK98: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 0.38/0.30 thf(func_def_159, type, sK99: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 0.38/0.30 thf(func_def_160, type, sK100: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 0.38/0.30 thf(func_def_161, type, sK101: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 0.38/0.30 thf(func_def_162, type, sK102: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 0.38/0.30 thf(func_def_163, type, sK103: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 0.38/0.30 thf(func_def_164, type, sK104: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 0.38/0.30 thf(func_def_165, type, sK105: !>[X0: $tType]:((set @ X0 > X0))).
% 0.38/0.30 thf(func_def_166, type, sK106: !>[X0: $tType]:((set @ X0 > X0))).
% 0.38/0.30 thf(func_def_167, type, sK107: !>[X0: $tType]:((set @ X0 > X0))).
% 0.38/0.30 thf(func_def_168, type, sK108: !>[X0: $tType]:((set @ X0 > X0))).
% 0.38/0.30 thf(func_def_169, type, sK109: !>[X0: $tType]:(((set @ X0 > $o) > set @ X0 > set @ X0))).
% 0.38/0.30 thf(func_def_170, type, sK110: !>[X0: $tType]:((set @ X0 > (set @ X0 > $o) > set @ X0))).
% 0.38/0.30 thf(func_def_171, type, sK111: !>[X0: $tType]:((X0 > set @ X0 > X0 > set @ X0 > set @ X0))).
% 0.38/0.30 thf(func_def_172, type, sK112: !>[X0: $tType]:((set @ X0 > X0))).
% 0.38/0.30 thf(func_def_173, type, sK113: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.38/0.30 thf(func_def_174, type, sK114: !>[X0: $tType]:((set @ X0 > X0))).
% 0.38/0.30 thf(func_def_175, type, sK115: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.38/0.30 thf(func_def_176, type, sK116: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.38/0.30 thf(f3,axiom,(
% 0.38/0.30 ~(finite_finite2 @ node @ (koenig317145564le_via @ node @ graph @ (uminus_uminus @ set @ node @ (insert @ node @ n @ bot_bot @ set @ node)) @ n))),
% 0.38/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__092_060open_062infinite_A_Ireachable__via_Agraph_A_I_N_A_123n_125_J_An_J_092_060close_062)).
% 0.38/0.30 thf(f104,axiom,(
% 0.38/0.30 ! [X0 : $tType] : (finite_finite2 @ X0 @ bot_bot @ set @ X0)),
% 0.38/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_finite_OemptyI)).
% 0.38/0.30 thf(f292,conjecture,(
% 0.38/0.30 ? [X0 : node,X1 : set @ node] : (~(finite_finite2 @ node @ (koenig317145564le_via @ node @ graph @ (uminus_uminus @ set @ node @ (insert @ node @ X0 @ X1)) @ X0)) & (finite_finite2 @ node @ X1) & (((f @ (product_Pair @ node @ set @ node @ n @ bot_bot @ set @ node))) = ((f @ (product_Pair @ node @ set @ node @ X0 @ X1)))))),
% 0.38/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 0.38/0.30 thf(f293,negated_conjecture,(
% 0.38/0.30 ~ ? [X0 : node,X1 : set @ node] : (~(finite_finite2 @ node @ (koenig317145564le_via @ node @ graph @ (uminus_uminus @ set @ node @ (insert @ node @ X0 @ X1)) @ X0)) & (finite_finite2 @ node @ X1) & (((f @ (product_Pair @ node @ set @ node @ n @ bot_bot @ set @ node))) = ((f @ (product_Pair @ node @ set @ node @ X0 @ X1)))))),
% 0.38/0.30 inference(negated_conjecture,[status(cth)],[f292])).
% 0.38/0.30 thf(f296,plain,(
% 0.38/0.30 ~(finite_finite2 @ node @ (koenig317145564le_via @ node @ graph @ (uminus_uminus @ set @ node @ (insert @ node @ n @ bot_bot @ set @ node)) @ n))),
% 0.38/0.30 inference(rectify,[],[f3])).
% 0.38/0.30 thf(f297,plain,(
% 0.38/0.30 ~ (((finite_finite2 @ node @ (koenig317145564le_via @ node @ graph @ (uminus_uminus @ set @ node @ (insert @ node @ n @ bot_bot @ set @ node)) @ n))) = $true)),
% 0.38/0.30 inference(fool_elimination,[],[f296])).
% 0.38/0.30 thf(f468,plain,(
% 0.38/0.30 ! [X0 : $tType] : (finite_finite2 @ X0 @ bot_bot @ set @ X0)),
% 0.38/0.30 inference(rectify,[],[f104])).
% 0.38/0.30 thf(f469,plain,(
% 0.38/0.30 ! [X0 : $tType] : (((finite_finite2 @ X0 @ bot_bot @ set @ X0)) = $true)),
% 0.38/0.30 inference(fool_elimination,[],[f468])).
% 0.38/0.30 thf(f774,plain,(
% 0.38/0.30 ~ ? [X0 : node,X1 : set @ node] : (~(finite_finite2 @ node @ (koenig317145564le_via @ node @ graph @ (uminus_uminus @ set @ node @ (insert @ node @ X0 @ X1)) @ X0)) & (finite_finite2 @ node @ X1) & (((f @ (product_Pair @ node @ set @ node @ n @ bot_bot @ set @ node))) = ((f @ (product_Pair @ node @ set @ node @ X0 @ X1)))))),
% 0.38/0.30 inference(rectify,[],[f293])).
% 0.38/0.30 thf(f775,plain,(
% 0.38/0.30 ~ ? [X0 : node,X1 : set @ node] : (~ (((finite_finite2 @ node @ (koenig317145564le_via @ node @ graph @ (uminus_uminus @ set @ node @ (insert @ node @ X0 @ X1)) @ X0))) = $true) & (((finite_finite2 @ node @ X1)) = $true) & (((f @ (product_Pair @ node @ set @ node @ X0 @ X1))) = ((f @ (product_Pair @ node @ set @ node @ n @ bot_bot @ set @ node)))))),
% 0.38/0.30 inference(fool_elimination,[],[f774])).
% 0.38/0.30 thf(f776,plain,(
% 0.38/0.30 (((finite_finite2 @ node @ (koenig317145564le_via @ node @ graph @ (uminus_uminus @ set @ node @ (insert @ node @ n @ bot_bot @ set @ node)) @ n))) != $true)),
% 0.38/0.30 inference(flattening,[],[f297])).
% 0.38/0.30 thf(f815,plain,(
% 0.38/0.30 ~ ? [X0 : node,X1 : set @ node] : ((((finite_finite2 @ node @ (koenig317145564le_via @ node @ graph @ (uminus_uminus @ set @ node @ (insert @ node @ X0 @ X1)) @ X0))) != $true) & (((finite_finite2 @ node @ X1)) = $true) & (((f @ (product_Pair @ node @ set @ node @ X0 @ X1))) = ((f @ (product_Pair @ node @ set @ node @ n @ bot_bot @ set @ node)))))),
% 0.38/0.30 inference(flattening,[],[f775])).
% 0.38/0.30 thf(f1048,plain,(
% 0.38/0.30 ! [X0 : node,X1 : set @ node] : ((((finite_finite2 @ node @ (koenig317145564le_via @ node @ graph @ (uminus_uminus @ set @ node @ (insert @ node @ X0 @ X1)) @ X0))) = $true) | (((finite_finite2 @ node @ X1)) != $true) | (((f @ (product_Pair @ node @ set @ node @ X0 @ X1))) != ((f @ (product_Pair @ node @ set @ node @ n @ bot_bot @ set @ node)))))),
% 0.38/0.30 inference(ennf_transformation,[],[f815])).
% 0.38/0.30 thf(f1113,plain,(
% 0.38/0.30 (((finite_finite2 @ node @ (koenig317145564le_via @ node @ graph @ (uminus_uminus @ set @ node @ (insert @ node @ n @ bot_bot @ set @ node)) @ n))) != $true)),
% 0.38/0.30 inference(cnf_transformation,[],[f776])).
% 0.38/0.30 thf(f1242,plain,(
% 0.38/0.30 ( ! [X0 : $tType] : ((((finite_finite2 @ X0 @ bot_bot @ set @ X0)) = $true)) )),
% 0.38/0.30 inference(cnf_transformation,[],[f469])).
% 0.38/0.30 thf(f1471,plain,(
% 0.38/0.30 ( ! [X0 : node,X1 : set @ node] : ((((f @ (product_Pair @ node @ set @ node @ X0 @ X1))) != ((f @ (product_Pair @ node @ set @ node @ n @ bot_bot @ set @ node)))) | (((finite_finite2 @ node @ X1)) != $true) | (((finite_finite2 @ node @ (koenig317145564le_via @ node @ graph @ (uminus_uminus @ set @ node @ (insert @ node @ X0 @ X1)) @ X0))) = $true)) )),
% 0.38/0.30 inference(cnf_transformation,[],[f1048])).
% 0.38/0.30 thf(f1888,plain,(
% 0.38/0.30 ($true != ((finite_finite2 @ node @ bot_bot @ set @ node))) | (((finite_finite2 @ node @ (koenig317145564le_via @ node @ graph @ (uminus_uminus @ set @ node @ (insert @ node @ n @ bot_bot @ set @ node)) @ n))) = $true)),
% 0.38/0.30 inference(equality_resolution,[],[f1471])).
% 0.38/0.30 thf(f1889,plain,(
% 0.38/0.30 ($true != ((finite_finite2 @ node @ bot_bot @ set @ node)))),
% 0.38/0.30 inference(forward_subsumption_resolution,[],[f1888,f1113])).
% 0.38/0.30 thf(f2037,plain,(
% 0.38/0.30 $false),
% 0.38/0.30 inference(forward_subsumption_resolution,[],[f1889,f1242])).
% 0.38/0.30 % SZS output end Proof for theBenchmark
% 0.38/0.30 % (2435984)------------------------------
% 0.38/0.30 % (2435984)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.38/0.30 % (2435984)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.38/0.30 % (2435984)CaDiCaL version: 2.1.3
% 0.38/0.30 % (2435984)Termination reason: Refutation
% 0.38/0.30 % (2435984)Time elapsed: 0.055 s
% 0.38/0.30 % (2435984)Peak memory usage: 13 MB
% 0.38/0.30 % (2435984)Instructions burned: 113 (million)
% 0.38/0.30 % (2435977)Success in time 0.093 s
% 0.38/0.30 % Vampire exiting
%------------------------------------------------------------------------------