%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP049^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n012.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 08:10:30 AM UTC 2026
% Result : Theorem 0.09s 0.20s
% Output : Refutation 0.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ITP049^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Tue Sep 29 19:43:02 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.13 Running first-order model finding
% 0.09/0.13 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
% 0.09/0.20 % (586960)Will run a generic schedule for satisfiability detection.
% 0.09/0.20 % (586966)% WARNING: option uhcvi not known.
% 0.09/0.20 % (586966)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1185763889:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.09/0.20 % (586967)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4038927386:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.09/0.20 % (586969)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3821741927:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.09/0.20 % (586965)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2305965755_2999 on theBenchmark for (2999ds/0Mi)
% 0.09/0.20 % (586968)dis+10_1_sil=32000:sp=arity:random_seed=2564458203:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.09/0.20 % (586970)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3207231438:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.09/0.20 % (586971)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3416364344:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.09/0.20 % (586969)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.09/0.20 % (586966)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.09/0.20 % (586966)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.09/0.20 % Exception at run slice level
% 0.09/0.20 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.09/0.20 % (586968)Instruction limit reached!
% 0.09/0.20 % (586968)------------------------------
% 0.09/0.20 % (586968)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.20 % (586968)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.20 % (586968)CaDiCaL version: 2.1.3
% 0.09/0.20 % (586968)Termination reason: Instruction limit
% 0.09/0.20 % (586968)Termination phase: Saturation
% 0.09/0.20 % (586968)Time elapsed: 0.026 s
% 0.09/0.20 % (586968)Peak memory usage: 12 MB
% 0.09/0.20 % (586968)Instructions burned: 104 (million)
% 0.09/0.20 % (586969)Instruction limit reached!
% 0.09/0.20 % (586969)------------------------------
% 0.09/0.20 % (586969)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.20 % (586969)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.20 % (586969)CaDiCaL version: 2.1.3
% 0.09/0.20 % (586969)Termination reason: Instruction limit
% 0.09/0.20 % (586969)Termination phase: Saturation
% 0.09/0.20 % (586969)Time elapsed: 0.028 s
% 0.09/0.20 % (586969)Peak memory usage: 13 MB
% 0.09/0.20 % (586969)Instructions burned: 120 (million)
% 0.09/0.20 % (586966) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-586960-586966"...
% 0.09/0.20 % (586966)...printing done.
% 0.09/0.20 % (586966)Refutation found. Thanks to Tanya!
% 0.09/0.20 % SZS status Theorem for theBenchmark
% 0.09/0.20 % SZS output start Proof for theBenchmark
% 0.09/0.20 thf(type_def_5, type, product_prod: ($tType * $tType) > $tType).
% 0.09/0.20 thf(type_def_6, type, list: $tType > $tType).
% 0.09/0.20 thf(type_def_7, type, set: $tType > $tType).
% 0.09/0.20 thf(type_def_8, type, nat: $tType).
% 0.09/0.20 thf(type_def_9, type, a: $tType).
% 0.09/0.20 thf(type_def_10, type, sTfun: ($tType * $tType) > $tType).
% 0.09/0.20 thf(func_def_0, type, type: !>[X0: $tType]:($o)).
% 0.09/0.20 thf(func_def_1, type, ord: !>[X0: $tType]:($o)).
% 0.09/0.20 thf(func_def_2, type, order: !>[X0: $tType]:($o)).
% 0.09/0.20 thf(func_def_3, type, finite_finite: !>[X0: $tType]:($o)).
% 0.09/0.20 thf(func_def_4, type, linorder: !>[X0: $tType]:($o)).
% 0.09/0.20 thf(func_def_5, type, preorder: !>[X0: $tType]:($o)).
% 0.09/0.20 thf(func_def_6, type, linordered_idom: !>[X0: $tType]:($o)).
% 0.09/0.20 thf(func_def_7, type, bNF_Ca1785829860lChain: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X0 > (X0 > X1) > $o))).
% 0.09/0.20 thf(func_def_8, type, edmond2129202899alysis: !>[X0: $tType]:(((product_prod @ nat @ nat > X0) > $o))).
% 0.09/0.20 thf(func_def_9, type, edmond1803015688pEdges: !>[X0: $tType]:(((product_prod @ nat @ nat > X0) > nat > nat > set @ product_prod @ nat @ nat))).
% 0.09/0.20 thf(func_def_10, type, finite_finite2: !>[X0: $tType]:((set @ X0 > $o))).
% 0.09/0.20 thf(func_def_11, type, finite_Graph: !>[X0: $tType]:(((product_prod @ nat @ nat > X0) > $o))).
% 0.09/0.20 thf(func_def_12, type, e: !>[X0: $tType]:(((product_prod @ nat @ nat > X0) > set @ product_prod @ nat @ nat))).
% 0.09/0.20 thf(func_def_13, type, v: !>[X0: $tType]:(((product_prod @ nat @ nat > X0) > set @ nat))).
% 0.09/0.20 thf(func_def_14, type, adjacent_nodes: !>[X0: $tType]:(((product_prod @ nat @ nat > X0) > nat > set @ nat))).
% 0.09/0.20 thf(func_def_15, type, connected: !>[X0: $tType]:(((product_prod @ nat @ nat > X0) > nat > nat > $o))).
% 0.09/0.20 thf(func_def_16, type, incoming: !>[X0: $tType]:(((product_prod @ nat @ nat > X0) > nat > set @ product_prod @ nat @ nat))).
% 0.09/0.20 thf(func_def_17, type, incoming2: !>[X0: $tType]:(((product_prod @ nat @ nat > X0) > set @ nat > set @ product_prod @ nat @ nat))).
% 0.09/0.20 thf(func_def_18, type, isPath: !>[X0: $tType]:(((product_prod @ nat @ nat > X0) > nat > list @ product_prod @ nat @ nat > nat > $o))).
% 0.09/0.20 thf(func_def_19, type, isShortestPath: !>[X0: $tType]:(((product_prod @ nat @ nat > X0) > nat > list @ product_prod @ nat @ nat > nat > $o))).
% 0.09/0.20 thf(func_def_20, type, isSimplePath: !>[X0: $tType]:(((product_prod @ nat @ nat > X0) > nat > list @ product_prod @ nat @ nat > nat > $o))).
% 0.09/0.20 thf(func_def_21, type, outgoing: !>[X0: $tType]:(((product_prod @ nat @ nat > X0) > nat > set @ product_prod @ nat @ nat))).
% 0.09/0.20 thf(func_def_22, type, outgoing2: !>[X0: $tType]:(((product_prod @ nat @ nat > X0) > set @ nat > set @ product_prod @ nat @ nat))).
% 0.09/0.20 thf(func_def_23, type, reachableNodes: !>[X0: $tType]:(((product_prod @ nat @ nat > X0) > nat > set @ nat))).
% 0.09/0.20 thf(func_def_24, type, set2: !>[X0: $tType]:((list @ X0 > set @ X0))).
% 0.09/0.20 thf(func_def_25, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.09/0.20 thf(func_def_26, type, product_Pair: !>[X0: $tType, X1: $tType]:((X0 > X1 > product_prod @ X0 @ X1))).
% 0.09/0.20 thf(func_def_27, type, product_Sigma: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > set @ X1) > set @ product_prod @ X0 @ X1))).
% 0.09/0.20 thf(func_def_28, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 0.09/0.20 thf(func_def_29, type, product_swap: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > product_prod @ X1 @ X0))).
% 0.09/0.20 thf(func_def_30, type, domain: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X1 > set @ X0))).
% 0.09/0.20 thf(func_def_31, type, image: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X1 > set @ X0 > set @ X1))).
% 0.09/0.20 thf(func_def_32, type, range: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X1 > set @ X1))).
% 0.09/0.20 thf(func_def_33, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.09/0.20 thf(func_def_34, type, transitive_rtrancl: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > set @ product_prod @ X0 @ X0))).
% 0.09/0.20 thf(func_def_35, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.09/0.20 thf(func_def_36, type, c: (product_prod @ nat @ nat > a)).
% 0.09/0.20 thf(func_def_37, type, s: nat).
% 0.09/0.20 thf(func_def_38, type, t: nat).
% 0.09/0.20 thf(func_def_42, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.09/0.20 thf(func_def_43, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.09/0.20 thf(func_def_44, type, vAND: ($o > $o > $o)).
% 0.09/0.20 thf(func_def_45, type, db1: !>[X0: $tType]:(X0)).
% 0.09/0.20 thf(func_def_46, type, db0: !>[X0: $tType]:(X0)).
% 0.09/0.20 thf(func_def_47, type, vOR: ($o > $o > $o)).
% 0.09/0.20 thf(func_def_48, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.09/0.20 thf(func_def_49, type, vIMP: ($o > $o > $o)).
% 0.09/0.20 thf(func_def_50, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.09/0.20 thf(func_def_51, type, db2: !>[X0: $tType]:(X0)).
% 0.09/0.20 thf(func_def_52, type, db4: !>[X0: $tType]:(X0)).
% 0.09/0.20 thf(func_def_53, type, db3: !>[X0: $tType]:(X0)).
% 0.09/0.20 thf(func_def_54, type, vNOT: ($o > $o)).
% 0.09/0.20 thf(func_def_55, type, sP0: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.09/0.20 thf(func_def_56, type, sP1: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.09/0.20 thf(func_def_57, type, sP2: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.09/0.20 thf(func_def_58, type, sK3: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > set @ X1 > X1 > X0))).
% 0.09/0.20 thf(func_def_59, type, sK4: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > set @ X1 > X1))).
% 0.09/0.20 thf(func_def_60, type, sK5: (nat > nat > list @ product_prod @ nat @ nat)).
% 0.09/0.20 thf(func_def_61, type, sK6: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.09/0.20 thf(func_def_62, type, sK7: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > set @ X0 > set @ X1 > X0))).
% 0.09/0.20 thf(func_def_63, type, sK8: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > set @ X0 > set @ X1 > X1))).
% 0.09/0.20 thf(func_def_64, type, sK9: !>[X0: $tType]:((X0 > set @ X0 > X0))).
% 0.09/0.20 thf(func_def_65, type, sK10: !>[X0: $tType]:((X0 > set @ X0 > X0))).
% 0.09/0.20 thf(func_def_66, type, sK11: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.09/0.20 thf(func_def_67, type, sK12: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.09/0.20 thf(func_def_68, type, sK13: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > set @ product_prod @ X1 @ X0 > X1))).
% 0.09/0.20 thf(func_def_69, type, sK14: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > set @ product_prod @ X1 @ X0 > X0))).
% 0.09/0.20 thf(func_def_70, type, sK15: !>[X0: $tType, X1: $tType]:(((X1 > $o) > set @ product_prod @ X1 @ X0 > X1))).
% 0.09/0.20 thf(func_def_71, type, sK16: !>[X0: $tType, X1: $tType]:(((X1 > $o) > set @ product_prod @ X1 @ X0 > X0))).
% 0.09/0.20 thf(func_def_72, type, sK17: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > X1 > X0))).
% 0.09/0.20 thf(func_def_73, type, sK18: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > X1 > X0))).
% 0.09/0.20 thf(func_def_74, type, sK19: !>[X0: $tType, X1: $tType]:(((X1 > $o) > set @ product_prod @ X0 @ X1 > X0))).
% 0.09/0.20 thf(func_def_75, type, sK20: !>[X0: $tType, X1: $tType]:(((X1 > $o) > set @ product_prod @ X0 @ X1 > X1))).
% 0.09/0.20 thf(func_def_76, type, sK21: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > X0 > X1))).
% 0.09/0.20 thf(func_def_77, type, sK22: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > X0 > X1))).
% 0.09/0.20 thf(func_def_78, type, sK23: !>[X0: $tType]:((set @ X0 > list @ X0))).
% 0.09/0.20 thf(func_def_79, type, sK24: !>[X0: $tType]:((nat > nat > (product_prod @ nat @ nat > X0) > list @ product_prod @ nat @ nat))).
% 0.09/0.20 thf(func_def_80, type, sK25: !>[X0: $tType, X1: $tType]:(((X1 > set @ X0) > set @ X1 > X1))).
% 0.09/0.20 thf(func_def_81, type, sK26: !>[X0: $tType, X1: $tType]:((set @ X1 > set @ product_prod @ X1 @ X0 > X0 > X1))).
% 0.09/0.20 thf(func_def_82, type, sK27: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > set @ product_prod @ product_prod @ X0 @ X1 @ product_prod @ X0 @ X1 > X1 > X0 > X0))).
% 0.09/0.20 thf(func_def_83, type, sK28: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > set @ product_prod @ product_prod @ X0 @ X1 @ product_prod @ X0 @ X1 > X1 > X0 > X1))).
% 0.09/0.20 thf(func_def_84, type, sK29: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > set @ product_prod @ product_prod @ X0 @ X1 @ product_prod @ X0 @ X1 > X1 > X0 > X0))).
% 0.09/0.20 thf(func_def_85, type, sK30: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > set @ product_prod @ product_prod @ X0 @ X1 @ product_prod @ X0 @ X1 > X1 > X0 > X1))).
% 0.09/0.20 thf(func_def_86, type, sK31: !>[X0: $tType, X1: $tType]:((set @ product_prod @ product_prod @ X1 @ X0 @ product_prod @ X1 @ X0 > X0 > X1 > X0 > X1 > X1))).
% 0.09/0.20 thf(func_def_87, type, sK32: !>[X0: $tType, X1: $tType]:((set @ product_prod @ product_prod @ X1 @ X0 @ product_prod @ X1 @ X0 > X0 > X1 > X0 > X1 > X0))).
% 0.09/0.20 thf(func_def_88, type, sK33: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > set @ product_prod @ product_prod @ X0 @ X1 @ product_prod @ X0 @ X1 > X1 > X0 > X0))).
% 0.09/0.20 thf(func_def_89, type, sK34: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > set @ product_prod @ product_prod @ X0 @ X1 @ product_prod @ X0 @ X1 > X1 > X0 > X1))).
% 0.09/0.20 thf(func_def_90, type, sK35: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > set @ product_prod @ product_prod @ X0 @ X1 @ product_prod @ X0 @ X1 > X1 > X0 > X0))).
% 0.09/0.20 thf(func_def_91, type, sK36: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > set @ product_prod @ product_prod @ X0 @ X1 @ product_prod @ X0 @ X1 > X1 > X0 > X1))).
% 0.09/0.20 thf(func_def_92, type, sK37: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 0.09/0.20 thf(func_def_93, type, sK38: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 0.09/0.20 thf(func_def_94, type, sK39: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 0.09/0.20 thf(func_def_95, type, sK40: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 0.09/0.20 thf(func_def_96, type, sK41: !>[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))).
% 0.09/0.20 thf(func_def_97, type, sK42: !>[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))).
% 0.09/0.20 thf(func_def_98, type, sK43: !>[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))).
% 0.09/0.20 thf(func_def_99, type, sK44: !>[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))).
% 0.09/0.20 thf(func_def_100, type, sK45: !>[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))).
% 0.09/0.20 thf(func_def_101, type, sK46: !>[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))).
% 0.09/0.20 thf(func_def_102, type, sK47: !>[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))).
% 0.09/0.20 thf(func_def_103, type, sK48: !>[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))).
% 0.09/0.20 thf(func_def_104, type, sK49: !>[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))).
% 0.09/0.20 thf(func_def_105, type, sK50: !>[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))).
% 0.09/0.20 thf(func_def_106, type, sK51: !>[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))).
% 0.09/0.20 thf(func_def_107, type, sK52: !>[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))).
% 0.09/0.20 thf(func_def_108, type, sK53: !>[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))).
% 0.09/0.20 thf(func_def_109, type, sK54: !>[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))).
% 0.09/0.20 thf(func_def_110, type, sK55: !>[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))).
% 0.09/0.20 thf(func_def_111, type, sK56: !>[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))).
% 0.09/0.20 thf(func_def_112, type, sK57: !>[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))).
% 0.09/0.20 thf(func_def_113, type, sK58: !>[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))).
% 0.09/0.20 thf(func_def_114, type, sK59: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3))).
% 0.09/0.20 thf(func_def_115, type, sK60: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 0.09/0.20 thf(func_def_116, type, sK61: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 0.09/0.20 thf(func_def_117, type, sK62: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 0.09/0.20 thf(func_def_118, type, sK63: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 0.09/0.20 thf(func_def_119, type, sK64: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 0.09/0.20 thf(func_def_120, type, sK65: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 0.09/0.20 thf(func_def_121, type, sK66: !>[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))).
% 0.09/0.20 thf(func_def_122, type, sK67: !>[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))).
% 0.09/0.20 thf(func_def_123, type, sK68: !>[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))).
% 0.09/0.20 thf(func_def_124, 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 > X3))).
% 0.09/0.20 thf(func_def_125, 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 > X4))).
% 0.09/0.20 thf(func_def_126, 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 > X5))).
% 0.09/0.20 thf(func_def_127, 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 > X6))).
% 0.09/0.20 thf(func_def_128, type, sK73: !>[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))).
% 0.09/0.20 thf(func_def_129, type, sK74: !>[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))).
% 0.09/0.20 thf(func_def_130, type, sK75: !>[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))).
% 0.09/0.20 thf(func_def_131, type, sK76: !>[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))).
% 0.09/0.20 thf(func_def_132, type, sK77: !>[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))).
% 0.09/0.20 thf(func_def_133, type, sK78: !>[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))).
% 0.09/0.20 thf(func_def_134, type, sK79: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X0))).
% 0.09/0.20 thf(func_def_135, type, sK80: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X1))).
% 0.09/0.20 thf(func_def_136, type, sK81: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X2))).
% 0.09/0.20 thf(func_def_137, type, sK82: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X3))).
% 0.09/0.20 thf(func_def_138, type, sK83: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X4))).
% 0.09/0.20 thf(func_def_139, type, sK84: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X0))).
% 0.09/0.20 thf(func_def_140, type, sK85: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X1))).
% 0.09/0.20 thf(func_def_141, type, sK86: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X2))).
% 0.09/0.20 thf(func_def_142, type, sK87: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X3))).
% 0.09/0.20 thf(func_def_143, type, sK88: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X0))).
% 0.09/0.20 thf(func_def_144, type, sK89: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X1))).
% 0.09/0.20 thf(func_def_145, type, sK90: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X2))).
% 0.09/0.20 thf(func_def_146, type, sK91: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 0.09/0.20 thf(func_def_147, type, sK92: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 0.09/0.20 thf(func_def_148, type, sK93: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 0.09/0.20 thf(func_def_149, type, sK94: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 0.09/0.20 thf(func_def_150, type, sK95: !>[X0: $tType, X1: $tType]:(((X1 > set @ X0) > (X1 > set @ X0) > set @ X1 > X1))).
% 0.09/0.20 thf(func_def_151, type, sK96: !>[X0: $tType, X1: $tType]:(((X0 > set @ X1) > set @ X0 > product_prod @ X0 @ X1 > X0))).
% 0.09/0.20 thf(func_def_152, type, sK97: !>[X0: $tType, X1: $tType]:(((X0 > set @ X1) > set @ X0 > product_prod @ X0 @ X1 > X1))).
% 0.09/0.20 thf(func_def_153, type, sK98: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0 > X0 > X0))).
% 0.09/0.20 thf(func_def_154, type, sK99: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0 > X0 > X0))).
% 0.09/0.20 thf(func_def_155, type, sK100: !>[X0: $tType]:(((X0 > $o) > set @ product_prod @ X0 @ X0 > X0 > X0))).
% 0.09/0.20 thf(func_def_156, type, sK101: !>[X0: $tType]:(((X0 > $o) > set @ product_prod @ X0 @ X0 > X0 > X0))).
% 0.09/0.20 thf(func_def_157, type, sK102: !>[X0: $tType]:(((X0 > X0 > $o) > set @ product_prod @ X0 @ X0 > X0))).
% 0.09/0.20 thf(func_def_158, type, sK103: !>[X0: $tType]:(((X0 > X0 > $o) > set @ product_prod @ X0 @ X0 > X0))).
% 0.09/0.20 thf(func_def_159, type, sK104: !>[X0: $tType]:(((X0 > X0 > $o) > set @ product_prod @ X0 @ X0 > X0))).
% 0.09/0.20 thf(func_def_160, type, sK105: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.09/0.20 thf(func_def_161, type, sK106: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0 > X0 > X0))).
% 0.09/0.20 thf(func_def_162, type, sK107: !>[X0: $tType]:(((X0 > $o) > set @ product_prod @ X0 @ X0 > X0 > X0))).
% 0.09/0.20 thf(func_def_163, type, sK108: !>[X0: $tType]:(((X0 > $o) > set @ product_prod @ X0 @ X0 > X0 > X0))).
% 0.09/0.20 thf(func_def_164, type, sK109: !>[X0: $tType, X1: $tType]:(((X1 > set @ X0) > (X1 > set @ X0) > set @ X1 > X1))).
% 0.09/0.20 thf(func_def_165, type, sK110: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.09/0.20 thf(func_def_166, type, sK111: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > (X1 > X0 > $o) > X1))).
% 0.09/0.20 thf(func_def_167, type, sK112: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > (X1 > X0 > $o) > X0))).
% 0.09/0.20 thf(func_def_168, type, sK113: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.09/0.20 thf(func_def_169, type, sK114: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.09/0.20 thf(func_def_170, type, sK115: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.09/0.20 thf(func_def_171, type, sK116: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.09/0.20 thf(func_def_172, type, sK117: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.09/0.20 thf(func_def_173, type, sK118: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.09/0.20 thf(func_def_174, type, sK119: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.09/0.20 thf(func_def_175, type, sK120: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.09/0.20 thf(func_def_176, type, sK121: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.09/0.20 thf(func_def_177, type, sK122: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.09/0.20 thf(func_def_178, type, sK123: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.09/0.20 thf(func_def_179, type, sK124: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.09/0.20 thf(func_def_180, type, sK125: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.09/0.20 thf(func_def_181, type, sK126: (nat > nat > list @ product_prod @ nat @ nat)).
% 0.09/0.20 thf(func_def_182, type, sK127: (nat > nat > list @ product_prod @ nat @ nat)).
% 0.09/0.20 thf(func_def_183, type, sK128: (nat > list @ product_prod @ nat @ nat > nat)).
% 0.09/0.20 thf(func_def_184, type, sK129: (nat > list @ product_prod @ nat @ nat > nat)).
% 0.09/0.20 thf(func_def_185, type, sK130: (nat > list @ product_prod @ nat @ nat > nat)).
% 0.09/0.20 thf(func_def_186, type, sK131: (nat > list @ product_prod @ nat @ nat > nat)).
% 0.09/0.20 thf(func_def_187, type, sK132: (nat > nat > list @ product_prod @ nat @ nat)).
% 0.09/0.20 thf(func_def_188, type, sK133: !>[X0: $tType]:((X0 > X0 > set @ product_prod @ X0 @ X0 > X0))).
% 0.09/0.20 thf(func_def_189, type, sK134: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.09/0.20 thf(func_def_190, type, sK135: !>[X0: $tType]:((X0 > set @ product_prod @ X0 @ X0 > X0 > X0))).
% 0.09/0.20 thf(func_def_191, type, sK136: !>[X0: $tType]:((X0 > set @ product_prod @ X0 @ X0 > X0 > X0))).
% 0.09/0.20 thf(func_def_192, type, sK137: !>[X0: $tType]:((X0 > set @ product_prod @ X0 @ X0 > X0 > X0))).
% 0.09/0.20 thf(func_def_193, type, sK138: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > set @ X1 > X0 > X1))).
% 0.09/0.20 thf(func_def_194, type, sK139: !>[X0: $tType]:((list @ X0 > set @ X0 > X0))).
% 0.09/0.20 thf(func_def_195, type, sK140: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > X0 > X1))).
% 0.09/0.20 thf(func_def_196, type, sK141: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > X0 > X0))).
% 0.09/0.20 thf(func_def_197, type, sK142: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > X0 > X1))).
% 0.09/0.20 thf(func_def_198, type, sK143: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X1 > X0 > X1))).
% 0.09/0.20 thf(func_def_199, type, sK144: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > X1 > X0))).
% 0.09/0.20 thf(func_def_200, type, sK145: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > X1 > X1))).
% 0.09/0.20 thf(func_def_201, type, sK146: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > (X1 > $o) > X1))).
% 0.09/0.20 thf(f2,axiom,(
% 0.09/0.20 (finite_finite2 @ product_prod @ nat @ nat @ (e @ a @ c)) => (finite_finite2 @ product_prod @ nat @ nat @ (edmond1803015688pEdges @ a @ c @ s @ t))),
% 0.09/0.20 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__092_060open_062finite_AE_A_092_060Longrightarrow_062_Afinite_AspEdges_092_060close_062)).
% 0.09/0.20 thf(f4,axiom,(
% 0.09/0.20 (finite_finite2 @ product_prod @ nat @ nat @ (e @ a @ c))),
% 0.09/0.20 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_finite__E)).
% 0.09/0.20 thf(f281,conjecture,(
% 0.09/0.20 (finite_finite2 @ product_prod @ nat @ nat @ (edmond1803015688pEdges @ a @ c @ s @ t))),
% 0.09/0.20 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 0.09/0.20 thf(f282,negated_conjecture,(
% 0.09/0.20 ~(finite_finite2 @ product_prod @ nat @ nat @ (edmond1803015688pEdges @ a @ c @ s @ t))),
% 0.09/0.20 inference(negated_conjecture,[status(cth)],[f281])).
% 0.09/0.20 thf(f285,plain,(
% 0.09/0.20 (finite_finite2 @ product_prod @ nat @ nat @ (e @ a @ c)) => (finite_finite2 @ product_prod @ nat @ nat @ (edmond1803015688pEdges @ a @ c @ s @ t))),
% 0.09/0.20 inference(rectify,[],[f2])).
% 0.09/0.20 thf(f286,plain,(
% 0.09/0.20 (((finite_finite2 @ product_prod @ nat @ nat @ (e @ a @ c))) = $true) => (((finite_finite2 @ product_prod @ nat @ nat @ (edmond1803015688pEdges @ a @ c @ s @ t))) = $true)),
% 0.09/0.20 inference(fool_elimination,[],[f285])).
% 0.09/0.20 thf(f289,plain,(
% 0.09/0.20 (finite_finite2 @ product_prod @ nat @ nat @ (e @ a @ c))),
% 0.09/0.20 inference(rectify,[],[f4])).
% 0.09/0.20 thf(f290,plain,(
% 0.09/0.20 (((finite_finite2 @ product_prod @ nat @ nat @ (e @ a @ c))) = $true)),
% 0.09/0.20 inference(fool_elimination,[],[f289])).
% 0.09/0.20 thf(f807,plain,(
% 0.09/0.20 ~(finite_finite2 @ product_prod @ nat @ nat @ (edmond1803015688pEdges @ a @ c @ s @ t))),
% 0.09/0.20 inference(rectify,[],[f282])).
% 0.09/0.20 thf(f808,plain,(
% 0.09/0.20 ~ (((finite_finite2 @ product_prod @ nat @ nat @ (edmond1803015688pEdges @ a @ c @ s @ t))) = $true)),
% 0.09/0.20 inference(fool_elimination,[],[f807])).
% 0.09/0.20 thf(f836,plain,(
% 0.09/0.20 (((finite_finite2 @ product_prod @ nat @ nat @ (edmond1803015688pEdges @ a @ c @ s @ t))) != $true)),
% 0.09/0.20 inference(flattening,[],[f808])).
% 0.09/0.20 thf(f837,plain,(
% 0.09/0.20 (((finite_finite2 @ product_prod @ nat @ nat @ (edmond1803015688pEdges @ a @ c @ s @ t))) = $true) | (((finite_finite2 @ product_prod @ nat @ nat @ (e @ a @ c))) != $true)),
% 0.09/0.20 inference(ennf_transformation,[],[f286])).
% 0.09/0.20 thf(f1206,plain,(
% 0.09/0.20 (((finite_finite2 @ product_prod @ nat @ nat @ (edmond1803015688pEdges @ a @ c @ s @ t))) = $true) | (((finite_finite2 @ product_prod @ nat @ nat @ (e @ a @ c))) != $true)),
% 0.09/0.20 inference(cnf_transformation,[],[f837])).
% 0.09/0.20 thf(f1208,plain,(
% 0.09/0.20 (((finite_finite2 @ product_prod @ nat @ nat @ (e @ a @ c))) = $true)),
% 0.09/0.20 inference(cnf_transformation,[],[f290])).
% 0.09/0.20 thf(f1546,plain,(
% 0.09/0.20 (((finite_finite2 @ product_prod @ nat @ nat @ (edmond1803015688pEdges @ a @ c @ s @ t))) != $true)),
% 0.09/0.20 inference(cnf_transformation,[],[f836])).
% 0.09/0.20 thf(f1797,definition,(
% 0.09/0.20 spl147_6 <=> (((finite_finite2 @ product_prod @ nat @ nat @ (e @ a @ c))) = $true)),
% 0.09/0.20 introduced(definition,[new_symbols(definition,[spl147_6])],[avatar_definition])).
% 0.09/0.20 thf(f1809,plain,(
% 0.09/0.20 spl147_6),
% 0.09/0.20 inference(avatar_split_clause,[],[f1208,f1797])).
% 0.09/0.20 thf(f1811,definition,(
% 0.09/0.20 spl147_8 <=> (((finite_finite2 @ product_prod @ nat @ nat @ (edmond1803015688pEdges @ a @ c @ s @ t))) = $true)),
% 0.09/0.20 introduced(definition,[new_symbols(definition,[spl147_8])],[avatar_definition])).
% 0.09/0.20 thf(f1814,plain,(
% 0.09/0.20 ~spl147_6 | spl147_8),
% 0.09/0.20 inference(avatar_split_clause,[],[f1206,f1811,f1797])).
% 0.09/0.20 thf(f1815,plain,(
% 0.09/0.20 ~spl147_8),
% 0.09/0.20 inference(avatar_split_clause,[],[f1546,f1811])).
% 0.09/0.20 cnf(s10, plain, spl147_6, inference(sat_conversion,[],[f1809])).
% 0.09/0.20 cnf(s11, plain, ~spl147_6 | spl147_8, inference(sat_conversion,[],[f1814])).
% 0.09/0.20 cnf(s12, plain, ~spl147_8, inference(sat_conversion,[],[f1815])).
% 0.09/0.20 cnf(s13, plain, ~spl147_6, inference(rat,[],[s11,s12])).
% 0.09/0.20 cnf(s14, plain, $false, inference(rat,[],[s10,s13])).
% 0.09/0.20 thf(f1816,plain,(
% 0.09/0.20 $false),
% 0.09/0.20 inference(avatar_sat_refutation,[],[s14])).
% 0.09/0.20 % SZS output end Proof for theBenchmark
% 0.09/0.20 % (586966)------------------------------
% 0.09/0.20 % (586966)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.20 % (586966)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.20 % (586966)CaDiCaL version: 2.1.3
% 0.09/0.20 % (586966)Termination reason: Refutation
% 0.09/0.20 % (586966)Time elapsed: 0.031 s
% 0.09/0.20 % (586966)Peak memory usage: 13 MB
% 0.09/0.20 % (586966)Instructions burned: 129 (million)
% 0.09/0.20 % (586960)Success in time 0.067 s
% 0.09/0.20 % Vampire exiting
%------------------------------------------------------------------------------