%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP093^2 : 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 : n019.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 08:10:40 AM UTC 2026
% Result : Theorem 2.23s 0.60s
% Output : Refutation 2.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP093^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.16 % Computer : n019.cluster.edu
% 0.08/0.16 % Model : x86_64 x86_64
% 0.08/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.16 % Memory : 8046.5625MB
% 0.08/0.16 % OS : Linux 6.8.0-71-generic
% 0.08/0.16 % CPULimit : 300
% 0.08/0.16 % WCLimit : 300
% 0.08/0.16 % DateTime : Tue Sep 29 19:52:48 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.20 Running first-order model finding
% 0.08/0.20 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
% 2.23/0.60 % (1265980)Will run a generic schedule for satisfiability detection.
% 2.23/0.60 % (1265987)% WARNING: option uhcvi not known.
% 2.23/0.60 % (1265987)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=476856842:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 2.23/0.60 % (1265986)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=40464438_2999 on theBenchmark for (2999ds/0Mi)
% 2.23/0.60 % (1265989)dis+10_1_sil=32000:sp=arity:random_seed=3781640027:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 2.23/0.60 % (1265987)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.23/0.60 % (1265988)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2448746901:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 2.23/0.60 % (1265992)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2749535638:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 2.23/0.60 % (1265991)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4036484427:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 2.23/0.60 % (1265987)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.23/0.60 % (1265990)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=834138497:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 2.23/0.60 % Exception at run slice level
% 2.23/0.60 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.23/0.60 % (1265989)Instruction limit reached!
% 2.23/0.60 % (1265989)------------------------------
% 2.23/0.60 % (1265989)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.23/0.60 % (1265989)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.23/0.60 % (1265989)CaDiCaL version: 2.1.3
% 2.23/0.60 % (1265989)Termination reason: Instruction limit
% 2.23/0.60 % (1265989)Termination phase: Saturation
% 2.23/0.60 % (1265989)Time elapsed: 0.047 s
% 2.23/0.60 % (1265989)Peak memory usage: 12 MB
% 2.23/0.60 % (1265989)Instructions burned: 104 (million)
% 2.23/0.60 % (1265990)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.23/0.60 % (1266006)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=465190644:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 2.23/0.60 % (1266009)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=320246174:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 2.23/0.60 % (1265992)Instruction limit reached!
% 2.23/0.60 % (1265992)------------------------------
% 2.23/0.60 % (1265992)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.23/0.60 % (1265992)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.23/0.60 % (1265992)CaDiCaL version: 2.1.3
% 2.23/0.60 % (1265992)Termination reason: Instruction limit
% 2.23/0.60 % (1265992)Termination phase: Saturation
% 2.23/0.60 % (1265992)Time elapsed: 0.079 s
% 2.23/0.60 % (1265992)Peak memory usage: 14 MB
% 2.23/0.60 % (1265992)Instructions burned: 160 (million)
% 2.23/0.60 % Exception at run slice level
% 2.23/0.60 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.23/0.60 % (1266016)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=217780184:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 2.23/0.60 % (1265991)Instruction limit reached!
% 2.23/0.60 % (1265991)------------------------------
% 2.23/0.60 % (1265991)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.23/0.60 % (1265991)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.23/0.60 % (1265991)CaDiCaL version: 2.1.3
% 2.23/0.60 % (1265991)Termination reason: Instruction limit
% 2.23/0.60 % (1265991)Termination phase: Saturation
% 2.23/0.60 % (1265991)Time elapsed: 0.109 s
% 2.23/0.60 % (1265991)Peak memory usage: 13 MB
% 2.23/0.60 % (1265991)Instructions burned: 131 (million)
% 2.23/0.60 % (1266017)ott-21_1_sil=16000:fs=off:random_seed=1943352249:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 2.23/0.60 % (1266016)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.23/0.60 % (1265990)Instruction limit reached!
% 2.23/0.60 % (1265990)------------------------------
% 2.23/0.60 % (1265990)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.23/0.60 % (1265990)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.23/0.60 % (1265990)CaDiCaL version: 2.1.3
% 2.23/0.60 % (1265990)Termination reason: Instruction limit
% 2.23/0.60 % (1265990)Termination phase: Saturation
% 2.23/0.60 % (1265990)Time elapsed: 0.103 s
% 2.23/0.60 % (1265990)Peak memory usage: 13 MB
% 2.23/0.60 % (1265990)Instructions burned: 116 (million)
% 2.23/0.60 % (1266009)Instruction limit reached!
% 2.23/0.60 % (1266009)------------------------------
% 2.23/0.60 % (1266009)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.23/0.60 % (1266009)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.23/0.60 % (1266009)CaDiCaL version: 2.1.3
% 2.23/0.60 % (1266009)Termination reason: Instruction limit
% 2.23/0.60 % (1266009)Termination phase: Saturation
% 2.23/0.60 % (1266009)Time elapsed: 0.061 s
% 2.23/0.60 % (1266009)Peak memory usage: 13 MB
% 2.23/0.60 % (1266009)Instructions burned: 133 (million)
% 2.23/0.60 % (1266020)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=268342592:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 2.23/0.60 % (1266022)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=4098460502:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 2.23/0.60 % (1266021)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3212772590:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 2.23/0.60 % (1266016)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.23/0.60 % Exception at run slice level
% 2.23/0.60 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.23/0.60 % (1266017)Instruction limit reached!
% 2.23/0.60 % (1266017)------------------------------
% 2.23/0.60 % (1266017)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.23/0.60 % (1266017)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.23/0.60 % (1266017)CaDiCaL version: 2.1.3
% 2.23/0.60 % (1266017)Termination reason: Instruction limit
% 2.23/0.60 % (1266017)Termination phase: Saturation
% 2.23/0.60 % (1266017)Time elapsed: 0.086 s
% 2.23/0.60 % (1266017)Peak memory usage: 13 MB
% 2.23/0.60 % (1266017)Instructions burned: 181 (million)
% 2.23/0.60 % (1266026)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=403529246:i=889:ins=1_2997 on theBenchmark for (2997ds/889Mi)
% 2.23/0.60 % (1266027)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=2437162464:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2997 on theBenchmark for (2997ds/692Mi)
% 2.23/0.60 % (1266027)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.23/0.60 % Exception at run slice level
% 2.23/0.60 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.23/0.60 % (1266030)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=2774087677:i=879:kws=inv_precedence:fsr=off_2996 on theBenchmark for (2996ds/879Mi)
% 2.23/0.60 % (1266030)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.23/0.60 % (1266027) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1265980-1266027"...
% 2.23/0.60 % (1266027)...printing done.
% 2.23/0.60 % (1266027)Refutation found. Thanks to Tanya!
% 2.23/0.60 % SZS status Theorem for theBenchmark
% 2.23/0.60 % SZS output start Proof for theBenchmark
% 2.23/0.60 thf(type_def_5, type, pair_p1731315293ph_ext: ($tType * $tType) > $tType).
% 2.23/0.60 thf(type_def_6, type, product_unit: $tType).
% 2.23/0.60 thf(type_def_7, type, product_prod: ($tType * $tType) > $tType).
% 2.23/0.60 thf(type_def_8, type, set: $tType > $tType).
% 2.23/0.60 thf(type_def_9, type, nat: $tType).
% 2.23/0.60 thf(type_def_10, type, a: $tType).
% 2.23/0.60 thf(type_def_11, type, sTfun: ($tType * $tType) > $tType).
% 2.23/0.60 thf(func_def_0, type, type: !>[X0: $tType]:($o)).
% 2.23/0.60 thf(func_def_1, type, bot: !>[X0: $tType]:($o)).
% 2.23/0.60 thf(func_def_2, type, ord: !>[X0: $tType]:($o)).
% 2.23/0.60 thf(func_def_3, type, order: !>[X0: $tType]:($o)).
% 2.23/0.60 thf(func_def_4, type, finite_finite: !>[X0: $tType]:($o)).
% 2.23/0.60 thf(func_def_5, type, linorder: !>[X0: $tType]:($o)).
% 2.23/0.60 thf(func_def_6, type, preorder: !>[X0: $tType]:($o)).
% 2.23/0.60 thf(func_def_7, type, order_bot: !>[X0: $tType]:($o)).
% 2.23/0.60 thf(func_def_8, type, bNF_Ca1785829860lChain: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X0 > (X0 > X1) > $o))).
% 2.23/0.60 thf(func_def_9, type, finite_Fpow: !>[X0: $tType]:((set @ X0 > set @ set @ X0))).
% 2.23/0.60 thf(func_def_10, type, finite_card: !>[X0: $tType]:((set @ X0 > nat))).
% 2.23/0.60 thf(func_def_11, type, finite_finite2: !>[X0: $tType]:((set @ X0 > $o))).
% 2.23/0.60 thf(func_def_12, type, bot_bot: !>[X0: $tType]:(X0)).
% 2.23/0.60 thf(func_def_13, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 2.23/0.60 thf(func_def_14, type, pair_p1033978749igraph: !>[X0: $tType]:((pair_p1731315293ph_ext @ X0 @ product_unit > $o))).
% 2.23/0.60 thf(func_def_15, type, pair_pair_digraph: !>[X0: $tType]:((pair_p1731315293ph_ext @ X0 @ product_unit > $o))).
% 2.23/0.60 thf(func_def_16, type, pair_p953238171igraph: !>[X0: $tType]:((pair_p1731315293ph_ext @ X0 @ product_unit > $o))).
% 2.23/0.60 thf(func_def_17, type, pair_p1373739070axioms: !>[X0: $tType]:((pair_p1731315293ph_ext @ X0 @ product_unit > $o))).
% 2.23/0.60 thf(func_def_18, type, pair_pair_graph: !>[X0: $tType]:((pair_p1731315293ph_ext @ X0 @ product_unit > $o))).
% 2.23/0.60 thf(func_def_19, type, pair_p1282390076igraph: !>[X0: $tType]:((pair_p1731315293ph_ext @ X0 @ product_unit > $o))).
% 2.23/0.60 thf(func_def_20, type, pair_p814123999axioms: !>[X0: $tType]:((pair_p1731315293ph_ext @ X0 @ product_unit > $o))).
% 2.23/0.60 thf(func_def_21, type, pair_pair_pre_more: !>[X0: $tType, X1: $tType]:((pair_p1731315293ph_ext @ X0 @ X1 > X1))).
% 2.23/0.60 thf(func_def_22, type, pair_p1108258481update: !>[X0: $tType, X1: $tType]:(((X0 > X0) > pair_p1731315293ph_ext @ X1 @ X0 > pair_p1731315293ph_ext @ X1 @ X0))).
% 2.23/0.60 thf(func_def_23, type, pair_p1152105390ph_ext: !>[X0: $tType, X1: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X1 > pair_p1731315293ph_ext @ X0 @ X1))).
% 2.23/0.60 thf(func_def_24, type, pair_pair_pre_parcs: !>[X0: $tType, X1: $tType]:((pair_p1731315293ph_ext @ X0 @ X1 > set @ product_prod @ X0 @ X0))).
% 2.23/0.60 thf(func_def_25, type, pair_pair_pre_pverts: !>[X0: $tType, X1: $tType]:((pair_p1731315293ph_ext @ X0 @ X1 > set @ X0))).
% 2.23/0.60 thf(func_def_26, type, pair_p389585203_graph: !>[X0: $tType]:((pair_p1731315293ph_ext @ X0 @ product_unit > $o))).
% 2.23/0.60 thf(func_def_27, type, pair_p460180511igraph: !>[X0: $tType]:((pair_p1731315293ph_ext @ X0 @ product_unit > $o))).
% 2.23/0.60 thf(func_def_28, type, pair_p477239746axioms: !>[X0: $tType]:((pair_p1731315293ph_ext @ X0 @ product_unit > $o))).
% 2.23/0.60 thf(func_def_29, type, pair_pair_wf_digraph: !>[X0: $tType]:((pair_p1731315293ph_ext @ X0 @ product_unit > $o))).
% 2.23/0.60 thf(func_def_30, type, pair_subdivide: !>[X0: $tType]:((pair_p1731315293ph_ext @ X0 @ product_unit > product_prod @ X0 @ X0 > X0 > pair_p1731315293ph_ext @ X0 @ product_unit))).
% 2.23/0.60 thf(func_def_31, type, product_Pair: !>[X0: $tType, X1: $tType]:((X0 > X1 > product_prod @ X0 @ X1))).
% 2.23/0.60 thf(func_def_32, type, product_Sigma: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > set @ X1) > set @ product_prod @ X0 @ X1))).
% 2.23/0.60 thf(func_def_33, type, produc2004651681e_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 2.23/0.60 thf(func_def_34, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 2.23/0.60 thf(func_def_35, type, product_case_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 2.23/0.60 thf(func_def_36, type, product_product: !>[X0: $tType, X1: $tType]:((set @ X0 > set @ X1 > set @ product_prod @ X0 @ X1))).
% 2.23/0.60 thf(func_def_37, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 2.23/0.60 thf(func_def_38, type, is_empty: !>[X0: $tType]:((set @ X0 > $o))).
% 2.23/0.60 thf(func_def_39, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 2.23/0.60 thf(func_def_40, type, g: pair_p1731315293ph_ext @ a @ product_unit).
% 2.23/0.60 thf(func_def_41, type, n: nat).
% 2.23/0.60 thf(func_def_45, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 2.23/0.60 thf(func_def_46, type, vAND: ($o > $o > $o)).
% 2.23/0.60 thf(func_def_47, type, db0: !>[X0: $tType]:(X0)).
% 2.23/0.60 thf(func_def_48, type, vOR: ($o > $o > $o)).
% 2.23/0.60 thf(func_def_49, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 2.23/0.60 thf(func_def_50, type, db2: !>[X0: $tType]:(X0)).
% 2.23/0.60 thf(func_def_51, type, db1: !>[X0: $tType]:(X0)).
% 2.23/0.60 thf(func_def_52, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 2.23/0.60 thf(func_def_53, type, vIMP: ($o > $o > $o)).
% 2.23/0.60 thf(func_def_54, type, vNOT: ($o > $o)).
% 2.23/0.60 thf(func_def_55, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 2.23/0.60 thf(func_def_56, type, db3: !>[X0: $tType]:(X0)).
% 2.23/0.60 thf(func_def_57, type, db4: !>[X0: $tType]:(X0)).
% 2.23/0.60 thf(func_def_58, type, sP0: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 2.23/0.60 thf(func_def_59, type, sP1: !>[X0: $tType, X1: $tType]:((set @ X1 > set @ X0 > (X1 > X0 > $o) > $o))).
% 2.23/0.60 thf(func_def_60, type, sP2: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 2.23/0.60 thf(func_def_61, type, sP3: !>[X0: $tType]:(((X0 > X0 > $o) > $o))).
% 2.23/0.60 thf(func_def_62, type, sP4: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 2.23/0.60 thf(func_def_63, type, sP5: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 2.23/0.60 thf(func_def_64, type, sP6: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 2.23/0.60 thf(func_def_65, type, sP7: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 2.23/0.60 thf(func_def_66, type, sP8: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 2.23/0.60 thf(func_def_67, type, sP9: !>[X0: $tType]:((set @ X0 > (X0 > $o) > (X0 > $o) > $o))).
% 2.23/0.60 thf(func_def_68, type, sP10: !>[X0: $tType]:(((X0 > X0 > $o) > $o))).
% 2.23/0.60 thf(func_def_69, type, sP11: !>[X0: $tType, X1: $tType]:(((X1 > set @ X0) > X1 > product_prod @ X1 @ X0 > $o))).
% 2.23/0.60 thf(func_def_70, type, sP12: !>[X0: $tType]:((nat > set @ X0 > $o))).
% 2.23/0.60 thf(func_def_71, type, sP13: !>[X0: $tType]:((set @ X0 > nat > $o))).
% 2.23/0.60 thf(func_def_72, type, sP14: !>[X0: $tType]:((set @ X0 > nat > $o))).
% 2.23/0.60 thf(func_def_73, type, sP15: ((nat > $o) > nat > $o)).
% 2.23/0.60 thf(func_def_74, type, sP16: !>[X0: $tType, X1: $tType]:((set @ X0 > set @ X1 > (X0 > X1 > $o) > $o))).
% 2.23/0.60 thf(func_def_75, type, sK17: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > set @ X1 > X1 > X0))).
% 2.23/0.60 thf(func_def_76, type, sK18: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > set @ X1 > X1))).
% 2.23/0.60 thf(func_def_77, type, sK19: !>[X0: $tType]:((X0 > set @ X0 > X0))).
% 2.23/0.60 thf(func_def_78, type, sK20: !>[X0: $tType, X1: $tType]:(((X1 > set @ X0) > set @ X1 > X1))).
% 2.23/0.60 thf(func_def_79, type, sK21: !>[X0: $tType]:(((X0 > $o) > X0))).
% 2.23/0.60 thf(func_def_80, type, sK22: !>[X0: $tType, X1: $tType]:((set @ X1 > set @ X0 > (X1 > X0 > $o) > X1))).
% 2.23/0.60 thf(func_def_81, type, sK23: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > set @ X0 > set @ X1 > X0))).
% 2.23/0.60 thf(func_def_82, type, sK24: !>[X0: $tType]:((X0 > set @ X0 > X0))).
% 2.23/0.60 thf(func_def_83, type, sK25: !>[X0: $tType, X1: $tType]:(((X1 > set @ X0) > (X1 > set @ X0) > set @ X1 > X1))).
% 2.23/0.60 thf(func_def_84, type, sK26: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 2.23/0.60 thf(func_def_85, type, sK27: !>[X0: $tType, X1: $tType]:(((X1 > set @ X0) > (X1 > set @ X0) > set @ X1 > X1))).
% 2.23/0.60 thf(func_def_86, type, sK28: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 2.23/0.60 thf(func_def_87, type, sK29: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 2.23/0.60 thf(func_def_88, type, sK30: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 2.23/0.60 thf(func_def_89, type, sK31: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 2.23/0.60 thf(func_def_90, type, sK32: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 2.23/0.60 thf(func_def_91, type, sK33: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 2.23/0.60 thf(func_def_92, type, sK34: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 2.23/0.60 thf(func_def_93, type, sK35: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 2.23/0.60 thf(func_def_94, type, sK36: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 2.23/0.60 thf(func_def_95, type, sK37: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.23/0.60 thf(func_def_96, type, sK38: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.23/0.60 thf(func_def_97, type, sK39: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 2.23/0.60 thf(func_def_98, type, sK40: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 2.23/0.60 thf(func_def_99, type, sK41: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.23/0.60 thf(func_def_100, type, sK42: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.23/0.60 thf(func_def_101, type, sK43: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 2.23/0.60 thf(func_def_102, type, sK44: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 2.23/0.60 thf(func_def_103, type, sK45: !>[X0: $tType]:((set @ X0 > (X0 > $o) > (X0 > $o) > X0))).
% 2.23/0.60 thf(func_def_104, type, sK46: !>[X0: $tType, X1: $tType]:(((pair_p1731315293ph_ext @ X1 @ X0 > $o) > set @ X1))).
% 2.23/0.60 thf(func_def_105, type, sK47: !>[X0: $tType, X1: $tType]:(((pair_p1731315293ph_ext @ X1 @ X0 > $o) > set @ product_prod @ X1 @ X1))).
% 2.23/0.60 thf(func_def_106, type, sK48: !>[X0: $tType, X1: $tType]:(((pair_p1731315293ph_ext @ X1 @ X0 > $o) > X0))).
% 2.23/0.60 thf(func_def_107, type, sK49: !>[X0: $tType, X1: $tType]:((pair_p1731315293ph_ext @ X0 @ X1 > set @ X0))).
% 2.23/0.60 thf(func_def_108, type, sK50: !>[X0: $tType, X1: $tType]:((pair_p1731315293ph_ext @ X0 @ X1 > set @ product_prod @ X0 @ X0))).
% 2.23/0.60 thf(func_def_109, type, sK51: !>[X0: $tType, X1: $tType]:((pair_p1731315293ph_ext @ X0 @ X1 > X1))).
% 2.23/0.60 thf(func_def_110, type, sK52: !>[X0: $tType]:(((X0 > X0) > (X0 > X0) > X0 > X0))).
% 2.23/0.60 thf(func_def_111, type, sK53: !>[X0: $tType]:(((X0 > X0) > (X0 > X0) > X0 > X0))).
% 2.23/0.60 thf(func_def_112, type, sK54: !>[X0: $tType]:((set @ X0 > X0))).
% 2.23/0.60 thf(func_def_113, type, sK55: !>[X0: $tType]:((set @ X0 > X0))).
% 2.23/0.60 thf(func_def_114, type, sK56: !>[X0: $tType]:((set @ X0 > X0))).
% 2.23/0.60 thf(func_def_115, type, sK57: !>[X0: $tType]:((set @ X0 > X0))).
% 2.23/0.60 thf(func_def_116, type, sK58: !>[X0: $tType, X1: $tType]:(((X1 > set @ X0) > set @ X1 > X1))).
% 2.23/0.60 thf(func_def_117, type, sK59: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 2.23/0.60 thf(func_def_118, type, sK60: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 2.23/0.60 thf(func_def_119, type, sK61: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 2.23/0.60 thf(func_def_120, type, sK62: !>[X0: $tType]:(((X0 > X0 > $o) > set @ X0 > X0))).
% 2.23/0.60 thf(func_def_121, type, sK63: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 2.23/0.60 thf(func_def_122, type, sK64: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 2.23/0.60 thf(func_def_123, type, sK65: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 2.23/0.60 thf(func_def_124, type, sK66: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 2.23/0.60 thf(func_def_125, type, sK67: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 2.23/0.60 thf(func_def_126, type, sK68: !>[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))).
% 2.23/0.60 thf(func_def_127, type, sK69: !>[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))).
% 2.23/0.60 thf(func_def_128, type, sK70: !>[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))).
% 2.23/0.60 thf(func_def_129, type, sK71: !>[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))).
% 2.23/0.60 thf(func_def_130, type, sK72: !>[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))).
% 2.23/0.60 thf(func_def_131, type, sK73: !>[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))).
% 2.23/0.60 thf(func_def_132, type, sK74: !>[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))).
% 2.23/0.60 thf(func_def_133, type, sK75: !>[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))).
% 2.23/0.60 thf(func_def_134, type, sK76: !>[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))).
% 2.23/0.60 thf(func_def_135, type, sK77: !>[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))).
% 2.23/0.60 thf(func_def_136, type, sK78: !>[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))).
% 2.23/0.60 thf(func_def_137, type, sK79: !>[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))).
% 2.23/0.60 thf(func_def_138, type, sK80: !>[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))).
% 2.23/0.60 thf(func_def_139, type, sK81: !>[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))).
% 2.23/0.60 thf(func_def_140, type, sK82: !>[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))).
% 2.23/0.60 thf(func_def_141, 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) > X2))).
% 2.23/0.60 thf(func_def_142, 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) > X1))).
% 2.23/0.60 thf(func_def_143, 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) > X0))).
% 2.23/0.60 thf(func_def_144, type, sK86: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3))).
% 2.23/0.60 thf(func_def_145, type, sK87: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 2.23/0.60 thf(func_def_146, type, sK88: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 2.23/0.60 thf(func_def_147, type, sK89: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 2.23/0.60 thf(func_def_148, type, sK90: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 2.23/0.60 thf(func_def_149, type, sK91: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 2.23/0.60 thf(func_def_150, type, sK92: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 2.23/0.60 thf(func_def_151, type, sK93: !>[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))).
% 2.23/0.60 thf(func_def_152, type, sK94: !>[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))).
% 2.23/0.60 thf(func_def_153, type, sK95: !>[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))).
% 2.23/0.60 thf(func_def_154, type, sK96: !>[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))).
% 2.23/0.60 thf(func_def_155, type, sK97: !>[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))).
% 2.23/0.60 thf(func_def_156, type, sK98: !>[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))).
% 2.23/0.60 thf(func_def_157, type, sK99: !>[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))).
% 2.23/0.60 thf(func_def_158, type, sK100: !>[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))).
% 2.23/0.60 thf(func_def_159, type, sK101: !>[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))).
% 2.23/0.60 thf(func_def_160, type, sK102: !>[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))).
% 2.23/0.60 thf(func_def_161, type, sK103: !>[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))).
% 2.23/0.60 thf(func_def_162, type, sK104: !>[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))).
% 2.23/0.60 thf(func_def_163, type, sK105: !>[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))).
% 2.23/0.60 thf(func_def_164, type, sK106: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X0))).
% 2.23/0.60 thf(func_def_165, type, sK107: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X1))).
% 2.23/0.60 thf(func_def_166, type, sK108: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X2))).
% 2.23/0.60 thf(func_def_167, type, sK109: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X3))).
% 2.23/0.60 thf(func_def_168, type, sK110: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X4))).
% 2.23/0.60 thf(func_def_169, type, sK111: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X0))).
% 2.23/0.60 thf(func_def_170, type, sK112: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X1))).
% 2.23/0.60 thf(func_def_171, type, sK113: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X2))).
% 2.23/0.60 thf(func_def_172, type, sK114: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X3))).
% 2.23/0.60 thf(func_def_173, type, sK115: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X0))).
% 2.23/0.60 thf(func_def_174, type, sK116: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X1))).
% 2.23/0.60 thf(func_def_175, type, sK117: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X2))).
% 2.23/0.60 thf(func_def_176, type, sK118: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 2.23/0.60 thf(func_def_177, type, sK119: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 2.23/0.60 thf(func_def_178, type, sK120: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 2.23/0.60 thf(func_def_179, type, sK121: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 2.23/0.60 thf(func_def_180, type, sK122: !>[X0: $tType]:(((pair_p1731315293ph_ext @ X0 @ product_unit > product_prod @ X0 @ X0 > X0 > $o) > pair_p1731315293ph_ext @ X0 @ product_unit))).
% 2.23/0.60 thf(func_def_181, type, sK123: !>[X0: $tType]:(((pair_p1731315293ph_ext @ X0 @ product_unit > product_prod @ X0 @ X0 > X0 > $o) > X0))).
% 2.23/0.60 thf(func_def_182, type, sK124: !>[X0: $tType]:(((pair_p1731315293ph_ext @ X0 @ product_unit > product_prod @ X0 @ X0 > X0 > $o) > X0))).
% 2.23/0.60 thf(func_def_183, type, sK125: !>[X0: $tType]:(((pair_p1731315293ph_ext @ X0 @ product_unit > product_prod @ X0 @ X0 > X0 > $o) > X0))).
% 2.23/0.60 thf(func_def_184, type, sK126: !>[X0: $tType]:((product_prod @ pair_p1731315293ph_ext @ X0 @ product_unit @ product_prod @ product_prod @ X0 @ X0 @ X0 > pair_p1731315293ph_ext @ X0 @ product_unit))).
% 2.23/0.60 thf(func_def_185, type, sK127: !>[X0: $tType]:((product_prod @ pair_p1731315293ph_ext @ X0 @ product_unit @ product_prod @ product_prod @ X0 @ X0 @ X0 > X0))).
% 2.23/0.60 thf(func_def_186, type, sK128: !>[X0: $tType]:((product_prod @ pair_p1731315293ph_ext @ X0 @ product_unit @ product_prod @ product_prod @ X0 @ X0 @ X0 > X0))).
% 2.23/0.60 thf(func_def_187, type, sK129: !>[X0: $tType]:((product_prod @ pair_p1731315293ph_ext @ X0 @ product_unit @ product_prod @ product_prod @ X0 @ X0 @ X0 > X0))).
% 2.23/0.60 thf(func_def_188, type, sK130: !>[X0: $tType, X1: $tType]:(((X1 > set @ X0) > X1 > product_prod @ X1 @ X0 > X0))).
% 2.23/0.60 thf(func_def_189, type, sK131: !>[X0: $tType, X1: $tType]:(((X0 > set @ X1) > set @ X0 > product_prod @ X0 @ X1 > X0))).
% 2.23/0.60 thf(func_def_190, type, sK132: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > set @ product_prod @ X1 @ X0 > X1))).
% 2.23/0.60 thf(func_def_191, type, sK133: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > set @ product_prod @ X1 @ X0 > X0))).
% 2.23/0.60 thf(func_def_192, type, sK134: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > (X1 > X0 > $o) > X1))).
% 2.23/0.60 thf(func_def_193, type, sK135: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > (X1 > X0 > $o) > X0))).
% 2.23/0.60 thf(func_def_194, type, sK136: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > product_prod @ X1 @ X0 > X1))).
% 2.23/0.60 thf(func_def_195, type, sK137: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > product_prod @ X1 @ X0 > X0))).
% 2.23/0.60 thf(func_def_196, type, sK138: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > (X0 > X1 > $o) > X0))).
% 2.23/0.60 thf(func_def_197, type, sK139: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > (X0 > X1 > $o) > X1))).
% 2.23/0.60 thf(func_def_198, type, sK140: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ X2 > (X0 > X2 > X1) > (X1 > $o) > X0))).
% 2.23/0.60 thf(func_def_199, type, sK141: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ X2 > (X0 > X2 > X1) > (X1 > $o) > X2))).
% 2.23/0.60 thf(func_def_200, type, sK142: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ X1 > X0) > (X2 > X1 > X0) > X2))).
% 2.23/0.60 thf(func_def_201, type, sK143: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ X1 > X0) > (X2 > X1 > X0) > X1))).
% 2.23/0.60 thf(func_def_202, type, sK144: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > X1 > X0) > (X2 > X1 > X0) > product_prod @ X2 @ X1 > X2))).
% 2.23/0.60 thf(func_def_203, type, sK145: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > X1 > X0) > (X2 > X1 > X0) > product_prod @ X2 @ X1 > X1))).
% 2.23/0.60 thf(func_def_204, type, sK146: !>[X0: $tType]:((nat > set @ X0 > set @ X0))).
% 2.23/0.60 thf(func_def_205, type, sK147: !>[X0: $tType]:((set @ X0 > nat > set @ X0))).
% 2.23/0.60 thf(func_def_206, type, sK148: !>[X0: $tType]:((set @ X0 > nat > set @ X0))).
% 2.23/0.60 thf(func_def_207, type, sK149: !>[X0: $tType]:((set @ X0 > nat > set @ X0))).
% 2.23/0.60 thf(func_def_208, type, sK150: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > X1 > set @ X0) > X0 > product_prod @ X2 @ X1 > X2))).
% 2.23/0.60 thf(func_def_209, type, sK151: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > X1 > set @ X0) > X0 > product_prod @ X2 @ X1 > X1))).
% 2.23/0.60 thf(func_def_210, type, sK152: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > (X0 > X1 > X2 > $o) > product_prod @ X0 @ X1 > X0))).
% 2.23/0.60 thf(func_def_211, type, sK153: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > (X0 > X1 > X2 > $o) > product_prod @ X0 @ X1 > X1))).
% 2.23/0.60 thf(func_def_212, type, sK154: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > product_prod @ X1 @ X0 > (X1 > X0 > X2 > $o) > X1))).
% 2.23/0.60 thf(func_def_213, type, sK155: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > product_prod @ X1 @ X0 > (X1 > X0 > X2 > $o) > X0))).
% 2.23/0.60 thf(func_def_214, type, sK156: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ X2 > (X0 > X2 > set @ X1) > X1 > X0))).
% 2.23/0.60 thf(func_def_215, type, sK157: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ X2 > (X0 > X2 > set @ X1) > X1 > X2))).
% 2.23/0.60 thf(func_def_216, type, sK158: ((nat > $o) > nat > nat)).
% 2.23/0.60 thf(func_def_217, type, sK159: ((nat > $o) > nat)).
% 2.23/0.60 thf(func_def_218, type, sK160: ((nat > nat) > nat)).
% 2.23/0.60 thf(func_def_219, type, sK161: !>[X0: $tType, X1: $tType]:((set @ X0 > set @ X1 > (X0 > X1 > $o) > X0))).
% 2.23/0.60 thf(func_def_220, type, sK162: !>[X0: $tType, X1: $tType]:((set @ X0 > set @ X1 > (X0 > X1 > $o) > X0))).
% 2.23/0.60 thf(func_def_221, type, sK163: !>[X0: $tType, X1: $tType]:((set @ X0 > set @ X1 > (X0 > X1 > $o) > X1))).
% 2.23/0.60 thf(func_def_222, type, sK164: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > set @ X0 > set @ X1 > X0))).
% 2.23/0.60 thf(func_def_223, type, sK165: (nat > set @ nat > nat)).
% 2.23/0.60 thf(func_def_224, type, sK166: (set @ nat > nat)).
% 2.23/0.60 thf(func_def_225, type, sK167: !>[X0: $tType]:((set @ X0 > X0))).
% 2.23/0.60 thf(func_def_226, type, sK168: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > set @ X0) > X1))).
% 2.23/0.60 thf(func_def_227, type, sK169: !>[X0: $tType]:(((X0 > $o) > X0))).
% 2.23/0.60 thf(func_def_228, type, sK170: !>[X0: $tType]:(((X0 > $o) > X0))).
% 2.23/0.60 thf(func_def_229, type, sK171: !>[X0: $tType]:((set @ X0 > X0))).
% 2.23/0.60 thf(func_def_230, type, sK172: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 2.23/0.60 thf(func_def_231, type, sK173: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 2.23/0.60 thf(f2,axiom,(
% 2.23/0.60 (finite_finite2 @ product_prod @ a @ a @ (product_Sigma @ a @ a @ (pair_pair_pre_pverts @ a @ product_unit @ g) @ (^[X0 : a] : ((pair_pair_pre_pverts @ a @ product_unit @ g)))))),
% 2.23/0.60 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__092_060open_062finite_A_Ipverts_AG_A_092_060times_062_Apverts_AG_J_092_060close_062)).
% 2.23/0.60 thf(f3,axiom,(
% 2.23/0.60 (ord_less_eq @ set @ product_prod @ a @ a @ (pair_pair_pre_parcs @ a @ product_unit @ g) @ (product_Sigma @ a @ a @ (pair_pair_pre_pverts @ a @ product_unit @ g) @ (^[X0 : a] : ((pair_pair_pre_pverts @ a @ product_unit @ g)))))),
% 2.23/0.60 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__092_060open_062parcs_AG_A_092_060subseteq_062_Apverts_AG_A_092_060times_062_Apverts_AG_092_060close_062)).
% 2.23/0.60 thf(f11,axiom,(
% 2.23/0.60 ! [X0 : $tType,X1 : set @ X0,X2 : set @ X0] : ((finite_finite2 @ X0 @ X1) => ((ord_less_eq @ set @ X0 @ X2 @ X1) => (finite_finite2 @ X0 @ X2)))),
% 2.23/0.60 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_rev__finite__subset)).
% 2.23/0.60 thf(f290,conjecture,(
% 2.23/0.60 (finite_finite2 @ product_prod @ a @ a @ (pair_pair_pre_parcs @ a @ product_unit @ g))),
% 2.23/0.60 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 2.23/0.60 thf(f291,negated_conjecture,(
% 2.23/0.60 ~(finite_finite2 @ product_prod @ a @ a @ (pair_pair_pre_parcs @ a @ product_unit @ g))),
% 2.23/0.60 inference(negated_conjecture,[status(cth)],[f290])).
% 2.23/0.60 thf(f294,plain,(
% 2.23/0.60 (finite_finite2 @ product_prod @ a @ a @ (product_Sigma @ a @ a @ (pair_pair_pre_pverts @ a @ product_unit @ g) @ (^[X0 : a] : ((pair_pair_pre_pverts @ a @ product_unit @ g)))))),
% 2.23/0.60 inference(rectify,[],[f2])).
% 2.23/0.60 thf(f295,plain,(
% 2.23/0.60 ($true = ((finite_finite2 @ product_prod @ a @ a @ (product_Sigma @ a @ a @ (pair_pair_pre_pverts @ a @ product_unit @ g) @ (^[Y0 : a]: (pair_pair_pre_pverts @ a @ product_unit @ g))))))),
% 2.23/0.60 inference(fool_elimination,[],[f294])).
% 2.23/0.60 thf(f296,plain,(
% 2.23/0.60 (ord_less_eq @ set @ product_prod @ a @ a @ (pair_pair_pre_parcs @ a @ product_unit @ g) @ (product_Sigma @ a @ a @ (pair_pair_pre_pverts @ a @ product_unit @ g) @ (^[X0 : a] : ((pair_pair_pre_pverts @ a @ product_unit @ g)))))),
% 2.23/0.60 inference(rectify,[],[f3])).
% 2.23/0.60 thf(f297,plain,(
% 2.23/0.60 ($true = ((ord_less_eq @ set @ product_prod @ a @ a @ (pair_pair_pre_parcs @ a @ product_unit @ g) @ (product_Sigma @ a @ a @ (pair_pair_pre_pverts @ a @ product_unit @ g) @ (^[Y0 : a]: (pair_pair_pre_pverts @ a @ product_unit @ g))))))),
% 2.23/0.60 inference(fool_elimination,[],[f296])).
% 2.23/0.60 thf(f312,plain,(
% 2.23/0.60 ! [X0 : $tType,X1 : set @ X0,X2 : set @ X0] : ((finite_finite2 @ X0 @ X1) => ((ord_less_eq @ set @ X0 @ X2 @ X1) => (finite_finite2 @ X0 @ X2)))),
% 2.23/0.60 inference(rectify,[],[f11])).
% 2.23/0.60 thf(f313,plain,(
% 2.23/0.60 ! [X0 : $tType,X1 : set @ X0,X2 : set @ X0] : ((((finite_finite2 @ X0 @ X1)) = $true) => ((((ord_less_eq @ set @ X0 @ X2 @ X1)) = $true) => (((finite_finite2 @ X0 @ X2)) = $true)))),
% 2.23/0.60 inference(fool_elimination,[],[f312])).
% 2.23/0.60 thf(f798,plain,(
% 2.23/0.60 ~(finite_finite2 @ product_prod @ a @ a @ (pair_pair_pre_parcs @ a @ product_unit @ g))),
% 2.23/0.60 inference(rectify,[],[f291])).
% 2.23/0.60 thf(f799,plain,(
% 2.23/0.60 ~ (((finite_finite2 @ product_prod @ a @ a @ (pair_pair_pre_parcs @ a @ product_unit @ g))) = $true)),
% 2.23/0.60 inference(fool_elimination,[],[f798])).
% 2.23/0.60 thf(f829,plain,(
% 2.23/0.60 (((finite_finite2 @ product_prod @ a @ a @ (pair_pair_pre_parcs @ a @ product_unit @ g))) != $true)),
% 2.23/0.60 inference(flattening,[],[f799])).
% 2.23/0.60 thf(f841,plain,(
% 2.23/0.60 ! [X0 : $tType,X1 : set @ X0,X2 : set @ X0] : (((((finite_finite2 @ X0 @ X2)) = $true) | (((ord_less_eq @ set @ X0 @ X2 @ X1)) != $true)) | (((finite_finite2 @ X0 @ X1)) != $true))),
% 2.23/0.60 inference(ennf_transformation,[],[f313])).
% 2.23/0.60 thf(f842,plain,(
% 2.23/0.60 ! [X0 : $tType,X1 : set @ X0,X2 : set @ X0] : ((((finite_finite2 @ X0 @ X2)) = $true) | (((ord_less_eq @ set @ X0 @ X2 @ X1)) != $true) | (((finite_finite2 @ X0 @ X1)) != $true))),
% 2.23/0.60 inference(flattening,[],[f841])).
% 2.23/0.60 thf(f1227,plain,(
% 2.23/0.60 ($true = ((finite_finite2 @ product_prod @ a @ a @ (product_Sigma @ a @ a @ (pair_pair_pre_pverts @ a @ product_unit @ g) @ (^[Y0 : a]: (pair_pair_pre_pverts @ a @ product_unit @ g))))))),
% 2.23/0.60 inference(cnf_transformation,[],[f295])).
% 2.23/0.60 thf(f1228,plain,(
% 2.23/0.60 ($true = ((ord_less_eq @ set @ product_prod @ a @ a @ (pair_pair_pre_parcs @ a @ product_unit @ g) @ (product_Sigma @ a @ a @ (pair_pair_pre_pverts @ a @ product_unit @ g) @ (^[Y0 : a]: (pair_pair_pre_pverts @ a @ product_unit @ g))))))),
% 2.23/0.60 inference(cnf_transformation,[],[f297])).
% 2.23/0.60 thf(f1237,plain,(
% 2.23/0.60 ( ! [X0 : $tType,X2 : set @ X0,X1 : set @ X0] : ((((ord_less_eq @ set @ X0 @ X2 @ X1)) != $true) | (((finite_finite2 @ X0 @ X2)) = $true) | (((finite_finite2 @ X0 @ X1)) != $true)) )),
% 2.23/0.60 inference(cnf_transformation,[],[f842])).
% 2.23/0.60 thf(f1602,plain,(
% 2.23/0.60 (((finite_finite2 @ product_prod @ a @ a @ (pair_pair_pre_parcs @ a @ product_unit @ g))) != $true)),
% 2.23/0.60 inference(cnf_transformation,[],[f829])).
% 2.23/0.60 thf(f2780,plain,(
% 2.23/0.60 ($true != $true) | (((finite_finite2 @ product_prod @ a @ a @ (pair_pair_pre_parcs @ a @ product_unit @ g))) = $true) | ($true != ((finite_finite2 @ product_prod @ a @ a @ (product_Sigma @ a @ a @ (pair_pair_pre_pverts @ a @ product_unit @ g) @ (^[Y0 : a]: (pair_pair_pre_pverts @ a @ product_unit @ g))))))),
% 2.23/0.60 inference(constrained_superposition,[],[f1237,f1228])).
% 2.23/0.60 thf(f2781,plain,(
% 2.23/0.60 (((finite_finite2 @ product_prod @ a @ a @ (pair_pair_pre_parcs @ a @ product_unit @ g))) = $true) | ($true != ((finite_finite2 @ product_prod @ a @ a @ (product_Sigma @ a @ a @ (pair_pair_pre_pverts @ a @ product_unit @ g) @ (^[Y0 : a]: (pair_pair_pre_pverts @ a @ product_unit @ g))))))),
% 2.23/0.60 inference(trivial_inequality_removal,[],[f2780])).
% 2.23/0.60 thf(f2782,plain,(
% 2.23/0.60 ($true != ((finite_finite2 @ product_prod @ a @ a @ (product_Sigma @ a @ a @ (pair_pair_pre_pverts @ a @ product_unit @ g) @ (^[Y0 : a]: (pair_pair_pre_pverts @ a @ product_unit @ g))))))),
% 2.23/0.60 inference(forward_subsumption_resolution,[],[f2781,f1602])).
% 2.23/0.60 thf(f2783,plain,(
% 2.23/0.60 $false),
% 2.23/0.60 inference(forward_subsumption_resolution,[],[f2782,f1227])).
% 2.23/0.60 % SZS output end Proof for theBenchmark
% 2.23/0.60 % (1266027)------------------------------
% 2.23/0.60 % (1266027)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.23/0.60 % (1266027)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.23/0.60 % (1266027)CaDiCaL version: 2.1.3
% 2.23/0.60 % (1266027)Termination reason: Refutation
% 2.23/0.60 % (1266027)Time elapsed: 0.107 s
% 2.23/0.60 % (1266027)Peak memory usage: 16 MB
% 2.23/0.60 % (1266027)Instructions burned: 209 (million)
% 2.23/0.60 % (1265980)Success in time 0.397 s
% 2.23/0.60 % Vampire exiting
%------------------------------------------------------------------------------