%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP177^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n005.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 08:11:00 AM UTC 2026
% Result : Theorem 3.21s 0.73s
% Output : Refutation 3.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP177^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n005.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 20:05:46 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 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
% 3.21/0.73 % (2141734)Will run a generic schedule for satisfiability detection.
% 3.21/0.73 % (2141744)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1900294887:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 3.21/0.73 % (2141740)% WARNING: option uhcvi not known.
% 3.21/0.73 % (2141740)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=912048429:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 3.21/0.73 % (2141739)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3796237345_2999 on theBenchmark for (2999ds/0Mi)
% 3.21/0.73 % (2141741)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3592645601:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 3.21/0.73 % (2141743)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3751799610:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 3.21/0.73 % (2141745)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3264998591:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 3.21/0.73 % (2141742)dis+10_1_sil=32000:sp=arity:random_seed=3695454121:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 3.21/0.73 % (2141740)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.21/0.73 % (2141743)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.21/0.73 % (2141744)Instruction limit reached!
% 3.21/0.73 % (2141744)------------------------------
% 3.21/0.73 % (2141744)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.21/0.73 % (2141744)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.21/0.73 % (2141744)CaDiCaL version: 2.1.3
% 3.21/0.73 % (2141744)Termination reason: Instruction limit
% 3.21/0.73 % (2141744)Termination phase: Saturation
% 3.21/0.73 % (2141744)Time elapsed: 0.031 s
% 3.21/0.73 % (2141744)Peak memory usage: 13 MB
% 3.21/0.73 % (2141744)Instructions burned: 131 (million)
% 3.21/0.73 % (2141753)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1063203870:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 3.21/0.73 % (2141742)Instruction limit reached!
% 3.21/0.73 % (2141742)------------------------------
% 3.21/0.73 % (2141742)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.21/0.73 % (2141742)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.21/0.73 % (2141742)CaDiCaL version: 2.1.3
% 3.21/0.73 % (2141742)Termination reason: Instruction limit
% 3.21/0.73 % (2141742)Termination phase: Property scanning
% 3.21/0.73 % (2141742)Time elapsed: 0.046 s
% 3.21/0.73 % (2141742)Peak memory usage: 11 MB
% 3.21/0.73 % (2141742)Instructions burned: 104 (million)
% 3.21/0.73 % (2141743)Instruction limit reached!
% 3.21/0.73 % (2141743)------------------------------
% 3.21/0.73 % (2141743)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.21/0.73 % (2141743)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.21/0.73 % (2141743)CaDiCaL version: 2.1.3
% 3.21/0.73 % (2141743)Termination reason: Instruction limit
% 3.21/0.73 % (2141743)Termination phase: Property scanning
% 3.21/0.73 % (2141743)Time elapsed: 0.051 s
% 3.21/0.73 % (2141743)Peak memory usage: 11 MB
% 3.21/0.73 % (2141743)Instructions burned: 116 (million)
% 3.21/0.73 % Exception at run slice level
% 3.21/0.73 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.21/0.73 % (2141740)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.21/0.73 % Exception at run slice level
% 3.21/0.73 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.21/0.73 % (2141755)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2859126471:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 3.21/0.73 % (2141756)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=3367829397:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 3.21/0.73 % (2141757)ott-21_1_sil=16000:fs=off:random_seed=2141234322:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 3.21/0.73 % (2141758)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3521493602:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 3.21/0.73 % (2141745)Instruction limit reached!
% 3.21/0.73 % (2141745)------------------------------
% 3.21/0.73 % (2141745)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.21/0.73 % (2141745)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.21/0.73 % (2141745)CaDiCaL version: 2.1.3
% 3.21/0.73 % (2141745)Termination reason: Instruction limit
% 3.21/0.73 % (2141745)Termination phase: Saturation
% 3.21/0.73 % (2141745)Time elapsed: 0.088 s
% 3.21/0.73 % (2141745)Peak memory usage: 12 MB
% 3.21/0.73 % (2141745)Instructions burned: 159 (million)
% 3.21/0.73 % (2141756)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.21/0.73 % (2141763)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=684559863:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 3.21/0.73 % (2141755)Instruction limit reached!
% 3.21/0.73 % (2141755)------------------------------
% 3.21/0.73 % (2141755)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.21/0.73 % (2141755)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.21/0.73 % (2141755)CaDiCaL version: 2.1.3
% 3.21/0.73 % (2141755)Termination reason: Instruction limit
% 3.21/0.73 % (2141755)Termination phase: Saturation
% 3.21/0.73 % (2141755)Time elapsed: 0.058 s
% 3.21/0.73 % (2141755)Peak memory usage: 13 MB
% 3.21/0.73 % (2141755)Instructions burned: 133 (million)
% 3.21/0.73 % (2141756)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.21/0.73 % (2141765)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=2534717014:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 3.21/0.73 % (2141757)Instruction limit reached!
% 3.21/0.73 % (2141757)------------------------------
% 3.21/0.73 % (2141757)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.21/0.73 % (2141757)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.21/0.73 % (2141757)CaDiCaL version: 2.1.3
% 3.21/0.73 % (2141757)Termination reason: Instruction limit
% 3.21/0.73 % (2141757)Termination phase: Saturation
% 3.21/0.73 % (2141757)Time elapsed: 0.085 s
% 3.21/0.73 % (2141757)Peak memory usage: 13 MB
% 3.21/0.73 % (2141757)Instructions burned: 180 (million)
% 3.21/0.73 % (2141767)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=552503270:i=889:ins=1_2997 on theBenchmark for (2997ds/889Mi)
% 3.21/0.73 % Exception at run slice level
% 3.21/0.73 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.21/0.73 % (2141758)Instruction limit reached!
% 3.21/0.73 % (2141758)------------------------------
% 3.21/0.73 % (2141758)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.21/0.73 % (2141758)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.21/0.73 % (2141758)CaDiCaL version: 2.1.3
% 3.21/0.73 % (2141758)Termination reason: Instruction limit
% 3.21/0.73 % (2141758)Termination phase: Saturation
% 3.21/0.73 % (2141758)Time elapsed: 0.129 s
% 3.21/0.73 % (2141758)Peak memory usage: 14 MB
% 3.21/0.73 % (2141758)Instructions burned: 478 (million)
% 3.21/0.73 % (2141770)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=3402095909:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 3.21/0.73 % (2141769)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=1968890805: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)
% 3.21/0.73 % (2141770)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.21/0.73 % Exception at run slice level
% 3.21/0.73 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.21/0.73 % (2141773)fmb+10_1_sil=64000:random_seed=1207048623:i=22061:nm=2:gsp=on_2997 on theBenchmark for (2997ds/22061Mi)
% 3.21/0.73 % (2141769)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.21/0.73 % (2141773)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.21/0.73 % Exception at run slice level
% 3.21/0.73 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.21/0.73 % (2141775)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=320796951:i=9515:nm=5_2996 on theBenchmark for (2996ds/9515Mi)
% 3.21/0.73 % (2141756)Instruction limit reached!
% 3.21/0.73 % (2141756)------------------------------
% 3.21/0.73 % (2141756)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.21/0.73 % (2141756)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.21/0.73 % (2141756)CaDiCaL version: 2.1.3
% 3.21/0.73 % (2141756)Termination reason: Instruction limit
% 3.21/0.73 % (2141756)Termination phase: Saturation
% 3.21/0.73 % (2141756)Time elapsed: 0.324 s
% 3.21/0.73 % (2141756)Peak memory usage: 16 MB
% 3.21/0.73 % (2141756)Instructions burned: 685 (million)
% 3.21/0.73 % Exception at run slice level
% 3.21/0.73 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.21/0.73 % (2141777)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=1597576507:fmbsr=1.7:i=920_2995 on theBenchmark for (2995ds/920Mi)
% 3.21/0.73 % (2141778)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=4072505472:i=5131_2995 on theBenchmark for (2995ds/5131Mi)
% 3.21/0.73 % (2141778)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.21/0.73 % (2141769) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2141734-2141769"...
% 3.21/0.73 % (2141769)...printing done.
% 3.21/0.73 % (2141769)Refutation found. Thanks to Tanya!
% 3.21/0.73 % SZS status Theorem for theBenchmark
% 3.21/0.73 % SZS output start Proof for theBenchmark
% 3.21/0.73 thf(type_def_5, type, standard_Constant: $tType > $tType).
% 3.21/0.73 thf(type_def_6, type, allegorical_term: $tType > $tType).
% 3.21/0.73 thf(type_def_7, type, labeled_graph: ($tType * $tType) > $tType).
% 3.21/0.73 thf(type_def_8, type, product_prod: ($tType * $tType) > $tType).
% 3.21/0.73 thf(type_def_9, type, set: $tType > $tType).
% 3.21/0.73 thf(type_def_10, type, nat: $tType).
% 3.21/0.73 thf(type_def_11, type, itself: $tType > $tType).
% 3.21/0.73 thf(type_def_12, type, b: $tType).
% 3.21/0.73 thf(type_def_13, type, a: $tType).
% 3.21/0.73 thf(type_def_14, type, sTfun: ($tType * $tType) > $tType).
% 3.21/0.73 thf(func_def_0, type, bNF_Gr: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > X1) > set @ product_prod @ X0 @ X1))).
% 3.21/0.73 thf(func_def_1, type, equiv_congruent: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X0 > (X0 > X1) > $o))).
% 3.21/0.73 thf(func_def_2, type, equiv_equiv: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > $o))).
% 3.21/0.73 thf(func_def_3, type, equiv_proj: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X1 > X0 > set @ X1))).
% 3.21/0.73 thf(func_def_4, type, hilbert_Eps: !>[X0: $tType]:(((X0 > $o) > X0))).
% 3.21/0.73 thf(func_def_5, type, if: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 3.21/0.73 thf(func_def_6, type, standard_S_Idt: !>[X0: $tType]:(standard_Constant @ X0)).
% 3.21/0.73 thf(func_def_7, type, getRel: !>[X0: $tType, X1: $tType]:((X0 > labeled_graph @ X0 @ X1 > set @ product_prod @ X1 @ X1))).
% 3.21/0.73 thf(func_def_8, type, semantics: !>[X0: $tType, X1: $tType]:((labeled_graph @ X0 @ X1 > allegorical_term @ X0 > set @ product_prod @ X1 @ X1))).
% 3.21/0.73 thf(func_def_9, type, edge_preserving: !>[X0: $tType, X1: $tType, X2: $tType]:((set @ product_prod @ X0 @ X1 > set @ product_prod @ X2 @ product_prod @ X0 @ X0 > set @ product_prod @ X2 @ product_prod @ X1 @ X1 > $o))).
% 3.21/0.73 thf(func_def_10, type, graph_homomorphism: !>[X0: $tType, X1: $tType, X2: $tType]:((labeled_graph @ X0 @ X1 > labeled_graph @ X0 @ X2 > set @ product_prod @ X1 @ X2 > $o))).
% 3.21/0.73 thf(func_def_11, type, graph_union: !>[X0: $tType, X1: $tType]:((labeled_graph @ X0 @ X1 > labeled_graph @ X0 @ X1 > labeled_graph @ X0 @ X1))).
% 3.21/0.73 thf(func_def_12, type, labeled_LG: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ product_prod @ X1 @ X1 > set @ X1 > labeled_graph @ X0 @ X1))).
% 3.21/0.73 thf(func_def_13, type, labele1974067554_graph: !>[X0: $tType, X1: $tType, X2: $tType]:(((set @ product_prod @ X0 @ product_prod @ X1 @ X1 > set @ X1 > X2) > labeled_graph @ X0 @ X1 > X2))).
% 3.21/0.73 thf(func_def_14, type, labeled_edges: !>[X0: $tType, X1: $tType]:((labeled_graph @ X0 @ X1 > set @ product_prod @ X0 @ product_prod @ X1 @ X1))).
% 3.21/0.73 thf(func_def_15, type, labeled_vertices: !>[X0: $tType, X1: $tType]:((labeled_graph @ X0 @ X1 > set @ X1))).
% 3.21/0.73 thf(func_def_16, type, map_graph: !>[X0: $tType, X1: $tType, X2: $tType]:((set @ product_prod @ X0 @ X1 > labeled_graph @ X2 @ X0 > labeled_graph @ X2 @ X1))).
% 3.21/0.73 thf(func_def_17, type, restrict: !>[X0: $tType, X1: $tType]:((labeled_graph @ X0 @ X1 > labeled_graph @ X0 @ X1))).
% 3.21/0.73 thf(func_def_18, type, bot_bot: !>[X0: $tType]:(X0)).
% 3.21/0.73 thf(func_def_19, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 3.21/0.73 thf(func_def_20, type, product_Pair: !>[X0: $tType, X1: $tType]:((X0 > X1 > product_prod @ X0 @ X1))).
% 3.21/0.73 thf(func_def_21, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 3.21/0.73 thf(func_def_22, type, id_on: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0))).
% 3.21/0.73 thf(func_def_23, type, image: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X1 > set @ X0 > set @ X1))).
% 3.21/0.73 thf(func_def_24, type, refl_on: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > $o))).
% 3.21/0.73 thf(func_def_25, type, relcomp: !>[X0: $tType, X1: $tType, X2: $tType]:((set @ product_prod @ X0 @ X1 > set @ product_prod @ X1 @ X2 > set @ product_prod @ X0 @ X2))).
% 3.21/0.73 thf(func_def_26, type, agree_on: !>[X0: $tType, X1: $tType, X2: $tType]:((labeled_graph @ X0 @ X1 > set @ product_prod @ X1 @ X2 > set @ product_prod @ X1 @ X2 > $o))).
% 3.21/0.73 thf(func_def_27, type, consequence_graph: !>[X0: $tType, X1: $tType, X2: $tType]:((set @ product_prod @ labeled_graph @ X0 @ X1 @ labeled_graph @ X0 @ X1 > labeled_graph @ X0 @ X2 > $o))).
% 3.21/0.73 thf(func_def_28, type, extensible: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ labeled_graph @ X0 @ X1 @ labeled_graph @ X0 @ X1 > labeled_graph @ X0 @ X2 > set @ product_prod @ X1 @ X2 > $o))).
% 3.21/0.73 thf(func_def_29, type, least: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((itself @ X0 > set @ product_prod @ labeled_graph @ X1 @ X2 @ labeled_graph @ X1 @ X2 > labeled_graph @ X1 @ X3 > labeled_graph @ X1 @ X3 > $o))).
% 3.21/0.73 thf(func_def_30, type, least_559130134_graph: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((itself @ X0 > set @ product_prod @ labeled_graph @ X1 @ X2 @ labeled_graph @ X1 @ X2 > labeled_graph @ X1 @ X3 > labeled_graph @ X1 @ X3 > $o))).
% 3.21/0.73 thf(func_def_31, type, maintained: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ labeled_graph @ X0 @ X1 @ labeled_graph @ X0 @ X1 > labeled_graph @ X0 @ X2 > $o))).
% 3.21/0.73 thf(func_def_32, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 3.21/0.73 thf(func_def_33, type, image2: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > set @ X1))).
% 3.21/0.73 thf(func_def_34, type, insert: !>[X0: $tType]:((X0 > set @ X0 > set @ X0))).
% 3.21/0.73 thf(func_def_35, type, the_elem: !>[X0: $tType]:((set @ X0 > X0))).
% 3.21/0.73 thf(func_def_36, type, standa2002409347_rules: !>[X0: $tType]:((set @ standard_Constant @ X0 > set @ product_prod @ labeled_graph @ standard_Constant @ X0 @ nat @ labeled_graph @ standard_Constant @ X0 @ nat))).
% 3.21/0.73 thf(func_def_37, type, standa244753842y_rule: !>[X0: $tType]:(product_prod @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat)).
% 3.21/0.73 thf(func_def_38, type, standa245363227y_rule: !>[X0: $tType]:((X0 > product_prod @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat))).
% 3.21/0.73 thf(func_def_39, type, standa1805702094y_rule: !>[X0: $tType]:((X0 > product_prod @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat))).
% 3.21/0.73 thf(func_def_40, type, standa2114124375e_rule: !>[X0: $tType]:((X0 > product_prod @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat))).
% 3.21/0.73 thf(func_def_41, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 3.21/0.73 thf(func_def_42, type, g: labeled_graph @ standard_Constant @ a @ b).
% 3.21/0.73 thf(func_def_43, type, l: set @ standard_Constant @ a).
% 3.21/0.73 thf(func_def_44, type, p: (b > b > $o)).
% 3.21/0.73 thf(func_def_45, type, f: (b > b)).
% 3.21/0.73 thf(func_def_46, type, l2: standard_Constant @ a).
% 3.21/0.73 thf(func_def_47, type, x: b).
% 3.21/0.73 thf(func_def_48, type, y: b).
% 3.21/0.73 thf(func_def_52, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 3.21/0.73 thf(func_def_53, type, vAND: ($o > $o > $o)).
% 3.21/0.73 thf(func_def_54, type, db0: !>[X0: $tType]:(X0)).
% 3.21/0.73 thf(func_def_55, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 3.21/0.73 thf(func_def_56, type, vIMP: ($o > $o > $o)).
% 3.21/0.73 thf(func_def_57, type, db2: !>[X0: $tType]:(X0)).
% 3.21/0.73 thf(func_def_58, type, db3: !>[X0: $tType]:(X0)).
% 3.21/0.73 thf(func_def_59, type, db1: !>[X0: $tType]:(X0)).
% 3.21/0.73 thf(func_def_60, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 3.21/0.73 thf(func_def_61, type, vNOT: ($o > $o)).
% 3.21/0.73 thf(func_def_62, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 3.21/0.73 thf(func_def_63, type, vOR: ($o > $o > $o)).
% 3.21/0.73 thf(func_def_64, type, sP0: !>[X0: $tType, X1: $tType, X2: $tType]:((labeled_graph @ X2 @ X1 > (X1 > X0) > set @ product_prod @ X2 @ product_prod @ X0 @ X0 > $o))).
% 3.21/0.73 thf(func_def_65, type, sP1: !>[X0: $tType, X1: $tType, X2: $tType]:((set @ product_prod @ X1 @ X2 > set @ product_prod @ X2 @ X0 > (X1 > X0 > $o) > $o))).
% 3.21/0.73 thf(func_def_66, type, sP2: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ X0 > set @ product_prod @ X2 @ X1 > set @ product_prod @ X1 @ X0 > $o))).
% 3.21/0.73 thf(func_def_67, type, sP3: !>[X0: $tType]:((set @ X0 > (X0 > $o) > (X0 > $o) > $o))).
% 3.21/0.73 thf(func_def_68, type, sK4: !>[X0: $tType, X1: $tType, X2: $tType]:(((X1 > X0) > (X1 > X0) > labeled_graph @ X2 @ X1 > X1))).
% 3.21/0.73 thf(func_def_69, type, sK5: !>[X0: $tType, X1: $tType]:(((labeled_graph @ X1 @ X0 > $o) > set @ product_prod @ X1 @ product_prod @ X0 @ X0))).
% 3.21/0.73 thf(func_def_70, type, sK6: !>[X0: $tType, X1: $tType]:(((labeled_graph @ X1 @ X0 > $o) > set @ X0))).
% 3.21/0.73 thf(func_def_71, type, sK7: !>[X0: $tType, X1: $tType]:((labeled_graph @ X0 @ X1 > set @ product_prod @ X0 @ product_prod @ X1 @ X1))).
% 3.21/0.73 thf(func_def_72, type, sK8: !>[X0: $tType, X1: $tType]:((labeled_graph @ X0 @ X1 > set @ X1))).
% 3.21/0.73 thf(func_def_73, type, sK9: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 3.21/0.73 thf(func_def_74, type, sK10: !>[X0: $tType]:((set @ X0 > product_prod @ X0 @ X0 > X0))).
% 3.21/0.73 thf(func_def_75, type, sK11: !>[X0: $tType, X1: $tType, X2: $tType]:((labeled_graph @ X2 @ X1 > (X1 > X0) > set @ product_prod @ X2 @ product_prod @ X0 @ X0 > X2))).
% 3.21/0.73 thf(func_def_76, type, sK12: !>[X0: $tType, X1: $tType, X2: $tType]:((labeled_graph @ X2 @ X1 > (X1 > X0) > set @ product_prod @ X2 @ product_prod @ X0 @ X0 > X1))).
% 3.21/0.73 thf(func_def_77, type, sK13: !>[X0: $tType, X1: $tType, X2: $tType]:((labeled_graph @ X2 @ X1 > (X1 > X0) > set @ product_prod @ X2 @ product_prod @ X0 @ X0 > X1))).
% 3.21/0.73 thf(func_def_78, type, sK14: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 3.21/0.73 thf(func_def_79, type, sK15: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 3.21/0.73 thf(func_def_80, type, sK16: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 3.21/0.73 thf(func_def_81, type, sK17: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 3.21/0.73 thf(func_def_82, type, sK18: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 3.21/0.73 thf(func_def_83, type, sK19: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 3.21/0.73 thf(func_def_84, type, sK20: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 3.21/0.73 thf(func_def_85, type, sK21: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 3.21/0.73 thf(func_def_86, type, sK22: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X0))).
% 3.21/0.73 thf(func_def_87, type, sK23: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X1))).
% 3.21/0.73 thf(func_def_88, type, sK24: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X2))).
% 3.21/0.73 thf(func_def_89, type, sK25: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X0))).
% 3.21/0.73 thf(func_def_90, type, sK26: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X1))).
% 3.21/0.73 thf(func_def_91, type, sK27: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X2))).
% 3.21/0.73 thf(func_def_92, type, sK28: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X3))).
% 3.21/0.73 thf(func_def_93, type, sK29: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X0))).
% 3.21/0.73 thf(func_def_94, type, sK30: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X1))).
% 3.21/0.73 thf(func_def_95, type, sK31: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X2))).
% 3.21/0.73 thf(func_def_96, type, sK32: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X3))).
% 3.21/0.73 thf(func_def_97, type, sK33: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X4))).
% 3.21/0.73 thf(func_def_98, type, sK34: !>[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))).
% 3.21/0.73 thf(func_def_99, type, sK35: !>[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))).
% 3.21/0.73 thf(func_def_100, type, sK36: !>[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))).
% 3.21/0.73 thf(func_def_101, type, sK37: !>[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))).
% 3.21/0.73 thf(func_def_102, type, sK38: !>[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))).
% 3.21/0.73 thf(func_def_103, type, sK39: !>[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))).
% 3.21/0.73 thf(func_def_104, type, sK40: !>[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))).
% 3.21/0.73 thf(func_def_105, type, sK41: !>[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))).
% 3.21/0.73 thf(func_def_106, type, sK42: !>[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))).
% 3.21/0.73 thf(func_def_107, type, sK43: !>[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))).
% 3.21/0.73 thf(func_def_108, type, sK44: !>[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))).
% 3.21/0.73 thf(func_def_109, type, sK45: !>[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))).
% 3.21/0.73 thf(func_def_110, type, sK46: !>[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))).
% 3.21/0.73 thf(func_def_111, type, sK47: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 3.21/0.73 thf(func_def_112, type, sK48: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 3.21/0.73 thf(func_def_113, type, sK49: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 3.21/0.73 thf(func_def_114, type, sK50: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3))).
% 3.21/0.73 thf(func_def_115, type, sK51: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 3.21/0.73 thf(func_def_116, type, sK52: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 3.21/0.73 thf(func_def_117, type, sK53: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 3.21/0.73 thf(func_def_118, 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))).
% 3.21/0.73 thf(func_def_119, 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))).
% 3.21/0.73 thf(func_def_120, 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))).
% 3.21/0.73 thf(func_def_121, 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))).
% 3.21/0.73 thf(func_def_122, 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))).
% 3.21/0.73 thf(func_def_123, type, sK59: !>[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))).
% 3.21/0.73 thf(func_def_124, type, sK60: !>[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))).
% 3.21/0.73 thf(func_def_125, type, sK61: !>[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))).
% 3.21/0.73 thf(func_def_126, type, sK62: !>[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))).
% 3.21/0.73 thf(func_def_127, type, sK63: !>[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))).
% 3.21/0.73 thf(func_def_128, type, sK64: !>[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))).
% 3.21/0.73 thf(func_def_129, type, sK65: !>[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))).
% 3.21/0.73 thf(func_def_130, type, sK66: !>[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))).
% 3.21/0.73 thf(func_def_131, type, sK67: !>[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))).
% 3.21/0.73 thf(func_def_132, 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) > X3))).
% 3.21/0.73 thf(func_def_133, 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) > X2))).
% 3.21/0.73 thf(func_def_134, 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) > X1))).
% 3.21/0.73 thf(func_def_135, 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) > X0))).
% 3.21/0.73 thf(func_def_136, type, sK72: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((labeled_graph @ X3 @ X2 > labeled_graph @ X3 @ X2 > set @ product_prod @ labeled_graph @ X3 @ X1 @ labeled_graph @ X3 @ X1 > labeled_graph @ X3 @ X0))).
% 3.21/0.73 thf(func_def_137, type, sK73: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((set @ product_prod @ labeled_graph @ X3 @ X1 @ labeled_graph @ X3 @ X1 > labeled_graph @ X3 @ X2 > labeled_graph @ X3 @ X2 > labeled_graph @ X3 @ X0))).
% 3.21/0.73 thf(func_def_138, type, sK74: !>[X0: $tType, X1: $tType, X2: $tType]:((labeled_graph @ X2 @ X0 > labeled_graph @ X2 @ X1 > labeled_graph @ X2 @ X0 > set @ product_prod @ X0 @ X1))).
% 3.21/0.73 thf(func_def_139, type, sK75: !>[X0: $tType, X1: $tType]:((set @ X1 > set @ product_prod @ X1 @ X0 > X0 > X1))).
% 3.21/0.73 thf(func_def_140, type, sK76: !>[X0: $tType, X1: $tType, X2: $tType]:((set @ product_prod @ X1 @ X2 > set @ product_prod @ X2 @ X0 > (X1 > X0 > $o) > X1))).
% 3.21/0.73 thf(func_def_141, type, sK77: !>[X0: $tType, X1: $tType, X2: $tType]:((set @ product_prod @ X1 @ X2 > set @ product_prod @ X2 @ X0 > (X1 > X0 > $o) > X2))).
% 3.21/0.73 thf(func_def_142, type, sK78: !>[X0: $tType, X1: $tType, X2: $tType]:((set @ product_prod @ X1 @ X2 > set @ product_prod @ X2 @ X0 > (X1 > X0 > $o) > X0))).
% 3.21/0.73 thf(func_def_143, type, sK79: !>[X0: $tType, X1: $tType, X2: $tType]:((set @ product_prod @ X2 @ X1 > set @ product_prod @ X0 @ X2 > X1 > X0 > X2))).
% 3.21/0.73 thf(func_def_144, type, sK80: !>[X0: $tType, X1: $tType, X2: $tType]:((set @ product_prod @ X2 @ X1 > set @ product_prod @ X0 @ X2 > X1 > X0 > X2))).
% 3.21/0.73 thf(func_def_145, type, sK81: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ X0 > set @ product_prod @ X2 @ X1 > set @ product_prod @ X1 @ X0 > X2))).
% 3.21/0.73 thf(func_def_146, type, sK82: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ X0 > set @ product_prod @ X2 @ X1 > set @ product_prod @ X1 @ X0 > X1))).
% 3.21/0.73 thf(func_def_147, type, sK83: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ X0 > set @ product_prod @ X2 @ X1 > set @ product_prod @ X1 @ X0 > X0))).
% 3.21/0.73 thf(func_def_148, type, sK84: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > set @ product_prod @ X1 @ X0 > X1))).
% 3.21/0.73 thf(func_def_149, type, sK85: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > set @ product_prod @ X1 @ X0 > X0))).
% 3.21/0.73 thf(func_def_150, type, sK86: !>[X0: $tType, X1: $tType, X2: $tType]:((set @ product_prod @ X2 @ X1 > labeled_graph @ X0 @ X1 > labeled_graph @ X0 @ X2 > set @ product_prod @ X2 @ X1))).
% 3.21/0.73 thf(func_def_151, type, sK87: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 3.21/0.73 thf(func_def_152, type, sK88: !>[X0: $tType]:((set @ X0 > X0))).
% 3.21/0.73 thf(func_def_153, type, sK89: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 3.21/0.73 thf(func_def_154, type, sK90: !>[X0: $tType]:((set @ X0 > X0 > set @ X0))).
% 3.21/0.73 thf(func_def_155, type, sK91: !>[X0: $tType]:((set @ X0 > X0 > set @ X0))).
% 3.21/0.73 thf(func_def_156, type, sK92: !>[X0: $tType, X1: $tType]:((X1 > labeled_graph @ X1 @ X0 > product_prod @ labeled_graph @ X1 @ nat @ labeled_graph @ X1 @ nat))).
% 3.21/0.73 thf(func_def_157, type, sK93: !>[X0: $tType]:((set @ X0 > (X0 > $o) > (X0 > $o) > X0))).
% 3.21/0.73 thf(func_def_158, type, sK94: !>[X0: $tType]:(((X0 > $o) > set @ X0 > X0))).
% 3.21/0.73 thf(func_def_159, type, sK95: !>[X0: $tType]:((X0 > set @ X0 > X0 > set @ X0 > set @ X0))).
% 3.21/0.73 thf(func_def_160, type, sK96: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 3.21/0.73 thf(func_def_161, type, sK97: !>[X0: $tType]:((set @ X0 > X0))).
% 3.21/0.73 thf(func_def_162, type, sK98: !>[X0: $tType]:((set @ X0 > X0))).
% 3.21/0.73 thf(func_def_163, type, sK99: !>[X0: $tType]:(((X0 > $o) > X0))).
% 3.21/0.73 thf(func_def_164, type, sK100: !>[X0: $tType]:(((X0 > $o) > X0))).
% 3.21/0.73 thf(func_def_165, type, sK101: !>[X0: $tType, X1: $tType, X2: $tType]:((labeled_graph @ X0 @ X1 > set @ product_prod @ X1 @ X2 > set @ product_prod @ X1 @ X2 > X1))).
% 3.21/0.73 thf(func_def_166, type, sK102: !>[X0: $tType, X1: $tType, X2: $tType]:((labeled_graph @ X0 @ X1 > set @ product_prod @ X1 @ X2 > set @ product_prod @ X1 @ X2 > X1))).
% 3.21/0.73 thf(func_def_167, type, sK103: !>[X0: $tType, X1: $tType, X2: $tType]:((labeled_graph @ X0 @ X2 > set @ product_prod @ X2 @ X1 > set @ product_prod @ X2 @ X1 > X2))).
% 3.21/0.73 thf(func_def_168, type, sK104: !>[X0: $tType, X1: $tType, X2: $tType]:((labeled_graph @ X0 @ X1 > set @ product_prod @ X1 @ X2 > set @ product_prod @ X1 @ X2 > X1))).
% 3.21/0.73 thf(func_def_169, type, sK105: !>[X0: $tType, X1: $tType, X2: $tType]:((labeled_graph @ X0 @ X1 > set @ product_prod @ X1 @ X2 > set @ product_prod @ X1 @ X2 > X1))).
% 3.21/0.73 thf(func_def_170, type, sK106: !>[X0: $tType, X1: $tType, X2: $tType]:((set @ product_prod @ X0 @ X1 > X0 > X2 > set @ product_prod @ X1 @ X2 > X2))).
% 3.21/0.73 thf(func_def_171, type, sK107: !>[X0: $tType, X1: $tType, X2: $tType]:((X1 > X2 > set @ product_prod @ X0 @ X2 > set @ product_prod @ X1 @ X0 > X0))).
% 3.21/0.73 thf(func_def_172, type, sK108: !>[X0: $tType, X1: $tType, X2: $tType]:((X1 > X2 > set @ product_prod @ X0 @ X2 > set @ product_prod @ X1 @ X0 > X1))).
% 3.21/0.73 thf(func_def_173, type, sK109: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > set @ X1 > X0 > X1))).
% 3.21/0.73 thf(func_def_174, type, db5: !>[X0: $tType]:(X0)).
% 3.21/0.73 thf(func_def_175, type, db4: !>[X0: $tType]:(X0)).
% 3.21/0.73 thf(func_def_176, type, sK110: !>[X0: $tType, X1: $tType, X2: $tType]:((labeled_graph @ X0 @ X1 > set @ product_prod @ X1 @ X2 > set @ product_prod @ X1 @ X2 > X1))).
% 3.21/0.73 thf(f3,axiom,(
% 3.21/0.73 (member @ b @ (f @ x) @ (labeled_vertices @ standard_Constant @ a @ b @ g))),
% 3.21/0.73 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_fv_I1_J)).
% 3.21/0.73 thf(f113,axiom,(
% 3.21/0.73 (f = (^[X0 : b] : ((if @ b @ (((image @ b @ b @ (getRel @ standard_Constant @ a @ b @ standard_S_Idt @ a @ g) @ (insert @ b @ X0 @ bot_bot @ set @ b))) = bot_bot @ set @ b) @ X0 @ (hilbert_Eps @ b @ (p @ X0))))))),
% 3.21/0.73 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112__092_060open_062f_A_092_060equiv_062_A_092_060lambda_062x_O_Aif_AgetRel_AS__Idt_AG_A_096_096_A_123x_125_A_061_A_123_125_Athen_Ax_Aelse_AEps_A_IP_Ax_J_092_060close_062)).
% 3.21/0.73 thf(f131,axiom,(
% 3.21/0.73 ! [X0 : b] : ((((image @ b @ b @ (getRel @ standard_Constant @ a @ b @ standard_S_Idt @ a @ g) @ (insert @ b @ X0 @ bot_bot @ set @ b))) = bot_bot @ set @ b) = ~(member @ b @ X0 @ (labeled_vertices @ standard_Constant @ a @ b @ g)))),
% 3.21/0.73 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_r2)).
% 3.21/0.73 thf(f236,axiom,(
% 3.21/0.73 (p = (^[X0 : b, X1 : b] : ((member @ b @ X1 @ (image @ b @ b @ (getRel @ standard_Constant @ a @ b @ standard_S_Idt @ a @ g) @ (insert @ b @ X0 @ bot_bot @ set @ b))))))),
% 3.21/0.73 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_P)).
% 3.21/0.73 thf(f238,axiom,(
% 3.21/0.73 ! [X0 : $tType] : (insert @ X0 = (^[X1 : X0, X2 : set @ X0] : ((collect @ X0 @ (^[X3 : X0] : ((member @ X0 @ X3 @ X2) | (X3 = X1)))))))),
% 3.21/0.73 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_insert__compr)).
% 3.21/0.73 thf(f242,axiom,(
% 3.21/0.73 ! [X0 : $tType,X1 : $tType,X2 : set @ product_prod @ X0 @ X1,X3 : X0] : (((image @ X0 @ X1 @ X2 @ (insert @ X0 @ X3 @ bot_bot @ set @ X0))) = ((collect @ X1 @ (^[X4 : X1] : ((member @ product_prod @ X0 @ X1 @ (product_Pair @ X0 @ X1 @ X3 @ X4) @ X2))))))),
% 3.21/0.73 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_Image__singleton)).
% 3.21/0.73 thf(f244,axiom,(
% 3.21/0.73 ! [X0 : $tType,X1 : $tType] : (labeled_vertices @ X1 @ X0 = ((labele1974067554_graph @ X1 @ X0 @ set @ X0 @ (^[X2 : set @ product_prod @ X1 @ product_prod @ X0 @ X0, X3 : set @ X0] : (X3)))))),
% 3.21/0.73 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_vertices__def)).
% 3.21/0.73 thf(f257,axiom,(
% 3.21/0.73 ! [X0 : $o] : ((X0 = $false) | (X0 = $true))),
% 3.21/0.73 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_T)).
% 3.21/0.73 thf(f259,axiom,(
% 3.21/0.73 ! [X0 : $tType,X1 : X0,X2 : X0] : (((if @ X0 @ $true @ X1 @ X2)) = X1)),
% 3.21/0.73 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_T)).
% 3.21/0.73 thf(f260,conjecture,(
% 3.21/0.73 (member @ b @ x @ (labeled_vertices @ standard_Constant @ a @ b @ g))),
% 3.21/0.73 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 3.21/0.73 thf(f261,negated_conjecture,(
% 3.21/0.73 ~(member @ b @ x @ (labeled_vertices @ standard_Constant @ a @ b @ g))),
% 3.21/0.73 inference(negated_conjecture,[status(cth)],[f260])).
% 3.21/0.73 thf(f266,plain,(
% 3.21/0.73 (member @ b @ (f @ x) @ (labeled_vertices @ standard_Constant @ a @ b @ g))),
% 3.21/0.73 inference(rectify,[],[f3])).
% 3.21/0.73 thf(f267,plain,(
% 3.21/0.73 (((member @ b @ (f @ x) @ (labeled_vertices @ standard_Constant @ a @ b @ g))) = $true)),
% 3.21/0.73 inference(fool_elimination,[],[f266])).
% 3.21/0.73 thf(f419,plain,(
% 3.21/0.73 (f = (^[X0 : b] : ((if @ b @ (((image @ b @ b @ (getRel @ standard_Constant @ a @ b @ standard_S_Idt @ a @ g) @ (insert @ b @ X0 @ bot_bot @ set @ b))) = bot_bot @ set @ b) @ X0 @ (hilbert_Eps @ b @ (p @ X0))))))),
% 3.21/0.73 inference(rectify,[],[f113])).
% 3.21/0.73 thf(f420,plain,(
% 3.21/0.73 (f = (^[Y0 : b]: (if @ b @ (bot_bot @ set @ b = (image @ b @ b @ (getRel @ standard_Constant @ a @ b @ standard_S_Idt @ a @ g) @ (insert @ b @ Y0 @ bot_bot @ set @ b))) @ Y0 @ (hilbert_Eps @ b @ (p @ Y0)))))),
% 3.21/0.73 inference(fool_elimination,[],[f419])).
% 3.21/0.73 thf(f435,plain,(
% 3.21/0.73 ! [X0 : b] : ((((image @ b @ b @ (getRel @ standard_Constant @ a @ b @ standard_S_Idt @ a @ g) @ (insert @ b @ X0 @ bot_bot @ set @ b))) = bot_bot @ set @ b) = ~(member @ b @ X0 @ (labeled_vertices @ standard_Constant @ a @ b @ g)))),
% 3.21/0.73 inference(rectify,[],[f131])).
% 3.21/0.73 thf(f436,plain,(
% 3.21/0.73 ! [X0 : b] : (((bot_bot @ set @ b = (image @ b @ b @ (getRel @ standard_Constant @ a @ b @ standard_S_Idt @ a @ g) @ (insert @ b @ X0 @ bot_bot @ set @ b)))) = ((~ (member @ b @ X0 @ (labeled_vertices @ standard_Constant @ a @ b @ g)))))),
% 3.21/0.73 inference(fool_elimination,[],[f435])).
% 3.21/0.73 thf(f619,plain,(
% 3.21/0.73 (p = (^[Y0 : b]: ((^[Y1 : b]: (member @ b @ Y1 @ (image @ b @ b @ (getRel @ standard_Constant @ a @ b @ standard_S_Idt @ a @ g) @ (insert @ b @ Y0 @ bot_bot @ set @ b)))))))),
% 3.21/0.73 inference(fool_elimination,[],[f236])).
% 3.21/0.73 thf(f622,plain,(
% 3.21/0.73 ! [X0 : $tType] : (insert @ X0 = (^[X1 : X0, X2 : set @ X0] : ((collect @ X0 @ (^[X3 : X0] : ((member @ X0 @ X3 @ X2) | (X3 = X1)))))))),
% 3.21/0.73 inference(rectify,[],[f238])).
% 3.21/0.73 thf(f623,plain,(
% 3.21/0.73 ! [X0 : $tType] : (insert @ X0 = (^[Y0 : X0]: ((^[Y1 : set @ X0]: (collect @ X0 @ (^[Y2 : X0]: ((Y0 = Y2) | (member @ X0 @ Y2 @ Y1))))))))),
% 3.21/0.73 inference(fool_elimination,[],[f622])).
% 3.21/0.73 thf(f630,plain,(
% 3.21/0.73 ! [X0 : $tType,X1 : $tType,X2 : set @ product_prod @ X0 @ X1,X3 : X0] : (((image @ X0 @ X1 @ X2 @ (insert @ X0 @ X3 @ bot_bot @ set @ X0))) = ((collect @ X1 @ (^[X4 : X1] : ((member @ product_prod @ X0 @ X1 @ (product_Pair @ X0 @ X1 @ X3 @ X4) @ X2))))))),
% 3.21/0.73 inference(rectify,[],[f242])).
% 3.21/0.73 thf(f631,plain,(
% 3.21/0.73 ! [X0 : $tType,X1 : $tType,X2 : set @ product_prod @ X0 @ X1,X3 : X0] : (((image @ X0 @ X1 @ X2 @ (insert @ X0 @ X3 @ bot_bot @ set @ X0))) = ((collect @ X1 @ (^[Y0 : X1]: (member @ product_prod @ X0 @ X1 @ (product_Pair @ X0 @ X1 @ X3 @ Y0) @ X2)))))),
% 3.21/0.73 inference(fool_elimination,[],[f630])).
% 3.21/0.73 thf(f634,plain,(
% 3.21/0.73 ! [X0 : $tType,X1 : $tType] : (labeled_vertices @ X1 @ X0 = ((labele1974067554_graph @ X1 @ X0 @ set @ X0 @ (^[X2 : set @ product_prod @ X1 @ product_prod @ X0 @ X0, X3 : set @ X0] : (X3)))))),
% 3.21/0.73 inference(rectify,[],[f244])).
% 3.21/0.73 thf(f635,plain,(
% 3.21/0.73 ! [X0 : $tType,X1 : $tType] : (labeled_vertices @ X1 @ X0 = ((labele1974067554_graph @ X1 @ X0 @ set @ X0 @ (^[Y0 : set @ product_prod @ X1 @ product_prod @ X0 @ X0]: ((^[Y1 : set @ X0]: (Y1)))))))),
% 3.21/0.73 inference(fool_elimination,[],[f634])).
% 3.21/0.73 thf(f654,plain,(
% 3.21/0.73 ! [X0 : $o] : (($false = X0) | ($true = X0))),
% 3.21/0.73 inference(fool_elimination,[],[f257])).
% 3.21/0.73 thf(f657,plain,(
% 3.21/0.73 ! [X0 : $tType,X1 : X0,X2 : X0] : (((if @ X0 @ $true @ X1 @ X2)) = X1)),
% 3.21/0.73 inference(rectify,[],[f259])).
% 3.21/0.73 thf(f658,plain,(
% 3.21/0.73 ! [X0 : $tType,X1 : X0,X2 : X0] : (((if @ X0 @ $true @ X1 @ X2)) = X1)),
% 3.21/0.73 inference(fool_elimination,[],[f657])).
% 3.21/0.73 thf(f659,plain,(
% 3.21/0.73 ~(member @ b @ x @ (labeled_vertices @ standard_Constant @ a @ b @ g))),
% 3.21/0.73 inference(rectify,[],[f261])).
% 3.21/0.73 thf(f660,plain,(
% 3.21/0.73 ~ (((member @ b @ x @ (labeled_vertices @ standard_Constant @ a @ b @ g))) = $true)),
% 3.21/0.73 inference(fool_elimination,[],[f659])).
% 3.21/0.73 thf(f679,plain,(
% 3.21/0.73 (((member @ b @ x @ (labeled_vertices @ standard_Constant @ a @ b @ g))) != $true)),
% 3.21/0.73 inference(flattening,[],[f660])).
% 3.21/0.73 thf(f944,plain,(
% 3.21/0.73 (((member @ b @ (f @ x) @ (labeled_vertices @ standard_Constant @ a @ b @ g))) = $true)),
% 3.21/0.73 inference(cnf_transformation,[],[f267])).
% 3.21/0.73 thf(f1066,plain,(
% 3.21/0.73 (f = (^[Y0 : b]: (if @ b @ (bot_bot @ set @ b = (image @ b @ b @ (getRel @ standard_Constant @ a @ b @ standard_S_Idt @ a @ g) @ (insert @ b @ Y0 @ bot_bot @ set @ b))) @ Y0 @ (hilbert_Eps @ b @ (p @ Y0)))))),
% 3.21/0.73 inference(cnf_transformation,[],[f420])).
% 3.21/0.73 thf(f1084,plain,(
% 3.21/0.73 ( ! [X0 : b] : ((((bot_bot @ set @ b = (image @ b @ b @ (getRel @ standard_Constant @ a @ b @ standard_S_Idt @ a @ g) @ (insert @ b @ X0 @ bot_bot @ set @ b)))) = ((~ (member @ b @ X0 @ (labeled_vertices @ standard_Constant @ a @ b @ g)))))) )),
% 3.21/0.73 inference(cnf_transformation,[],[f436])).
% 3.21/0.73 thf(f1207,plain,(
% 3.21/0.73 (p = (^[Y0 : b]: ((^[Y1 : b]: (member @ b @ Y1 @ (image @ b @ b @ (getRel @ standard_Constant @ a @ b @ standard_S_Idt @ a @ g) @ (insert @ b @ Y0 @ bot_bot @ set @ b)))))))),
% 3.21/0.73 inference(cnf_transformation,[],[f619])).
% 3.21/0.73 thf(f1209,plain,(
% 3.21/0.73 ( ! [X0 : $tType] : ((insert @ X0 = (^[Y0 : X0]: ((^[Y1 : set @ X0]: (collect @ X0 @ (^[Y2 : X0]: ((Y0 = Y2) | (member @ X0 @ Y2 @ Y1))))))))) )),
% 3.21/0.73 inference(cnf_transformation,[],[f623])).
% 3.21/0.73 thf(f1215,plain,(
% 3.21/0.73 ( ! [X1 : $tType,X0 : $tType,X2 : set @ product_prod @ X0 @ X1,X3 : X0] : ((((image @ X0 @ X1 @ X2 @ (insert @ X0 @ X3 @ bot_bot @ set @ X0))) = ((collect @ X1 @ (^[Y0 : X1]: (member @ product_prod @ X0 @ X1 @ (product_Pair @ X0 @ X1 @ X3 @ Y0) @ X2)))))) )),
% 3.21/0.73 inference(cnf_transformation,[],[f631])).
% 3.21/0.73 thf(f1217,plain,(
% 3.21/0.73 ( ! [X1 : $tType,X0 : $tType] : ((labeled_vertices @ X1 @ X0 = ((labele1974067554_graph @ X1 @ X0 @ set @ X0 @ (^[Y0 : set @ product_prod @ X1 @ product_prod @ X0 @ X0]: ((^[Y1 : set @ X0]: (Y1)))))))) )),
% 3.21/0.73 inference(cnf_transformation,[],[f635])).
% 3.21/0.73 thf(f1233,plain,(
% 3.21/0.73 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 3.21/0.73 inference(cnf_transformation,[],[f654])).
% 3.21/0.73 thf(f1235,plain,(
% 3.21/0.73 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((((if @ X0 @ $true @ X1 @ X2)) = X1)) )),
% 3.21/0.73 inference(cnf_transformation,[],[f658])).
% 3.21/0.73 thf(f1236,plain,(
% 3.21/0.73 (((member @ b @ x @ (labeled_vertices @ standard_Constant @ a @ b @ g))) != $true)),
% 3.21/0.73 inference(cnf_transformation,[],[f679])).
% 3.21/0.73 thf(f1241,plain,(
% 3.21/0.73 (p = (^[Y0 : b]: ((^[Y1 : b]: (member @ b @ Y1 @ (image @ b @ b @ (getRel @ standard_Constant @ a @ b @ standard_S_Idt @ a @ g) @ ((^[Y2 : b]: ((^[Y3 : set @ b]: (collect @ b @ (^[Y4 : b]: ((Y2 = Y4) | (member @ b @ Y4 @ Y3))))))) @ Y0 @ bot_bot @ set @ b)))))))),
% 3.21/0.73 inference(definition_unfolding,[],[f1207,f1209])).
% 3.21/0.73 thf(f1242,plain,(
% 3.21/0.73 (f = (^[Y0 : b]: (if @ b @ (bot_bot @ set @ b = (image @ b @ b @ (getRel @ standard_Constant @ a @ b @ standard_S_Idt @ a @ g) @ ((^[Y1 : b]: ((^[Y2 : set @ b]: (collect @ b @ (^[Y3 : b]: ((Y1 = Y3) | (member @ b @ Y3 @ Y2))))))) @ Y0 @ bot_bot @ set @ b))) @ Y0 @ (hilbert_Eps @ b @ ((^[Y1 : b]: ((^[Y2 : b]: (member @ b @ Y2 @ (image @ b @ b @ (getRel @ standard_Constant @ a @ b @ standard_S_Idt @ a @ g) @ ((^[Y3 : b]: ((^[Y4 : set @ b]: (collect @ b @ (^[Y5 : b]: ((Y3 = Y5) | (member @ b @ Y5 @ Y4))))))) @ Y1 @ bot_bot @ set @ b)))))) @ Y0)))))),
% 3.21/0.73 inference(definition_unfolding,[],[f1066,f1209,f1241])).
% 3.21/0.73 thf(f1248,plain,(
% 3.21/0.73 ($true = ((member @ b @ ((^[Y0 : b]: (if @ b @ (bot_bot @ set @ b = (image @ b @ b @ (getRel @ standard_Constant @ a @ b @ standard_S_Idt @ a @ g) @ ((^[Y1 : b]: ((^[Y2 : set @ b]: (collect @ b @ (^[Y3 : b]: ((Y1 = Y3) | (member @ b @ Y3 @ Y2))))))) @ Y0 @ bot_bot @ set @ b))) @ Y0 @ (hilbert_Eps @ b @ ((^[Y1 : b]: ((^[Y2 : b]: (member @ b @ Y2 @ (image @ b @ b @ (getRel @ standard_Constant @ a @ b @ standard_S_Idt @ a @ g) @ ((^[Y3 : b]: ((^[Y4 : set @ b]: (collect @ b @ (^[Y5 : b]: ((Y3 = Y5) | (member @ b @ Y5 @ Y4))))))) @ Y1 @ bot_bot @ set @ b)))))) @ Y0)))) @ x) @ (labele1974067554_graph @ standard_Constant @ a @ b @ set @ b @ (^[Y0 : set @ product_prod @ standard_Constant @ a @ product_prod @ b @ b]: ((^[Y1 : set @ b]: (Y1)))) @ g))))),
% 3.21/0.73 inference(definition_unfolding,[],[f944,f1242,f1217])).
% 3.21/0.73 thf(f1314,plain,(
% 3.21/0.73 ( ! [X0 : b] : ((((bot_bot @ set @ b = (image @ b @ b @ (getRel @ standard_Constant @ a @ b @ standard_S_Idt @ a @ g) @ ((^[Y0 : b]: ((^[Y1 : set @ b]: (collect @ b @ (^[Y2 : b]: ((Y0 = Y2) | (member @ b @ Y2 @ Y1))))))) @ X0 @ bot_bot @ set @ b)))) = ((~ (member @ b @ X0 @ (labele1974067554_graph @ standard_Constant @ a @ b @ set @ b @ (^[Y0 : set @ product_prod @ standard_Constant @ a @ product_prod @ b @ b]: ((^[Y1 : set @ b]: (Y1)))) @ g)))))) )),
% 3.21/0.73 inference(definition_unfolding,[],[f1084,f1209,f1217])).
% 3.21/0.73 thf(f1376,plain,(
% 3.21/0.73 ( ! [X1 : $tType,X0 : $tType,X2 : set @ product_prod @ X0 @ X1,X3 : X0] : ((((collect @ X1 @ (^[Y0 : X1]: (member @ product_prod @ X0 @ X1 @ (product_Pair @ X0 @ X1 @ X3 @ Y0) @ X2)))) = ((image @ X0 @ X1 @ X2 @ ((^[Y0 : X0]: ((^[Y1 : set @ X0]: (collect @ X0 @ (^[Y2 : X0]: ((Y0 = Y2) | (member @ X0 @ Y2 @ Y1))))))) @ X3 @ bot_bot @ set @ X0))))) )),
% 3.21/0.73 inference(definition_unfolding,[],[f1215,f1209])).
% 3.21/0.73 thf(f1381,plain,(
% 3.21/0.73 ($true != ((member @ b @ x @ (labele1974067554_graph @ standard_Constant @ a @ b @ set @ b @ (^[Y0 : set @ product_prod @ standard_Constant @ a @ product_prod @ b @ b]: ((^[Y1 : set @ b]: (Y1)))) @ g))))),
% 3.21/0.73 inference(definition_unfolding,[],[f1236,f1217])).
% 3.21/0.73 thf(f1422,plain,(
% 3.21/0.73 ( ! [X1 : $tType,X0 : $tType,X2 : set @ product_prod @ X0 @ X1,X3 : X0] : ((((collect @ X1 @ (^[Y0 : X1]: (member @ product_prod @ X0 @ X1 @ (product_Pair @ X0 @ X1 @ X3 @ Y0) @ X2)))) = ((image @ X0 @ X1 @ X2 @ (collect @ X0 @ (^[Y0 : X0]: ((X3 = Y0) | (member @ X0 @ Y0 @ bot_bot @ set @ X0)))))))) )),
% 3.21/0.73 inference(beta-eta_normalization,[],[f1376])).
% 3.21/0.73 thf(f1799,plain,(
% 3.21/0.73 ( ! [X0 : b] : (($true = ((bot_bot @ set @ b = (image @ b @ b @ (getRel @ standard_Constant @ a @ b @ standard_S_Idt @ a @ g) @ ((^[Y0 : b]: ((^[Y1 : set @ b]: (collect @ b @ (^[Y2 : b]: ((Y0 = Y2) | (member @ b @ Y2 @ Y1))))))) @ X0 @ bot_bot @ set @ b))))) | ($false = ((~ (member @ b @ X0 @ (labele1974067554_graph @ standard_Constant @ a @ b @ set @ b @ (^[Y0 : set @ product_prod @ standard_Constant @ a @ product_prod @ b @ b]: ((^[Y1 : set @ b]: (Y1)))) @ g)))))) )),
% 3.21/0.73 inference(iff_proxy_clausification,[],[f1314])).
% 3.21/0.73 thf(f1804,plain,(
% 3.21/0.73 ( ! [X0 : b] : ((bot_bot @ set @ b = ((image @ b @ b @ (getRel @ standard_Constant @ a @ b @ standard_S_Idt @ a @ g) @ ((^[Y0 : b]: ((^[Y1 : set @ b]: (collect @ b @ (^[Y2 : b]: ((Y0 = Y2) | (member @ b @ Y2 @ Y1))))))) @ X0 @ bot_bot @ set @ b)))) | ($false = ((~ (member @ b @ X0 @ (labele1974067554_graph @ standard_Constant @ a @ b @ set @ b @ (^[Y0 : set @ product_prod @ standard_Constant @ a @ product_prod @ b @ b]: ((^[Y1 : set @ b]: (Y1)))) @ g)))))) )),
% 3.21/0.73 inference(equality_proxy_clausification,[],[f1799])).
% 3.21/0.73 thf(f1805,plain,(
% 3.21/0.73 ( ! [X0 : b] : ((bot_bot @ set @ b = ((image @ b @ b @ (getRel @ standard_Constant @ a @ b @ standard_S_Idt @ a @ g) @ ((^[Y0 : b]: ((^[Y1 : set @ b]: (collect @ b @ (^[Y2 : b]: ((Y0 = Y2) | (member @ b @ Y2 @ Y1))))))) @ X0 @ bot_bot @ set @ b)))) | ($true = ((member @ b @ X0 @ (labele1974067554_graph @ standard_Constant @ a @ b @ set @ b @ (^[Y0 : set @ product_prod @ standard_Constant @ a @ product_prod @ b @ b]: ((^[Y1 : set @ b]: (Y1)))) @ g))))) )),
% 3.21/0.73 inference(not_proxy_clausification,[],[f1804])).
% 3.21/0.73 thf(f1806,plain,(
% 3.21/0.73 ( ! [X0 : b] : ((bot_bot @ set @ b = ((image @ b @ b @ (getRel @ standard_Constant @ a @ b @ standard_S_Idt @ a @ g) @ (collect @ b @ (^[Y0 : b]: ((X0 = Y0) | (member @ b @ Y0 @ bot_bot @ set @ b))))))) | ($true = ((member @ b @ X0 @ (labele1974067554_graph @ standard_Constant @ a @ b @ set @ b @ (^[Y0 : set @ product_prod @ standard_Constant @ a @ product_prod @ b @ b]: ((^[Y1 : set @ b]: (Y1)))) @ g))))) )),
% 3.21/0.73 inference(beta-eta_normalization,[],[f1805])).
% 3.21/0.73 thf(f1973,plain,(
% 3.21/0.73 ($true = ((member @ b @ (if @ b @ (bot_bot @ set @ b = (image @ b @ b @ (getRel @ standard_Constant @ a @ b @ standard_S_Idt @ a @ g) @ (collect @ b @ (^[Y0 : b]: ((x = Y0) | (member @ b @ Y0 @ bot_bot @ set @ b)))))) @ x @ (hilbert_Eps @ b @ (^[Y0 : b]: (member @ b @ Y0 @ (image @ b @ b @ (getRel @ standard_Constant @ a @ b @ standard_S_Idt @ a @ g) @ (collect @ b @ (^[Y1 : b]: ((x = Y1) | (member @ b @ Y1 @ bot_bot @ set @ b))))))))) @ (labele1974067554_graph @ standard_Constant @ a @ b @ set @ b @ (^[Y0 : set @ product_prod @ standard_Constant @ a @ product_prod @ b @ b]: ((^[Y1 : set @ b]: (Y1)))) @ g))))),
% 3.21/0.73 inference(beta-eta_normalization,[],[f1248])).
% 3.21/0.73 thf(f2040,plain,(
% 3.21/0.73 ( ! [X0 : b] : ((bot_bot @ set @ b = ((collect @ b @ (^[Y0 : b]: (member @ product_prod @ b @ b @ (product_Pair @ b @ b @ X0 @ Y0) @ (getRel @ standard_Constant @ a @ b @ standard_S_Idt @ a @ g)))))) | ($true = ((member @ b @ X0 @ (labele1974067554_graph @ standard_Constant @ a @ b @ set @ b @ (^[Y0 : set @ product_prod @ standard_Constant @ a @ product_prod @ b @ b]: ((^[Y1 : set @ b]: (Y1)))) @ g))))) )),
% 3.21/0.73 inference(forward_demodulation,[],[f1806,f1422])).
% 3.21/0.73 thf(f2059,plain,(
% 3.21/0.73 ($true = ((member @ b @ (if @ b @ (bot_bot @ set @ b = (collect @ b @ (^[Y0 : b]: (member @ product_prod @ b @ b @ (product_Pair @ b @ b @ x @ Y0) @ (getRel @ standard_Constant @ a @ b @ standard_S_Idt @ a @ g))))) @ x @ (hilbert_Eps @ b @ (^[Y0 : b]: (member @ b @ Y0 @ (collect @ b @ (^[Y1 : b]: (member @ product_prod @ b @ b @ (product_Pair @ b @ b @ x @ Y1) @ (getRel @ standard_Constant @ a @ b @ standard_S_Idt @ a @ g)))))))) @ (labele1974067554_graph @ standard_Constant @ a @ b @ set @ b @ (^[Y0 : set @ product_prod @ standard_Constant @ a @ product_prod @ b @ b]: ((^[Y1 : set @ b]: (Y1)))) @ g))))),
% 3.21/0.73 inference(forward_demodulation,[],[f1973,f1422])).
% 3.21/0.73 thf(f2148,plain,(
% 3.21/0.73 ($true = ((member @ b @ (if @ b @ $true @ x @ (hilbert_Eps @ b @ (^[Y0 : b]: (member @ b @ Y0 @ (collect @ b @ (^[Y1 : b]: (member @ product_prod @ b @ b @ (product_Pair @ b @ b @ x @ Y1) @ (getRel @ standard_Constant @ a @ b @ standard_S_Idt @ a @ g)))))))) @ (labele1974067554_graph @ standard_Constant @ a @ b @ set @ b @ (^[Y0 : set @ product_prod @ standard_Constant @ a @ product_prod @ b @ b]: ((^[Y1 : set @ b]: (Y1)))) @ g)))) | ($false = ((bot_bot @ set @ b = (collect @ b @ (^[Y0 : b]: (member @ product_prod @ b @ b @ (product_Pair @ b @ b @ x @ Y0) @ (getRel @ standard_Constant @ a @ b @ standard_S_Idt @ a @ g)))))))),
% 3.21/0.73 inference(constrained_superposition,[],[f2059,f1233])).
% 3.21/0.73 thf(f2149,plain,(
% 3.21/0.73 ($true = ((member @ b @ (if @ b @ $true @ x @ (hilbert_Eps @ b @ (^[Y0 : b]: (member @ b @ Y0 @ (collect @ b @ (^[Y1 : b]: (member @ product_prod @ b @ b @ (product_Pair @ b @ b @ x @ Y1) @ (getRel @ standard_Constant @ a @ b @ standard_S_Idt @ a @ g)))))))) @ (labele1974067554_graph @ standard_Constant @ a @ b @ set @ b @ (^[Y0 : set @ product_prod @ standard_Constant @ a @ product_prod @ b @ b]: ((^[Y1 : set @ b]: (Y1)))) @ g)))) | (bot_bot @ set @ b != ((collect @ b @ (^[Y0 : b]: (member @ product_prod @ b @ b @ (product_Pair @ b @ b @ x @ Y0) @ (getRel @ standard_Constant @ a @ b @ standard_S_Idt @ a @ g))))))),
% 3.21/0.73 inference(equality_proxy_clausification,[],[f2148])).
% 3.21/0.73 thf(f2150,plain,(
% 3.21/0.73 ($true = ((member @ b @ x @ (labele1974067554_graph @ standard_Constant @ a @ b @ set @ b @ (^[Y0 : set @ product_prod @ standard_Constant @ a @ product_prod @ b @ b]: ((^[Y1 : set @ b]: (Y1)))) @ g)))) | (bot_bot @ set @ b != ((collect @ b @ (^[Y0 : b]: (member @ product_prod @ b @ b @ (product_Pair @ b @ b @ x @ Y0) @ (getRel @ standard_Constant @ a @ b @ standard_S_Idt @ a @ g))))))),
% 3.21/0.73 inference(forward_demodulation,[],[f2149,f1235])).
% 3.21/0.73 thf(f2151,plain,(
% 3.21/0.73 ($true = ((member @ b @ x @ (labele1974067554_graph @ standard_Constant @ a @ b @ set @ b @ (^[Y0 : set @ product_prod @ standard_Constant @ a @ product_prod @ b @ b]: ((^[Y1 : set @ b]: (Y1)))) @ g))))),
% 3.21/0.73 inference(forward_subsumption_resolution,[],[f2150,f2040])).
% 3.21/0.73 thf(f2152,plain,(
% 3.21/0.73 $false),
% 3.21/0.73 inference(forward_subsumption_resolution,[],[f2151,f1381])).
% 3.21/0.73 % SZS output end Proof for theBenchmark
% 3.21/0.73 % (2141769)------------------------------
% 3.21/0.73 % (2141769)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.21/0.73 % (2141769)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.21/0.73 % (2141769)CaDiCaL version: 2.1.3
% 3.21/0.73 % (2141769)Termination reason: Refutation
% 3.21/0.73 % (2141769)Time elapsed: 0.219 s
% 3.21/0.73 % (2141769)Peak memory usage: 16 MB
% 3.21/0.73 % (2141769)Instructions burned: 292 (million)
% 3.21/0.73 % (2141734)Success in time 0.493 s
% 3.21/0.73 % Vampire exiting
%------------------------------------------------------------------------------