%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP160^2 : 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 : n018.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 08:10:56 AM UTC 2026
% Result : Theorem 2.12s 0.63s
% Output : Refutation 2.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP160^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n018.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 20:06:12 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.23 Running first-order model finding
% 0.08/0.23 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
% 2.12/0.63 % (576301)Will run a generic schedule for satisfiability detection.
% 2.12/0.63 % (576311)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3333792047:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 2.12/0.63 % (576307)% WARNING: option uhcvi not known.
% 2.12/0.63 % (576309)dis+10_1_sil=32000:sp=arity:random_seed=3567584655:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 2.12/0.63 % (576306)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3755765033_2999 on theBenchmark for (2999ds/0Mi)
% 2.12/0.63 % (576307)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3440957116:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 2.12/0.63 % (576308)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=292845196:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 2.12/0.63 % (576310)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1844998569:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 2.12/0.63 % (576312)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1951749672:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 2.12/0.63 % (576311)Instruction limit reached!
% 2.12/0.63 % (576311)------------------------------
% 2.12/0.63 % (576311)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.12/0.63 % (576311)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.12/0.63 % (576311)CaDiCaL version: 2.1.3
% 2.12/0.63 % (576311)Termination reason: Instruction limit
% 2.12/0.63 % (576311)Termination phase: Property scanning
% 2.12/0.63 % (576311)Time elapsed: 0.030 s
% 2.12/0.63 % (576311)Peak memory usage: 11 MB
% 2.12/0.63 % (576311)Instructions burned: 132 (million)
% 2.12/0.63 % (576320)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1914018875:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 2.12/0.63 % (576310)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.12/0.63 % (576307)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.12/0.63 % (576309)Instruction limit reached!
% 2.12/0.63 % (576309)------------------------------
% 2.12/0.63 % (576309)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.12/0.63 % (576309)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.12/0.63 % (576309)CaDiCaL version: 2.1.3
% 2.12/0.63 % (576309)Termination reason: Instruction limit
% 2.12/0.63 % (576309)Termination phase: Preprocessing 3
% 2.12/0.63 % (576309)Time elapsed: 0.044 s
% 2.12/0.63 % (576309)Peak memory usage: 11 MB
% 2.12/0.63 % (576309)Instructions burned: 105 (million)
% 2.12/0.63 % (576310)Instruction limit reached!
% 2.12/0.63 % (576310)------------------------------
% 2.12/0.63 % (576310)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.12/0.63 % (576310)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.12/0.63 % (576310)CaDiCaL version: 2.1.3
% 2.12/0.63 % (576310)Termination reason: Instruction limit
% 2.12/0.63 % (576310)Termination phase: Property scanning
% 2.12/0.63 % (576310)Time elapsed: 0.049 s
% 2.12/0.63 % (576310)Peak memory usage: 11 MB
% 2.12/0.63 % (576310)Instructions burned: 117 (million)
% 2.12/0.63 % (576322)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=145132134:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 2.12/0.63 % (576312)Instruction limit reached!
% 2.12/0.63 % (576312)------------------------------
% 2.12/0.63 % (576312)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.12/0.63 % (576312)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.12/0.63 % (576312)CaDiCaL version: 2.1.3
% 2.12/0.63 % (576312)Termination reason: Instruction limit
% 2.12/0.63 % (576312)Termination phase: Property scanning
% 2.12/0.63 % (576312)Time elapsed: 0.068 s
% 2.12/0.63 % (576312)Peak memory usage: 12 MB
% 2.12/0.63 % (576312)Instructions burned: 160 (million)
% 2.12/0.63 % (576323)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=3444323014:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 2.12/0.63 % Exception at run slice level
% 2.12/0.63 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.12/0.63 % Exception at run slice level
% 2.12/0.63 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.12/0.63 % (576307)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.12/0.63 % (576328)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2247714522:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 2.12/0.63 % (576326)ott-21_1_sil=16000:fs=off:random_seed=1715820214:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 2.12/0.63 % (576327)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2939444551:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 2.12/0.63 % (576323)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.12/0.63 % (576322)Instruction limit reached!
% 2.12/0.63 % (576322)------------------------------
% 2.12/0.63 % (576322)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.12/0.63 % (576322)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.12/0.63 % (576322)CaDiCaL version: 2.1.3
% 2.12/0.63 % (576322)Termination reason: Instruction limit
% 2.12/0.63 % (576322)Termination phase: Property scanning
% 2.12/0.63 % (576322)Time elapsed: 0.055 s
% 2.12/0.63 % (576322)Peak memory usage: 12 MB
% 2.12/0.63 % (576322)Instructions burned: 131 (million)
% 2.12/0.63 % Exception at run slice level
% 2.12/0.63 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.12/0.63 % (576332)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=335067622:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 2.12/0.63 % (576333)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=2200858793:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 2.12/0.63 % (576323)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.12/0.63 % (576326)Instruction limit reached!
% 2.12/0.63 % (576326)------------------------------
% 2.12/0.63 % (576326)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.12/0.63 % (576326)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.12/0.63 % (576326)CaDiCaL version: 2.1.3
% 2.12/0.63 % (576326)Termination reason: Instruction limit
% 2.12/0.63 % (576326)Termination phase: Property scanning
% 2.12/0.63 % (576326)Time elapsed: 0.076 s
% 2.12/0.63 % (576326)Peak memory usage: 12 MB
% 2.12/0.63 % (576326)Instructions burned: 180 (million)
% 2.12/0.63 % Exception at run slice level
% 2.12/0.63 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.12/0.63 % (576336)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=2083641799: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)
% 2.12/0.63 % (576337)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=935652770:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 2.12/0.63 % (576337)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.12/0.63 % (576336)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.12/0.63 % (576336) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-576301-576336"...
% 2.12/0.63 % (576336)...printing done.
% 2.12/0.63 % (576327)Instruction limit reached!
% 2.12/0.63 % (576327)------------------------------
% 2.12/0.63 % (576327)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.12/0.63 % (576327)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.12/0.63 % (576327)CaDiCaL version: 2.1.3
% 2.12/0.63 % (576327)Termination reason: Instruction limit
% 2.12/0.63 % (576327)Termination phase: Saturation
% 2.12/0.63 % (576327)Time elapsed: 0.229 s
% 2.12/0.63 % (576327)Peak memory usage: 15 MB
% 2.12/0.63 % (576327)Instructions burned: 478 (million)
% 2.12/0.63 % (576336)Refutation found. Thanks to Tanya!
% 2.12/0.63 % SZS status Theorem for theBenchmark
% 2.12/0.63 % SZS output start Proof for theBenchmark
% 2.12/0.63 thf(type_def_5, type, refine1665802226e_nres: $tType > $tType).
% 2.12/0.63 thf(type_def_6, type, autoref_annot: $tType).
% 2.12/0.63 thf(type_def_7, type, product_prod: ($tType * $tType) > $tType).
% 2.12/0.63 thf(type_def_8, type, set: $tType > $tType).
% 2.12/0.63 thf(type_def_9, type, nat: $tType).
% 2.12/0.63 thf(type_def_10, type, int: $tType).
% 2.12/0.63 thf(type_def_11, type, d: $tType).
% 2.12/0.63 thf(type_def_12, type, c: $tType).
% 2.12/0.63 thf(type_def_13, type, b: $tType).
% 2.12/0.63 thf(type_def_14, type, a: $tType).
% 2.12/0.63 thf(type_def_15, type, sTfun: ($tType * $tType) > $tType).
% 2.12/0.63 thf(func_def_0, type, type: !>[X0: $tType]:($o)).
% 2.12/0.63 thf(func_def_1, type, ord: !>[X0: $tType]:($o)).
% 2.12/0.63 thf(func_def_2, type, order: !>[X0: $tType]:($o)).
% 2.12/0.63 thf(func_def_3, type, linorder: !>[X0: $tType]:($o)).
% 2.12/0.63 thf(func_def_4, type, preorder: !>[X0: $tType]:($o)).
% 2.12/0.63 thf(func_def_5, type, autoref_ANNOT: !>[X0: $tType]:((X0 > autoref_annot > X0))).
% 2.12/0.63 thf(func_def_6, type, autoref_APP: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0 > X1))).
% 2.12/0.63 thf(func_def_7, type, autoref_OP: !>[X0: $tType]:((X0 > X0))).
% 2.12/0.63 thf(func_def_8, type, autoref_rel_annot: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X1 > autoref_annot))).
% 2.12/0.63 thf(func_def_9, type, autore2013370551TERNAL: !>[X0: $tType]:((X0 > X0))).
% 2.12/0.63 thf(func_def_10, type, autore813025987NAL_EQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 2.12/0.63 thf(func_def_11, type, comp: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1) > (X2 > X0) > X2 > X1))).
% 2.12/0.63 thf(func_def_12, type, fun_upd: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0 > X1 > X0 > X1))).
% 2.12/0.63 thf(func_def_13, type, id: !>[X0: $tType]:((X0 > X0))).
% 2.12/0.63 thf(func_def_14, type, if: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 2.12/0.63 thf(func_def_15, type, all_interval_nat: ((nat > $o) > nat > nat > $o)).
% 2.12/0.63 thf(func_def_16, type, uncurry: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 2.12/0.63 thf(func_def_17, type, case_nat: !>[X0: $tType]:((X0 > (nat > X0) > nat > X0))).
% 2.12/0.63 thf(func_def_18, type, rec_nat: !>[X0: $tType]:((X0 > (nat > X0 > X0) > nat > X0))).
% 2.12/0.63 thf(func_def_19, type, ord_less: !>[X0: $tType]:((X0 > X0 > $o))).
% 2.12/0.63 thf(func_def_20, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 2.12/0.63 thf(func_def_21, type, product_Pair: !>[X0: $tType, X1: $tType]:((X0 > X1 > product_prod @ X0 @ X1))).
% 2.12/0.63 thf(func_def_22, type, product_apfst: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1) > product_prod @ X0 @ X2 > product_prod @ X1 @ X2))).
% 2.12/0.63 thf(func_def_23, type, product_apsnd: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1) > product_prod @ X2 @ X0 > product_prod @ X2 @ X1))).
% 2.12/0.63 thf(func_def_24, type, product_case_bool: !>[X0: $tType]:((X0 > X0 > $o > X0))).
% 2.12/0.63 thf(func_def_25, type, product_curry: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X0 @ X1 > X2) > X0 > X1 > X2))).
% 2.12/0.63 thf(func_def_26, type, produc2004651681e_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 2.12/0.63 thf(func_def_27, type, product_map_prod: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X0 > X1) > (X2 > X3) > product_prod @ X0 @ X2 > product_prod @ X1 @ X3))).
% 2.12/0.63 thf(func_def_28, type, product_rec_bool: !>[X0: $tType]:((X0 > X0 > $o > X0))).
% 2.12/0.63 thf(func_def_29, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 2.12/0.63 thf(func_def_30, type, product_case_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 2.12/0.63 thf(func_def_31, type, product_fst: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 2.12/0.63 thf(func_def_32, type, product_snd: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 2.12/0.63 thf(func_def_33, type, product_swap: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > product_prod @ X1 @ X0))).
% 2.12/0.63 thf(func_def_34, type, refine1687780735RETURN: !>[X0: $tType]:((X0 > refine1665802226e_nres @ X0))).
% 2.12/0.63 thf(func_def_35, type, refine463715084e_bind: !>[X0: $tType, X1: $tType]:((refine1665802226e_nres @ X0 > (X0 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1))).
% 2.12/0.63 thf(func_def_36, type, refine1580981607t_assn: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X1 > (X1 > $o) > X0 > $o))).
% 2.12/0.63 thf(func_def_37, type, refine476890328es_rel: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X1 > set @ product_prod @ refine1665802226e_nres @ X0 @ refine1665802226e_nres @ X1))).
% 2.12/0.63 thf(func_def_38, type, refine171938416RT_bnd: !>[X0: $tType]:(($o > refine1665802226e_nres @ X0 > refine1665802226e_nres @ X0))).
% 2.12/0.63 thf(func_def_39, type, refine1361002633n_bool: set @ product_prod @ $o @ $o).
% 2.12/0.63 thf(func_def_40, type, id2: !>[X0: $tType]:(set @ product_prod @ X0 @ X0)).
% 2.12/0.63 thf(func_def_41, type, fun_rel: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((set @ product_prod @ X0 @ X1 > set @ product_prod @ X2 @ X3 > set @ product_prod @ (X0 > X2) @ (X1 > X3)))).
% 2.12/0.63 thf(func_def_42, type, prod_rel: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((set @ product_prod @ X0 @ X1 > set @ product_prod @ X2 @ X3 > set @ product_prod @ product_prod @ X0 @ X2 @ product_prod @ X1 @ X3))).
% 2.12/0.63 thf(func_def_43, type, relAPP: !>[X0: $tType, X1: $tType, X2: $tType]:(((set @ product_prod @ X0 @ X1 > X2) > set @ product_prod @ X0 @ X1 > X2))).
% 2.12/0.63 thf(func_def_44, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 2.12/0.63 thf(func_def_45, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 2.12/0.63 thf(func_def_46, type, r1: set @ product_prod @ a @ c).
% 2.12/0.63 thf(func_def_47, type, r2: set @ product_prod @ b @ d).
% 2.12/0.63 thf(func_def_49, type, vIMP: ($o > $o > $o)).
% 2.12/0.63 thf(func_def_50, type, vNOT: ($o > $o)).
% 2.12/0.63 thf(func_def_51, type, vOR: ($o > $o > $o)).
% 2.12/0.63 thf(func_def_52, type, vAND: ($o > $o > $o)).
% 2.12/0.63 thf(func_def_55, type, db0: !>[X0: $tType]:(X0)).
% 2.12/0.63 thf(func_def_56, type, db1: !>[X0: $tType]:(X0)).
% 2.12/0.63 thf(func_def_57, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 2.12/0.63 thf(func_def_58, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 2.12/0.63 thf(func_def_59, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 2.12/0.63 thf(func_def_60, type, db3: !>[X0: $tType]:(X0)).
% 2.12/0.63 thf(func_def_61, type, db2: !>[X0: $tType]:(X0)).
% 2.12/0.63 thf(func_def_62, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 2.12/0.63 thf(func_def_63, type, sP0: !>[X0: $tType, X1: $tType]:(($o > $o > refine1665802226e_nres @ X1 > refine1665802226e_nres @ X0 > set @ product_prod @ X1 @ X0 > $o))).
% 2.12/0.63 thf(func_def_64, type, sP1: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((set @ product_prod @ X3 @ X1 > (X3 > X2) > (X1 > X0) > X1 > set @ product_prod @ X2 @ X0 > $o))).
% 2.12/0.63 thf(func_def_65, type, sP2: !>[X0: $tType, X1: $tType]:(($o > X1 > X0 > set @ product_prod @ X1 @ X0 > $o))).
% 2.12/0.63 thf(func_def_66, type, sP3: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X2 @ X0 > X3 > set @ product_prod @ X3 @ X2 > X1 > set @ product_prod @ X1 @ X0 > $o))).
% 2.12/0.63 thf(func_def_67, type, sP4: ($o > $o > $o > $o > $o)).
% 2.12/0.63 thf(func_def_68, type, sP5: ($o > $o > $o > $o > $o)).
% 2.12/0.63 thf(func_def_69, type, sP6: !>[X0: $tType, X1: $tType]:(($o > $o > X1 > X0 > set @ product_prod @ X1 @ X0 > $o))).
% 2.12/0.63 thf(func_def_70, type, sP7: !>[X0: $tType, X1: $tType]:(($o > $o > X1 > X0 > set @ product_prod @ X1 @ X0 > $o))).
% 2.12/0.63 thf(func_def_71, type, sP8: !>[X0: $tType]:(($o > X0 > X0 > $o))).
% 2.12/0.63 thf(func_def_72, type, sP9: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ X4 > product_prod @ X2 @ X1 > (X5 > X4 > X3) > (X2 > X1 > X0) > set @ product_prod @ X3 @ X0 > $o))).
% 2.12/0.63 thf(func_def_73, type, sP10: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ X4 > product_prod @ X2 @ X1 > set @ product_prod @ X5 @ X2 > set @ product_prod @ X4 @ X1 > (X5 > X4 > X3) > (X2 > X1 > X0) > set @ product_prod @ X3 @ X0 > $o))).
% 2.12/0.63 thf(func_def_74, type, sP11: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > (X1 > X0 > $o) > X1 > X0 > $o))).
% 2.12/0.63 thf(func_def_75, type, sP12: ((nat > $o) > nat > $o)).
% 2.12/0.63 thf(func_def_76, type, sP13: !>[X0: $tType]:(($o > X0 > X0 > $o))).
% 2.12/0.63 thf(func_def_77, type, sP14: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 2.12/0.63 thf(func_def_78, type, sP15: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 2.12/0.63 thf(func_def_79, type, sP16: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 2.12/0.63 thf(func_def_80, type, sP17: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 2.12/0.63 thf(func_def_81, type, sP18: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 2.12/0.63 thf(func_def_82, type, sP19: !>[X0: $tType]:(((X0 > X0 > $o) > $o))).
% 2.12/0.63 thf(func_def_83, type, sK20: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((set @ product_prod @ X3 @ X2 > (X1 > X2) > (X0 > X3) > set @ product_prod @ X0 @ X1 > X0))).
% 2.12/0.63 thf(func_def_84, type, sK21: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((set @ product_prod @ X3 @ X2 > (X1 > X2) > (X0 > X3) > set @ product_prod @ X0 @ X1 > X1))).
% 2.12/0.63 thf(func_def_85, type, sK22: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 2.12/0.63 thf(func_def_86, type, sK23: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 2.12/0.63 thf(func_def_87, type, sK24: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 2.12/0.63 thf(func_def_88, type, sK25: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 2.12/0.63 thf(func_def_89, type, sK26: !>[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))).
% 2.12/0.63 thf(func_def_90, type, sK27: !>[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))).
% 2.12/0.63 thf(func_def_91, type, sK28: !>[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))).
% 2.12/0.63 thf(func_def_92, type, sK29: !>[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))).
% 2.12/0.63 thf(func_def_93, type, sK30: !>[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))).
% 2.12/0.63 thf(func_def_94, type, sK31: !>[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))).
% 2.12/0.63 thf(func_def_95, type, sK32: !>[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))).
% 2.12/0.63 thf(func_def_96, type, sK33: !>[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))).
% 2.12/0.63 thf(func_def_97, type, sK34: !>[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))).
% 2.12/0.63 thf(func_def_98, type, sK35: !>[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))).
% 2.12/0.63 thf(func_def_99, type, sK36: !>[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))).
% 2.12/0.63 thf(func_def_100, type, sK37: !>[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))).
% 2.12/0.63 thf(func_def_101, type, sK38: !>[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))).
% 2.12/0.63 thf(func_def_102, type, sK39: !>[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))).
% 2.12/0.63 thf(func_def_103, type, sK40: !>[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))).
% 2.12/0.63 thf(func_def_104, type, sK41: !>[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))).
% 2.12/0.63 thf(func_def_105, type, sK42: !>[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))).
% 2.12/0.63 thf(func_def_106, type, sK43: !>[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))).
% 2.12/0.63 thf(func_def_107, type, sK44: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3))).
% 2.12/0.63 thf(func_def_108, type, sK45: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 2.12/0.63 thf(func_def_109, type, sK46: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 2.12/0.63 thf(func_def_110, type, sK47: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 2.12/0.63 thf(func_def_111, type, sK48: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 2.12/0.63 thf(func_def_112, type, sK49: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 2.12/0.63 thf(func_def_113, type, sK50: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 2.12/0.63 thf(func_def_114, type, sK51: !>[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))).
% 2.12/0.63 thf(func_def_115, type, sK52: !>[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))).
% 2.12/0.63 thf(func_def_116, type, sK53: !>[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))).
% 2.12/0.63 thf(func_def_117, type, sK54: !>[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))).
% 2.12/0.63 thf(func_def_118, type, sK55: !>[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))).
% 2.12/0.63 thf(func_def_119, type, sK56: !>[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))).
% 2.12/0.63 thf(func_def_120, type, sK57: !>[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))).
% 2.12/0.63 thf(func_def_121, type, sK58: !>[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))).
% 2.12/0.63 thf(func_def_122, type, sK59: !>[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))).
% 2.12/0.63 thf(func_def_123, type, sK60: !>[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))).
% 2.12/0.63 thf(func_def_124, type, sK61: !>[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))).
% 2.12/0.63 thf(func_def_125, type, sK62: !>[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))).
% 2.12/0.63 thf(func_def_126, type, sK63: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X5))).
% 2.12/0.63 thf(func_def_127, type, sK64: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X0))).
% 2.12/0.63 thf(func_def_128, type, sK65: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X1))).
% 2.12/0.63 thf(func_def_129, type, sK66: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X2))).
% 2.12/0.63 thf(func_def_130, type, sK67: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X3))).
% 2.12/0.63 thf(func_def_131, type, sK68: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X4))).
% 2.12/0.63 thf(func_def_132, type, sK69: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X0))).
% 2.12/0.63 thf(func_def_133, type, sK70: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X1))).
% 2.12/0.63 thf(func_def_134, type, sK71: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X2))).
% 2.12/0.63 thf(func_def_135, type, sK72: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X3))).
% 2.12/0.63 thf(func_def_136, type, sK73: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X0))).
% 2.12/0.63 thf(func_def_137, type, sK74: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X1))).
% 2.12/0.63 thf(func_def_138, type, sK75: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X2))).
% 2.12/0.63 thf(func_def_139, type, sK76: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 2.12/0.63 thf(func_def_140, type, sK77: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 2.12/0.63 thf(func_def_141, type, sK78: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 2.12/0.63 thf(func_def_142, type, sK79: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 2.12/0.63 thf(func_def_143, type, sK80: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((set @ product_prod @ X3 @ X1 > (X3 > X2) > (X1 > X0) > X1 > set @ product_prod @ X2 @ X0 > X3))).
% 2.12/0.63 thf(func_def_144, type, sK81: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((set @ product_prod @ X3 @ X2 > (X0 > X2) > (X1 > X3) > set @ product_prod @ X1 @ X0 > X0 > X0))).
% 2.12/0.63 thf(func_def_145, type, sK82: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 2.12/0.63 thf(func_def_146, type, sK83: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 2.12/0.63 thf(func_def_147, type, sK84: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X2 @ X0 > X3 > set @ product_prod @ X3 @ X2 > X1 > set @ product_prod @ X1 @ X0 > X2))).
% 2.12/0.63 thf(func_def_148, type, sK85: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X2 @ X0 > X3 > set @ product_prod @ X3 @ X2 > X1 > set @ product_prod @ X1 @ X0 > X0))).
% 2.12/0.63 thf(func_def_149, type, sK86: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((set @ product_prod @ X3 @ X2 > set @ product_prod @ X0 @ X1 > product_prod @ X1 @ X2 > product_prod @ X0 @ X3 > X0))).
% 2.12/0.63 thf(func_def_150, type, sK87: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((set @ product_prod @ X3 @ X2 > set @ product_prod @ X0 @ X1 > product_prod @ X1 @ X2 > product_prod @ X0 @ X3 > X3))).
% 2.12/0.63 thf(func_def_151, type, sK88: !>[X0: $tType]:((product_prod @ X0 @ X0 > X0))).
% 2.12/0.63 thf(func_def_152, type, sK89: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ X2 > (X0 > X2 > set @ X1) > X1 > X0))).
% 2.12/0.63 thf(func_def_153, type, sK90: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ X2 > (X0 > X2 > set @ X1) > X1 > X2))).
% 2.12/0.63 thf(func_def_154, type, sK91: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ X4 > product_prod @ X2 @ X1 > (X5 > X4 > X3) > (X2 > X1 > X0) > set @ product_prod @ X3 @ X0 > X5))).
% 2.12/0.63 thf(func_def_155, type, sK92: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ X4 > product_prod @ X2 @ X1 > (X5 > X4 > X3) > (X2 > X1 > X0) > set @ product_prod @ X3 @ X0 > X4))).
% 2.12/0.63 thf(func_def_156, type, sK93: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ X4 > product_prod @ X2 @ X1 > (X5 > X4 > X3) > (X2 > X1 > X0) > set @ product_prod @ X3 @ X0 > X2))).
% 2.12/0.63 thf(func_def_157, type, sK94: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ X4 > product_prod @ X2 @ X1 > (X5 > X4 > X3) > (X2 > X1 > X0) > set @ product_prod @ X3 @ X0 > X1))).
% 2.12/0.63 thf(func_def_158, type, sK95: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ X4 > product_prod @ X2 @ X1 > set @ product_prod @ X5 @ X2 > set @ product_prod @ X4 @ X1 > (X5 > X4 > X3) > (X2 > X1 > X0) > set @ product_prod @ X3 @ X0 > X5))).
% 2.12/0.63 thf(func_def_159, type, sK96: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ X4 > product_prod @ X2 @ X1 > set @ product_prod @ X5 @ X2 > set @ product_prod @ X4 @ X1 > (X5 > X4 > X3) > (X2 > X1 > X0) > set @ product_prod @ X3 @ X0 > X4))).
% 2.12/0.63 thf(func_def_160, type, sK97: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ X4 > product_prod @ X2 @ X1 > set @ product_prod @ X5 @ X2 > set @ product_prod @ X4 @ X1 > (X5 > X4 > X3) > (X2 > X1 > X0) > set @ product_prod @ X3 @ X0 > X2))).
% 2.12/0.63 thf(func_def_161, type, sK98: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ X4 > product_prod @ X2 @ X1 > set @ product_prod @ X5 @ X2 > set @ product_prod @ X4 @ X1 > (X5 > X4 > X3) > (X2 > X1 > X0) > set @ product_prod @ X3 @ X0 > X1))).
% 2.12/0.63 thf(func_def_162, type, sK99: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > set @ product_prod @ X1 @ X0 > X1))).
% 2.12/0.63 thf(func_def_163, type, sK100: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > set @ product_prod @ X1 @ X0 > X0))).
% 2.12/0.63 thf(func_def_164, type, sK101: !>[X0: $tType, X1: $tType]:(((X1 > refine1665802226e_nres @ X0) > (X1 > refine1665802226e_nres @ X0) > refine1665802226e_nres @ X1 > X1))).
% 2.12/0.63 thf(func_def_165, type, sK102: !>[X0: $tType, X1: $tType]:(((X1 > refine1665802226e_nres @ X0) > (X1 > refine1665802226e_nres @ X0) > refine1665802226e_nres @ X1 > X1))).
% 2.12/0.63 thf(func_def_166, type, sK103: !>[X0: $tType, X1: $tType]:((((X1 > X0) > product_prod @ X1 @ X1 > $o) > X1 > X0))).
% 2.12/0.63 thf(func_def_167, type, sK104: !>[X0: $tType, X1: $tType]:((((X1 > X0) > product_prod @ X1 @ X1 > $o) > X1))).
% 2.12/0.63 thf(func_def_168, type, sK105: !>[X0: $tType, X1: $tType]:((((X1 > X0) > product_prod @ X1 @ X1 > $o) > X1))).
% 2.12/0.63 thf(func_def_169, type, sK106: !>[X0: $tType, X1: $tType]:((product_prod @ (X1 > X0) @ product_prod @ X1 @ X1 > X1 > X0))).
% 2.12/0.63 thf(func_def_170, type, sK107: !>[X0: $tType, X1: $tType]:((product_prod @ (X1 > X0) @ product_prod @ X1 @ X1 > X1))).
% 2.12/0.63 thf(func_def_171, type, sK108: !>[X0: $tType, X1: $tType]:((product_prod @ (X1 > X0) @ product_prod @ X1 @ X1 > X1))).
% 2.12/0.63 thf(func_def_172, type, sK109: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > set @ product_prod @ X0 @ X1 > X0))).
% 2.12/0.63 thf(func_def_173, type, sK110: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > set @ product_prod @ X0 @ X1 > X1))).
% 2.12/0.63 thf(func_def_174, type, sK111: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > X1 > X0) > (X2 > X1 > X0) > product_prod @ X2 @ X1 > X2))).
% 2.12/0.63 thf(func_def_175, type, sK112: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > X1 > X0) > (X2 > X1 > X0) > product_prod @ X2 @ X1 > X1))).
% 2.12/0.63 thf(func_def_176, type, sK113: ((nat > $o) > nat > nat)).
% 2.12/0.63 thf(func_def_177, type, sK114: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > (X1 > X0 > $o) > X1))).
% 2.12/0.63 thf(func_def_178, type, sK115: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > (X1 > X0 > $o) > X0))).
% 2.12/0.63 thf(func_def_179, type, sK116: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.12/0.63 thf(func_def_180, type, sK117: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.12/0.63 thf(func_def_181, type, sK118: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 2.12/0.63 thf(func_def_182, type, sK119: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 2.12/0.63 thf(func_def_183, type, sK120: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.12/0.63 thf(func_def_184, type, sK121: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.12/0.63 thf(func_def_185, type, sK122: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 2.12/0.63 thf(func_def_186, type, sK123: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 2.12/0.63 thf(func_def_187, type, sK124: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 2.12/0.63 thf(func_def_188, type, sK125: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 2.12/0.63 thf(func_def_189, type, sK126: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 2.12/0.63 thf(func_def_190, type, sK127: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 2.12/0.63 thf(func_def_191, type, sK128: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > product_prod @ X1 @ X0))).
% 2.12/0.63 thf(func_def_192, type, sK129: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > X0))).
% 2.12/0.63 thf(func_def_193, type, sK130: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > X1))).
% 2.12/0.63 thf(func_def_194, type, sK131: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > X0))).
% 2.12/0.63 thf(func_def_195, type, sK132: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > X1))).
% 2.12/0.63 thf(func_def_196, type, sK133: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > product_prod @ X1 @ X0))).
% 2.12/0.63 thf(func_def_197, type, sK134: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > X0) > (X1 > X2) > (X1 > X0) > X1))).
% 2.12/0.63 thf(func_def_198, type, sK135: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 2.12/0.63 thf(func_def_199, type, sK136: !>[X0: $tType]:(((X0 > X0) > X0))).
% 2.12/0.63 thf(func_def_200, type, sK137: !>[X0: $tType, X1: $tType]:(((X0 > $o) > set @ product_prod @ X1 @ X0 > X1 > X0))).
% 2.12/0.63 thf(f1,axiom,(
% 2.12/0.63 ! [X2 : $tType,X0 : $tType,X4 : $tType,X1 : $tType,X7 : set @ product_prod @ X0 @ X2,X8 : set @ product_prod @ X1 @ X4] : (member @ product_prod @ (refine1665802226e_nres @ X0 > (X0 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1) @ (refine1665802226e_nres @ X2 > (X2 > refine1665802226e_nres @ X4) > refine1665802226e_nres @ X4) @ (product_Pair @ (refine1665802226e_nres @ X0 > (X0 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1) @ (refine1665802226e_nres @ X2 > (X2 > refine1665802226e_nres @ X4) > refine1665802226e_nres @ X4) @ refine463715084e_bind @ X0 @ X1 @ refine463715084e_bind @ X2 @ X4) @ (relAPP @ ((X0 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1) @ ((X2 > refine1665802226e_nres @ X4) > refine1665802226e_nres @ X4) @ set @ product_prod @ (refine1665802226e_nres @ X0 > (X0 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1) @ (refine1665802226e_nres @ X2 > (X2 > refine1665802226e_nres @ X4) > refine1665802226e_nres @ X4) @ (relAPP @ refine1665802226e_nres @ X0 @ refine1665802226e_nres @ X2 @ (set @ product_prod @ ((X0 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1) @ ((X2 > refine1665802226e_nres @ X4) > refine1665802226e_nres @ X4) > set @ product_prod @ (refine1665802226e_nres @ X0 > (X0 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1) @ (refine1665802226e_nres @ X2 > (X2 > refine1665802226e_nres @ X4) > refine1665802226e_nres @ X4)) @ fun_rel @ refine1665802226e_nres @ X0 @ refine1665802226e_nres @ X2 @ ((X0 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1) @ ((X2 > refine1665802226e_nres @ X4) > refine1665802226e_nres @ X4) @ (relAPP @ X0 @ X2 @ set @ product_prod @ refine1665802226e_nres @ X0 @ refine1665802226e_nres @ X2 @ refine476890328es_rel @ X0 @ X2 @ X7)) @ (relAPP @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X4 @ set @ product_prod @ ((X0 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1) @ ((X2 > refine1665802226e_nres @ X4) > refine1665802226e_nres @ X4) @ (relAPP @ (X0 > refine1665802226e_nres @ X1) @ (X2 > refine1665802226e_nres @ X4) @ (set @ product_prod @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X4 > set @ product_prod @ ((X0 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1) @ ((X2 > refine1665802226e_nres @ X4) > refine1665802226e_nres @ X4)) @ fun_rel @ (X0 > refine1665802226e_nres @ X1) @ (X2 > refine1665802226e_nres @ X4) @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X4 @ (relAPP @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X4 @ set @ product_prod @ (X0 > refine1665802226e_nres @ X1) @ (X2 > refine1665802226e_nres @ X4) @ (relAPP @ X0 @ X2 @ (set @ product_prod @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X4 > set @ product_prod @ (X0 > refine1665802226e_nres @ X1) @ (X2 > refine1665802226e_nres @ X4)) @ fun_rel @ X0 @ X2 @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X4 @ X7) @ (relAPP @ X1 @ X4 @ set @ product_prod @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X4 @ refine476890328es_rel @ X1 @ X4 @ X8))) @ (relAPP @ X1 @ X4 @ set @ product_prod @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X4 @ refine476890328es_rel @ X1 @ X4 @ X8))))),
% 2.12/0.63 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_param__bind)).
% 2.12/0.63 thf(f29,axiom,(
% 2.12/0.63 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (relAPP @ X2 @ X1 @ X0 = (^[X3 : (set @ product_prod @ X2 @ X1 > X0)] : (X3)))),
% 2.12/0.63 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_relAPP__def)).
% 2.12/0.63 thf(f277,conjecture,(
% 2.12/0.63 (member @ product_prod @ (refine1665802226e_nres @ a > (a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ (refine1665802226e_nres @ c > (c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ (product_Pair @ (refine1665802226e_nres @ a > (a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ (refine1665802226e_nres @ c > (c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ refine463715084e_bind @ a @ b @ refine463715084e_bind @ c @ d) @ (relAPP @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ set @ product_prod @ (refine1665802226e_nres @ a > (a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ (refine1665802226e_nres @ c > (c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ (relAPP @ refine1665802226e_nres @ a @ refine1665802226e_nres @ c @ (set @ product_prod @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) > set @ product_prod @ (refine1665802226e_nres @ a > (a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ (refine1665802226e_nres @ c > (c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d)) @ fun_rel @ refine1665802226e_nres @ a @ refine1665802226e_nres @ c @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ (relAPP @ a @ c @ set @ product_prod @ refine1665802226e_nres @ a @ refine1665802226e_nres @ c @ refine476890328es_rel @ a @ c @ r1)) @ (relAPP @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ set @ product_prod @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ (relAPP @ (a > refine1665802226e_nres @ b) @ (c > refine1665802226e_nres @ d) @ (set @ product_prod @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d > set @ product_prod @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d)) @ fun_rel @ (a > refine1665802226e_nres @ b) @ (c > refine1665802226e_nres @ d) @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ (relAPP @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ set @ product_prod @ (a > refine1665802226e_nres @ b) @ (c > refine1665802226e_nres @ d) @ (relAPP @ a @ c @ (set @ product_prod @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d > set @ product_prod @ (a > refine1665802226e_nres @ b) @ (c > refine1665802226e_nres @ d)) @ fun_rel @ a @ c @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ r1) @ (relAPP @ b @ d @ set @ product_prod @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ refine476890328es_rel @ b @ d @ r2))) @ (relAPP @ b @ d @ set @ product_prod @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ refine476890328es_rel @ b @ d @ r2))))),
% 2.12/0.63 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 2.12/0.63 thf(f278,negated_conjecture,(
% 2.12/0.63 ~(member @ product_prod @ (refine1665802226e_nres @ a > (a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ (refine1665802226e_nres @ c > (c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ (product_Pair @ (refine1665802226e_nres @ a > (a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ (refine1665802226e_nres @ c > (c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ refine463715084e_bind @ a @ b @ refine463715084e_bind @ c @ d) @ (relAPP @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ set @ product_prod @ (refine1665802226e_nres @ a > (a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ (refine1665802226e_nres @ c > (c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ (relAPP @ refine1665802226e_nres @ a @ refine1665802226e_nres @ c @ (set @ product_prod @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) > set @ product_prod @ (refine1665802226e_nres @ a > (a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ (refine1665802226e_nres @ c > (c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d)) @ fun_rel @ refine1665802226e_nres @ a @ refine1665802226e_nres @ c @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ (relAPP @ a @ c @ set @ product_prod @ refine1665802226e_nres @ a @ refine1665802226e_nres @ c @ refine476890328es_rel @ a @ c @ r1)) @ (relAPP @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ set @ product_prod @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ (relAPP @ (a > refine1665802226e_nres @ b) @ (c > refine1665802226e_nres @ d) @ (set @ product_prod @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d > set @ product_prod @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d)) @ fun_rel @ (a > refine1665802226e_nres @ b) @ (c > refine1665802226e_nres @ d) @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ (relAPP @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ set @ product_prod @ (a > refine1665802226e_nres @ b) @ (c > refine1665802226e_nres @ d) @ (relAPP @ a @ c @ (set @ product_prod @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d > set @ product_prod @ (a > refine1665802226e_nres @ b) @ (c > refine1665802226e_nres @ d)) @ fun_rel @ a @ c @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ r1) @ (relAPP @ b @ d @ set @ product_prod @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ refine476890328es_rel @ b @ d @ r2))) @ (relAPP @ b @ d @ set @ product_prod @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ refine476890328es_rel @ b @ d @ r2))))),
% 2.12/0.63 inference(negated_conjecture,[status(cth)],[f277])).
% 2.12/0.63 thf(f279,plain,(
% 2.12/0.63 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : $tType,X4 : set @ product_prod @ X1 @ X0,X5 : set @ product_prod @ X3 @ X2] : (member @ product_prod @ (refine1665802226e_nres @ X1 > (X1 > refine1665802226e_nres @ X3) > refine1665802226e_nres @ X3) @ (refine1665802226e_nres @ X0 > (X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2) @ (product_Pair @ (refine1665802226e_nres @ X1 > (X1 > refine1665802226e_nres @ X3) > refine1665802226e_nres @ X3) @ (refine1665802226e_nres @ X0 > (X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2) @ refine463715084e_bind @ X1 @ X3 @ refine463715084e_bind @ X0 @ X2) @ (relAPP @ ((X1 > refine1665802226e_nres @ X3) > refine1665802226e_nres @ X3) @ ((X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2) @ set @ product_prod @ (refine1665802226e_nres @ X1 > (X1 > refine1665802226e_nres @ X3) > refine1665802226e_nres @ X3) @ (refine1665802226e_nres @ X0 > (X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2) @ (relAPP @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X0 @ (set @ product_prod @ ((X1 > refine1665802226e_nres @ X3) > refine1665802226e_nres @ X3) @ ((X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2) > set @ product_prod @ (refine1665802226e_nres @ X1 > (X1 > refine1665802226e_nres @ X3) > refine1665802226e_nres @ X3) @ (refine1665802226e_nres @ X0 > (X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2)) @ fun_rel @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X0 @ ((X1 > refine1665802226e_nres @ X3) > refine1665802226e_nres @ X3) @ ((X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2) @ (relAPP @ X1 @ X0 @ set @ product_prod @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X0 @ refine476890328es_rel @ X1 @ X0 @ X4)) @ (relAPP @ refine1665802226e_nres @ X3 @ refine1665802226e_nres @ X2 @ set @ product_prod @ ((X1 > refine1665802226e_nres @ X3) > refine1665802226e_nres @ X3) @ ((X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2) @ (relAPP @ (X1 > refine1665802226e_nres @ X3) @ (X0 > refine1665802226e_nres @ X2) @ (set @ product_prod @ refine1665802226e_nres @ X3 @ refine1665802226e_nres @ X2 > set @ product_prod @ ((X1 > refine1665802226e_nres @ X3) > refine1665802226e_nres @ X3) @ ((X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2)) @ fun_rel @ (X1 > refine1665802226e_nres @ X3) @ (X0 > refine1665802226e_nres @ X2) @ refine1665802226e_nres @ X3 @ refine1665802226e_nres @ X2 @ (relAPP @ refine1665802226e_nres @ X3 @ refine1665802226e_nres @ X2 @ set @ product_prod @ (X1 > refine1665802226e_nres @ X3) @ (X0 > refine1665802226e_nres @ X2) @ (relAPP @ X1 @ X0 @ (set @ product_prod @ refine1665802226e_nres @ X3 @ refine1665802226e_nres @ X2 > set @ product_prod @ (X1 > refine1665802226e_nres @ X3) @ (X0 > refine1665802226e_nres @ X2)) @ fun_rel @ X1 @ X0 @ refine1665802226e_nres @ X3 @ refine1665802226e_nres @ X2 @ X4) @ (relAPP @ X3 @ X2 @ set @ product_prod @ refine1665802226e_nres @ X3 @ refine1665802226e_nres @ X2 @ refine476890328es_rel @ X3 @ X2 @ X5))) @ (relAPP @ X3 @ X2 @ set @ product_prod @ refine1665802226e_nres @ X3 @ refine1665802226e_nres @ X2 @ refine476890328es_rel @ X3 @ X2 @ X5))))),
% 2.12/0.63 inference(rectify,[],[f1])).
% 2.12/0.63 thf(f280,plain,(
% 2.12/0.63 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : $tType,X4 : set @ product_prod @ X1 @ X0,X5 : set @ product_prod @ X3 @ X2] : (((member @ product_prod @ (refine1665802226e_nres @ X1 > (X1 > refine1665802226e_nres @ X3) > refine1665802226e_nres @ X3) @ (refine1665802226e_nres @ X0 > (X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2) @ (product_Pair @ (refine1665802226e_nres @ X1 > (X1 > refine1665802226e_nres @ X3) > refine1665802226e_nres @ X3) @ (refine1665802226e_nres @ X0 > (X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2) @ refine463715084e_bind @ X1 @ X3 @ refine463715084e_bind @ X0 @ X2) @ (relAPP @ ((X1 > refine1665802226e_nres @ X3) > refine1665802226e_nres @ X3) @ ((X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2) @ set @ product_prod @ (refine1665802226e_nres @ X1 > (X1 > refine1665802226e_nres @ X3) > refine1665802226e_nres @ X3) @ (refine1665802226e_nres @ X0 > (X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2) @ (relAPP @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X0 @ (set @ product_prod @ ((X1 > refine1665802226e_nres @ X3) > refine1665802226e_nres @ X3) @ ((X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2) > set @ product_prod @ (refine1665802226e_nres @ X1 > (X1 > refine1665802226e_nres @ X3) > refine1665802226e_nres @ X3) @ (refine1665802226e_nres @ X0 > (X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2)) @ fun_rel @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X0 @ ((X1 > refine1665802226e_nres @ X3) > refine1665802226e_nres @ X3) @ ((X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2) @ (relAPP @ X1 @ X0 @ set @ product_prod @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X0 @ refine476890328es_rel @ X1 @ X0 @ X4)) @ (relAPP @ refine1665802226e_nres @ X3 @ refine1665802226e_nres @ X2 @ set @ product_prod @ ((X1 > refine1665802226e_nres @ X3) > refine1665802226e_nres @ X3) @ ((X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2) @ (relAPP @ (X1 > refine1665802226e_nres @ X3) @ (X0 > refine1665802226e_nres @ X2) @ (set @ product_prod @ refine1665802226e_nres @ X3 @ refine1665802226e_nres @ X2 > set @ product_prod @ ((X1 > refine1665802226e_nres @ X3) > refine1665802226e_nres @ X3) @ ((X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2)) @ fun_rel @ (X1 > refine1665802226e_nres @ X3) @ (X0 > refine1665802226e_nres @ X2) @ refine1665802226e_nres @ X3 @ refine1665802226e_nres @ X2 @ (relAPP @ refine1665802226e_nres @ X3 @ refine1665802226e_nres @ X2 @ set @ product_prod @ (X1 > refine1665802226e_nres @ X3) @ (X0 > refine1665802226e_nres @ X2) @ (relAPP @ X1 @ X0 @ (set @ product_prod @ refine1665802226e_nres @ X3 @ refine1665802226e_nres @ X2 > set @ product_prod @ (X1 > refine1665802226e_nres @ X3) @ (X0 > refine1665802226e_nres @ X2)) @ fun_rel @ X1 @ X0 @ refine1665802226e_nres @ X3 @ refine1665802226e_nres @ X2 @ X4) @ (relAPP @ X3 @ X2 @ set @ product_prod @ refine1665802226e_nres @ X3 @ refine1665802226e_nres @ X2 @ refine476890328es_rel @ X3 @ X2 @ X5))) @ (relAPP @ X3 @ X2 @ set @ product_prod @ refine1665802226e_nres @ X3 @ refine1665802226e_nres @ X2 @ refine476890328es_rel @ X3 @ X2 @ X5))))) = $true)),
% 2.12/0.63 inference(fool_elimination,[],[f279])).
% 2.12/0.63 thf(f317,plain,(
% 2.12/0.63 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (relAPP @ X2 @ X1 @ X0 = (^[Y0 : set @ product_prod @ X2 @ X1 > X0]: (Y0)))),
% 2.12/0.63 inference(fool_elimination,[],[f29])).
% 2.12/0.63 thf(f611,plain,(
% 2.12/0.63 ~(member @ product_prod @ (refine1665802226e_nres @ a > (a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ (refine1665802226e_nres @ c > (c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ (product_Pair @ (refine1665802226e_nres @ a > (a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ (refine1665802226e_nres @ c > (c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ refine463715084e_bind @ a @ b @ refine463715084e_bind @ c @ d) @ (relAPP @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ set @ product_prod @ (refine1665802226e_nres @ a > (a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ (refine1665802226e_nres @ c > (c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ (relAPP @ refine1665802226e_nres @ a @ refine1665802226e_nres @ c @ (set @ product_prod @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) > set @ product_prod @ (refine1665802226e_nres @ a > (a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ (refine1665802226e_nres @ c > (c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d)) @ fun_rel @ refine1665802226e_nres @ a @ refine1665802226e_nres @ c @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ (relAPP @ a @ c @ set @ product_prod @ refine1665802226e_nres @ a @ refine1665802226e_nres @ c @ refine476890328es_rel @ a @ c @ r1)) @ (relAPP @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ set @ product_prod @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ (relAPP @ (a > refine1665802226e_nres @ b) @ (c > refine1665802226e_nres @ d) @ (set @ product_prod @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d > set @ product_prod @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d)) @ fun_rel @ (a > refine1665802226e_nres @ b) @ (c > refine1665802226e_nres @ d) @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ (relAPP @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ set @ product_prod @ (a > refine1665802226e_nres @ b) @ (c > refine1665802226e_nres @ d) @ (relAPP @ a @ c @ (set @ product_prod @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d > set @ product_prod @ (a > refine1665802226e_nres @ b) @ (c > refine1665802226e_nres @ d)) @ fun_rel @ a @ c @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ r1) @ (relAPP @ b @ d @ set @ product_prod @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ refine476890328es_rel @ b @ d @ r2))) @ (relAPP @ b @ d @ set @ product_prod @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ refine476890328es_rel @ b @ d @ r2))))),
% 2.12/0.63 inference(rectify,[],[f278])).
% 2.12/0.63 thf(f612,plain,(
% 2.12/0.63 ~ (((member @ product_prod @ (refine1665802226e_nres @ a > (a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ (refine1665802226e_nres @ c > (c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ (product_Pair @ (refine1665802226e_nres @ a > (a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ (refine1665802226e_nres @ c > (c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ refine463715084e_bind @ a @ b @ refine463715084e_bind @ c @ d) @ (relAPP @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ set @ product_prod @ (refine1665802226e_nres @ a > (a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ (refine1665802226e_nres @ c > (c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ (relAPP @ refine1665802226e_nres @ a @ refine1665802226e_nres @ c @ (set @ product_prod @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) > set @ product_prod @ (refine1665802226e_nres @ a > (a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ (refine1665802226e_nres @ c > (c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d)) @ fun_rel @ refine1665802226e_nres @ a @ refine1665802226e_nres @ c @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ (relAPP @ a @ c @ set @ product_prod @ refine1665802226e_nres @ a @ refine1665802226e_nres @ c @ refine476890328es_rel @ a @ c @ r1)) @ (relAPP @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ set @ product_prod @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ (relAPP @ (a > refine1665802226e_nres @ b) @ (c > refine1665802226e_nres @ d) @ (set @ product_prod @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d > set @ product_prod @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d)) @ fun_rel @ (a > refine1665802226e_nres @ b) @ (c > refine1665802226e_nres @ d) @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ (relAPP @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ set @ product_prod @ (a > refine1665802226e_nres @ b) @ (c > refine1665802226e_nres @ d) @ (relAPP @ a @ c @ (set @ product_prod @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d > set @ product_prod @ (a > refine1665802226e_nres @ b) @ (c > refine1665802226e_nres @ d)) @ fun_rel @ a @ c @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ r1) @ (relAPP @ b @ d @ set @ product_prod @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ refine476890328es_rel @ b @ d @ r2))) @ (relAPP @ b @ d @ set @ product_prod @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ refine476890328es_rel @ b @ d @ r2))))) = $true)),
% 2.12/0.63 inference(fool_elimination,[],[f611])).
% 2.12/0.63 thf(f622,plain,(
% 2.12/0.63 (((member @ product_prod @ (refine1665802226e_nres @ a > (a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ (refine1665802226e_nres @ c > (c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ (product_Pair @ (refine1665802226e_nres @ a > (a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ (refine1665802226e_nres @ c > (c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ refine463715084e_bind @ a @ b @ refine463715084e_bind @ c @ d) @ (relAPP @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ set @ product_prod @ (refine1665802226e_nres @ a > (a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ (refine1665802226e_nres @ c > (c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ (relAPP @ refine1665802226e_nres @ a @ refine1665802226e_nres @ c @ (set @ product_prod @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) > set @ product_prod @ (refine1665802226e_nres @ a > (a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ (refine1665802226e_nres @ c > (c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d)) @ fun_rel @ refine1665802226e_nres @ a @ refine1665802226e_nres @ c @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ (relAPP @ a @ c @ set @ product_prod @ refine1665802226e_nres @ a @ refine1665802226e_nres @ c @ refine476890328es_rel @ a @ c @ r1)) @ (relAPP @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ set @ product_prod @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ (relAPP @ (a > refine1665802226e_nres @ b) @ (c > refine1665802226e_nres @ d) @ (set @ product_prod @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d > set @ product_prod @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d)) @ fun_rel @ (a > refine1665802226e_nres @ b) @ (c > refine1665802226e_nres @ d) @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ (relAPP @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ set @ product_prod @ (a > refine1665802226e_nres @ b) @ (c > refine1665802226e_nres @ d) @ (relAPP @ a @ c @ (set @ product_prod @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d > set @ product_prod @ (a > refine1665802226e_nres @ b) @ (c > refine1665802226e_nres @ d)) @ fun_rel @ a @ c @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ r1) @ (relAPP @ b @ d @ set @ product_prod @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ refine476890328es_rel @ b @ d @ r2))) @ (relAPP @ b @ d @ set @ product_prod @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ refine476890328es_rel @ b @ d @ r2))))) != $true)),
% 2.12/0.63 inference(flattening,[],[f612])).
% 2.12/0.63 thf(f894,plain,(
% 2.12/0.63 ( ! [X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X4 : set @ product_prod @ X1 @ X0,X5 : set @ product_prod @ X3 @ X2] : ((((member @ product_prod @ (refine1665802226e_nres @ X1 > (X1 > refine1665802226e_nres @ X3) > refine1665802226e_nres @ X3) @ (refine1665802226e_nres @ X0 > (X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2) @ (product_Pair @ (refine1665802226e_nres @ X1 > (X1 > refine1665802226e_nres @ X3) > refine1665802226e_nres @ X3) @ (refine1665802226e_nres @ X0 > (X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2) @ refine463715084e_bind @ X1 @ X3 @ refine463715084e_bind @ X0 @ X2) @ (relAPP @ ((X1 > refine1665802226e_nres @ X3) > refine1665802226e_nres @ X3) @ ((X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2) @ set @ product_prod @ (refine1665802226e_nres @ X1 > (X1 > refine1665802226e_nres @ X3) > refine1665802226e_nres @ X3) @ (refine1665802226e_nres @ X0 > (X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2) @ (relAPP @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X0 @ (set @ product_prod @ ((X1 > refine1665802226e_nres @ X3) > refine1665802226e_nres @ X3) @ ((X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2) > set @ product_prod @ (refine1665802226e_nres @ X1 > (X1 > refine1665802226e_nres @ X3) > refine1665802226e_nres @ X3) @ (refine1665802226e_nres @ X0 > (X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2)) @ fun_rel @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X0 @ ((X1 > refine1665802226e_nres @ X3) > refine1665802226e_nres @ X3) @ ((X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2) @ (relAPP @ X1 @ X0 @ set @ product_prod @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X0 @ refine476890328es_rel @ X1 @ X0 @ X4)) @ (relAPP @ refine1665802226e_nres @ X3 @ refine1665802226e_nres @ X2 @ set @ product_prod @ ((X1 > refine1665802226e_nres @ X3) > refine1665802226e_nres @ X3) @ ((X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2) @ (relAPP @ (X1 > refine1665802226e_nres @ X3) @ (X0 > refine1665802226e_nres @ X2) @ (set @ product_prod @ refine1665802226e_nres @ X3 @ refine1665802226e_nres @ X2 > set @ product_prod @ ((X1 > refine1665802226e_nres @ X3) > refine1665802226e_nres @ X3) @ ((X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2)) @ fun_rel @ (X1 > refine1665802226e_nres @ X3) @ (X0 > refine1665802226e_nres @ X2) @ refine1665802226e_nres @ X3 @ refine1665802226e_nres @ X2 @ (relAPP @ refine1665802226e_nres @ X3 @ refine1665802226e_nres @ X2 @ set @ product_prod @ (X1 > refine1665802226e_nres @ X3) @ (X0 > refine1665802226e_nres @ X2) @ (relAPP @ X1 @ X0 @ (set @ product_prod @ refine1665802226e_nres @ X3 @ refine1665802226e_nres @ X2 > set @ product_prod @ (X1 > refine1665802226e_nres @ X3) @ (X0 > refine1665802226e_nres @ X2)) @ fun_rel @ X1 @ X0 @ refine1665802226e_nres @ X3 @ refine1665802226e_nres @ X2 @ X4) @ (relAPP @ X3 @ X2 @ set @ product_prod @ refine1665802226e_nres @ X3 @ refine1665802226e_nres @ X2 @ refine476890328es_rel @ X3 @ X2 @ X5))) @ (relAPP @ X3 @ X2 @ set @ product_prod @ refine1665802226e_nres @ X3 @ refine1665802226e_nres @ X2 @ refine476890328es_rel @ X3 @ X2 @ X5))))) = $true)) )),
% 2.12/0.63 inference(cnf_transformation,[],[f280])).
% 2.12/0.63 thf(f924,plain,(
% 2.12/0.63 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : ((relAPP @ X2 @ X1 @ X0 = (^[Y0 : set @ product_prod @ X2 @ X1 > X0]: (Y0)))) )),
% 2.12/0.63 inference(cnf_transformation,[],[f317])).
% 2.12/0.63 thf(f1242,plain,(
% 2.12/0.63 (((member @ product_prod @ (refine1665802226e_nres @ a > (a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ (refine1665802226e_nres @ c > (c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ (product_Pair @ (refine1665802226e_nres @ a > (a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ (refine1665802226e_nres @ c > (c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ refine463715084e_bind @ a @ b @ refine463715084e_bind @ c @ d) @ (relAPP @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ set @ product_prod @ (refine1665802226e_nres @ a > (a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ (refine1665802226e_nres @ c > (c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ (relAPP @ refine1665802226e_nres @ a @ refine1665802226e_nres @ c @ (set @ product_prod @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) > set @ product_prod @ (refine1665802226e_nres @ a > (a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ (refine1665802226e_nres @ c > (c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d)) @ fun_rel @ refine1665802226e_nres @ a @ refine1665802226e_nres @ c @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ (relAPP @ a @ c @ set @ product_prod @ refine1665802226e_nres @ a @ refine1665802226e_nres @ c @ refine476890328es_rel @ a @ c @ r1)) @ (relAPP @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ set @ product_prod @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ (relAPP @ (a > refine1665802226e_nres @ b) @ (c > refine1665802226e_nres @ d) @ (set @ product_prod @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d > set @ product_prod @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d)) @ fun_rel @ (a > refine1665802226e_nres @ b) @ (c > refine1665802226e_nres @ d) @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ (relAPP @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ set @ product_prod @ (a > refine1665802226e_nres @ b) @ (c > refine1665802226e_nres @ d) @ (relAPP @ a @ c @ (set @ product_prod @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d > set @ product_prod @ (a > refine1665802226e_nres @ b) @ (c > refine1665802226e_nres @ d)) @ fun_rel @ a @ c @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ r1) @ (relAPP @ b @ d @ set @ product_prod @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ refine476890328es_rel @ b @ d @ r2))) @ (relAPP @ b @ d @ set @ product_prod @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ refine476890328es_rel @ b @ d @ r2))))) != $true)),
% 2.12/0.63 inference(cnf_transformation,[],[f622])).
% 2.12/0.63 thf(f1248,plain,(
% 2.12/0.63 ( ! [X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X4 : set @ product_prod @ X1 @ X0,X5 : set @ product_prod @ X3 @ X2] : (($true = ((member @ product_prod @ (refine1665802226e_nres @ X1 > (X1 > refine1665802226e_nres @ X3) > refine1665802226e_nres @ X3) @ (refine1665802226e_nres @ X0 > (X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2) @ (product_Pair @ (refine1665802226e_nres @ X1 > (X1 > refine1665802226e_nres @ X3) > refine1665802226e_nres @ X3) @ (refine1665802226e_nres @ X0 > (X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2) @ refine463715084e_bind @ X1 @ X3 @ refine463715084e_bind @ X0 @ X2) @ ((^[Y0 : set @ product_prod @ ((X1 > refine1665802226e_nres @ X3) > refine1665802226e_nres @ X3) @ ((X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2) > set @ product_prod @ (refine1665802226e_nres @ X1 > (X1 > refine1665802226e_nres @ X3) > refine1665802226e_nres @ X3) @ (refine1665802226e_nres @ X0 > (X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2)]: (Y0)) @ ((^[Y0 : set @ product_prod @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X0 > set @ product_prod @ ((X1 > refine1665802226e_nres @ X3) > refine1665802226e_nres @ X3) @ ((X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2) > set @ product_prod @ (refine1665802226e_nres @ X1 > (X1 > refine1665802226e_nres @ X3) > refine1665802226e_nres @ X3) @ (refine1665802226e_nres @ X0 > (X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2)]: (Y0)) @ fun_rel @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X0 @ ((X1 > refine1665802226e_nres @ X3) > refine1665802226e_nres @ X3) @ ((X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2) @ ((^[Y0 : set @ product_prod @ X1 @ X0 > set @ product_prod @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X0]: (Y0)) @ refine476890328es_rel @ X1 @ X0 @ X4)) @ ((^[Y0 : set @ product_prod @ refine1665802226e_nres @ X3 @ refine1665802226e_nres @ X2 > set @ product_prod @ ((X1 > refine1665802226e_nres @ X3) > refine1665802226e_nres @ X3) @ ((X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2)]: (Y0)) @ ((^[Y0 : set @ product_prod @ (X1 > refine1665802226e_nres @ X3) @ (X0 > refine1665802226e_nres @ X2) > set @ product_prod @ refine1665802226e_nres @ X3 @ refine1665802226e_nres @ X2 > set @ product_prod @ ((X1 > refine1665802226e_nres @ X3) > refine1665802226e_nres @ X3) @ ((X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2)]: (Y0)) @ fun_rel @ (X1 > refine1665802226e_nres @ X3) @ (X0 > refine1665802226e_nres @ X2) @ refine1665802226e_nres @ X3 @ refine1665802226e_nres @ X2 @ ((^[Y0 : set @ product_prod @ refine1665802226e_nres @ X3 @ refine1665802226e_nres @ X2 > set @ product_prod @ (X1 > refine1665802226e_nres @ X3) @ (X0 > refine1665802226e_nres @ X2)]: (Y0)) @ ((^[Y0 : set @ product_prod @ X1 @ X0 > set @ product_prod @ refine1665802226e_nres @ X3 @ refine1665802226e_nres @ X2 > set @ product_prod @ (X1 > refine1665802226e_nres @ X3) @ (X0 > refine1665802226e_nres @ X2)]: (Y0)) @ fun_rel @ X1 @ X0 @ refine1665802226e_nres @ X3 @ refine1665802226e_nres @ X2 @ X4) @ ((^[Y0 : set @ product_prod @ X3 @ X2 > set @ product_prod @ refine1665802226e_nres @ X3 @ refine1665802226e_nres @ X2]: (Y0)) @ refine476890328es_rel @ X3 @ X2 @ X5))) @ ((^[Y0 : set @ product_prod @ X3 @ X2 > set @ product_prod @ refine1665802226e_nres @ X3 @ refine1665802226e_nres @ X2]: (Y0)) @ refine476890328es_rel @ X3 @ X2 @ X5))))))) )),
% 2.12/0.63 inference(definition_unfolding,[],[f894,f924,f924,f924,f924,f924,f924,f924,f924,f924])).
% 2.12/0.63 thf(f1400,plain,(
% 2.12/0.63 ($true != ((member @ product_prod @ (refine1665802226e_nres @ a > (a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ (refine1665802226e_nres @ c > (c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ (product_Pair @ (refine1665802226e_nres @ a > (a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ (refine1665802226e_nres @ c > (c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ refine463715084e_bind @ a @ b @ refine463715084e_bind @ c @ d) @ ((^[Y0 : set @ product_prod @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) > set @ product_prod @ (refine1665802226e_nres @ a > (a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ (refine1665802226e_nres @ c > (c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d)]: (Y0)) @ ((^[Y0 : set @ product_prod @ refine1665802226e_nres @ a @ refine1665802226e_nres @ c > set @ product_prod @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) > set @ product_prod @ (refine1665802226e_nres @ a > (a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ (refine1665802226e_nres @ c > (c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d)]: (Y0)) @ fun_rel @ refine1665802226e_nres @ a @ refine1665802226e_nres @ c @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ ((^[Y0 : set @ product_prod @ a @ c > set @ product_prod @ refine1665802226e_nres @ a @ refine1665802226e_nres @ c]: (Y0)) @ refine476890328es_rel @ a @ c @ r1)) @ ((^[Y0 : set @ product_prod @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d > set @ product_prod @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d)]: (Y0)) @ ((^[Y0 : set @ product_prod @ (a > refine1665802226e_nres @ b) @ (c > refine1665802226e_nres @ d) > set @ product_prod @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d > set @ product_prod @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d)]: (Y0)) @ fun_rel @ (a > refine1665802226e_nres @ b) @ (c > refine1665802226e_nres @ d) @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ ((^[Y0 : set @ product_prod @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d > set @ product_prod @ (a > refine1665802226e_nres @ b) @ (c > refine1665802226e_nres @ d)]: (Y0)) @ ((^[Y0 : set @ product_prod @ a @ c > set @ product_prod @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d > set @ product_prod @ (a > refine1665802226e_nres @ b) @ (c > refine1665802226e_nres @ d)]: (Y0)) @ fun_rel @ a @ c @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ r1) @ ((^[Y0 : set @ product_prod @ b @ d > set @ product_prod @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d]: (Y0)) @ refine476890328es_rel @ b @ d @ r2))) @ ((^[Y0 : set @ product_prod @ b @ d > set @ product_prod @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d]: (Y0)) @ refine476890328es_rel @ b @ d @ r2))))))),
% 2.12/0.63 inference(definition_unfolding,[],[f1242,f924,f924,f924,f924,f924,f924,f924,f924,f924])).
% 2.12/0.63 thf(f1436,plain,(
% 2.12/0.63 ($true != ((member @ product_prod @ (refine1665802226e_nres @ a > (a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ (refine1665802226e_nres @ c > (c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ (product_Pair @ (refine1665802226e_nres @ a > (a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ (refine1665802226e_nres @ c > (c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ refine463715084e_bind @ a @ b @ refine463715084e_bind @ c @ d) @ (fun_rel @ refine1665802226e_nres @ a @ refine1665802226e_nres @ c @ ((a > refine1665802226e_nres @ b) > refine1665802226e_nres @ b) @ ((c > refine1665802226e_nres @ d) > refine1665802226e_nres @ d) @ (refine476890328es_rel @ a @ c @ r1) @ (fun_rel @ (a > refine1665802226e_nres @ b) @ (c > refine1665802226e_nres @ d) @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ (fun_rel @ a @ c @ refine1665802226e_nres @ b @ refine1665802226e_nres @ d @ r1 @ (refine476890328es_rel @ b @ d @ r2)) @ (refine476890328es_rel @ b @ d @ r2))))))),
% 2.12/0.63 inference(beta-eta_normalization,[],[f1400])).
% 2.12/0.63 thf(f1767,plain,(
% 2.12/0.63 ( ! [X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X4 : set @ product_prod @ X1 @ X0,X5 : set @ product_prod @ X3 @ X2] : (($true = ((member @ product_prod @ (refine1665802226e_nres @ X1 > (X1 > refine1665802226e_nres @ X3) > refine1665802226e_nres @ X3) @ (refine1665802226e_nres @ X0 > (X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2) @ (product_Pair @ (refine1665802226e_nres @ X1 > (X1 > refine1665802226e_nres @ X3) > refine1665802226e_nres @ X3) @ (refine1665802226e_nres @ X0 > (X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2) @ refine463715084e_bind @ X1 @ X3 @ refine463715084e_bind @ X0 @ X2) @ (fun_rel @ refine1665802226e_nres @ X1 @ refine1665802226e_nres @ X0 @ ((X1 > refine1665802226e_nres @ X3) > refine1665802226e_nres @ X3) @ ((X0 > refine1665802226e_nres @ X2) > refine1665802226e_nres @ X2) @ (refine476890328es_rel @ X1 @ X0 @ X4) @ (fun_rel @ (X1 > refine1665802226e_nres @ X3) @ (X0 > refine1665802226e_nres @ X2) @ refine1665802226e_nres @ X3 @ refine1665802226e_nres @ X2 @ (fun_rel @ X1 @ X0 @ refine1665802226e_nres @ X3 @ refine1665802226e_nres @ X2 @ X4 @ (refine476890328es_rel @ X3 @ X2 @ X5)) @ (refine476890328es_rel @ X3 @ X2 @ X5))))))) )),
% 2.12/0.63 inference(beta-eta_normalization,[],[f1248])).
% 2.12/0.63 thf(f1790,plain,(
% 2.12/0.63 $false),
% 2.12/0.63 inference(backward_subsumption_resolution,[],[f1436,f1767])).
% 2.12/0.63 % SZS output end Proof for theBenchmark
% 2.12/0.63 % (576336)------------------------------
% 2.12/0.63 % (576336)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.12/0.63 % (576336)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.12/0.63 % (576336)CaDiCaL version: 2.1.3
% 2.12/0.63 % (576336)Termination reason: Refutation
% 2.12/0.63 % (576336)Time elapsed: 0.138 s
% 2.12/0.63 % (576336)Peak memory usage: 16 MB
% 2.12/0.63 % (576336)Instructions burned: 293 (million)
% 2.12/0.63 % (576301)Success in time 0.39 s
% 2.12/0.63 % Vampire exiting
%------------------------------------------------------------------------------