%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP204^2 : 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 : n017.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 08:11:06 AM UTC 2026
% Result : Theorem 0.99s 0.54s
% Output : Refutation 0.99s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ITP204^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.27 % Computer : n017.cluster.edu
% 0.12/0.27 % Model : x86_64 x86_64
% 0.12/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.27 % Memory : 8046.5625MB
% 0.12/0.27 % OS : Linux 6.8.0-71-generic
% 0.12/0.27 % CPULimit : 300
% 0.12/0.27 % WCLimit : 300
% 0.12/0.27 % DateTime : Tue Sep 29 20:06:52 UTC 2026
% 0.12/0.27 % CPUTime :
% 0.12/0.27 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.26/0.31 Running first-order model finding
% 0.26/0.31 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.99/0.54 % (832884)Will run a generic schedule for satisfiability detection.
% 0.99/0.54 % (832889)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1737670931_2999 on theBenchmark for (2999ds/0Mi)
% 0.99/0.54 % (832890)% WARNING: option uhcvi not known.
% 0.99/0.54 % (832890)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4086236938:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.99/0.54 % (832891)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4266648253:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.99/0.54 % (832892)dis+10_1_sil=32000:sp=arity:random_seed=628067235:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.99/0.54 % (832893)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=691984915:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.99/0.54 % (832894)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2591401167:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.99/0.54 % (832895)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2358235648:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.99/0.54 % Exception at run slice level
% 0.99/0.54 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.99/0.54 % (832890)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.99/0.54 % (832893)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.99/0.54 % (832903)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1285600906:i=714:nm=2_2998 on theBenchmark for (2998ds/714Mi)
% 0.99/0.54 % (832892)Instruction limit reached!
% 0.99/0.54 % (832892)------------------------------
% 0.99/0.54 % (832892)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.99/0.54 % (832892)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.99/0.54 % (832892)CaDiCaL version: 2.1.3
% 0.99/0.54 % (832892)Termination reason: Instruction limit
% 0.99/0.54 % (832892)Termination phase: Property scanning
% 0.99/0.54 % (832892)Time elapsed: 0.081 s
% 0.99/0.54 % (832892)Peak memory usage: 11 MB
% 0.99/0.54 % (832892)Instructions burned: 103 (million)
% 0.99/0.54 % (832890)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.99/0.54 % Exception at run slice level
% 0.99/0.54 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.99/0.54 % (832893)Instruction limit reached!
% 0.99/0.54 % (832893)------------------------------
% 0.99/0.54 % (832893)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.99/0.54 % (832893)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.99/0.54 % (832893)CaDiCaL version: 2.1.3
% 0.99/0.54 % (832893)Termination reason: Instruction limit
% 0.99/0.54 % (832893)Termination phase: Saturation
% 0.99/0.54 % (832893)Time elapsed: 0.092 s
% 0.99/0.54 % (832893)Peak memory usage: 12 MB
% 0.99/0.54 % (832893)Instructions burned: 116 (million)
% 0.99/0.54 % (832894)Instruction limit reached!
% 0.99/0.54 % (832894)------------------------------
% 0.99/0.54 % (832894)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.99/0.54 % (832894)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.99/0.54 % (832894)CaDiCaL version: 2.1.3
% 0.99/0.54 % (832894)Termination reason: Instruction limit
% 0.99/0.54 % (832894)Termination phase: Saturation
% 0.99/0.54 % (832894)Time elapsed: 0.105 s
% 0.99/0.54 % (832894)Peak memory usage: 13 MB
% 0.99/0.54 % (832894)Instructions burned: 131 (million)
% 0.99/0.54 % (832907)ott-21_1_sil=16000:fs=off:random_seed=3552320411:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 0.99/0.54 % (832906)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=3268331753:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 0.99/0.54 % (832905)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3292000859:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 0.99/0.54 % (832891) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-832884-832891"...
% 0.99/0.54 % (832895)Instruction limit reached!
% 0.99/0.54 % (832895)------------------------------
% 0.99/0.54 % (832895)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.99/0.54 % (832895)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.99/0.54 % (832895)CaDiCaL version: 2.1.3
% 0.99/0.54 % (832895)Termination reason: Instruction limit
% 0.99/0.54 % (832895)Termination phase: Saturation
% 0.99/0.54 % (832895)Time elapsed: 0.130 s
% 0.99/0.54 % (832895)Peak memory usage: 14 MB
% 0.99/0.54 % (832895)Instructions burned: 159 (million)
% 0.99/0.54 % (832908)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=4100186807:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 0.99/0.54 % (832906)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.99/0.54 % (832891)...printing done.
% 0.99/0.54 % (832891)Refutation found. Thanks to Tanya!
% 0.99/0.54 % SZS status Theorem for theBenchmark
% 0.99/0.54 % SZS output start Proof for theBenchmark
% 0.99/0.54 thf(type_def_5, type, product_prod: ($tType * $tType) > $tType).
% 0.99/0.54 thf(type_def_6, type, variable: $tType).
% 0.99/0.54 thf(type_def_7, type, option: $tType > $tType).
% 0.99/0.54 thf(type_def_8, type, game: $tType).
% 0.99/0.54 thf(type_def_9, type, char: $tType).
% 0.99/0.54 thf(type_def_10, type, trm: $tType).
% 0.99/0.54 thf(type_def_11, type, fml: $tType).
% 0.99/0.54 thf(type_def_12, type, set: $tType > $tType).
% 0.99/0.54 thf(type_def_13, type, sTfun: ($tType * $tType) > $tType).
% 0.99/0.54 thf(func_def_0, type, bounded_lattice: !>[X0: $tType]:($o)).
% 0.99/0.54 thf(func_def_1, type, type: !>[X0: $tType]:($o)).
% 0.99/0.54 thf(func_def_2, type, bot: !>[X0: $tType]:($o)).
% 0.99/0.54 thf(func_def_3, type, ord: !>[X0: $tType]:($o)).
% 0.99/0.54 thf(func_def_4, type, order: !>[X0: $tType]:($o)).
% 0.99/0.54 thf(func_def_5, type, lattice: !>[X0: $tType]:($o)).
% 0.99/0.54 thf(func_def_6, type, linorder: !>[X0: $tType]:($o)).
% 0.99/0.54 thf(func_def_7, type, preorder: !>[X0: $tType]:($o)).
% 0.99/0.54 thf(func_def_8, type, order_bot: !>[X0: $tType]:($o)).
% 0.99/0.54 thf(func_def_9, type, semilattice_inf: !>[X0: $tType]:($o)).
% 0.99/0.54 thf(func_def_10, type, bounded_lattice_bot: !>[X0: $tType]:($o)).
% 0.99/0.54 thf(func_def_11, type, if: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 0.99/0.54 thf(func_def_12, type, inf_inf: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.99/0.54 thf(func_def_13, type, none: !>[X0: $tType]:(option @ X0)).
% 0.99/0.54 thf(func_def_14, type, some: !>[X0: $tType]:((X0 > option @ X0))).
% 0.99/0.54 thf(func_def_15, type, case_option: !>[X0: $tType, X1: $tType]:((X0 > (X1 > X0) > option @ X1 > X0))).
% 0.99/0.54 thf(func_def_16, type, the: !>[X0: $tType]:((option @ X0 > X0))).
% 0.99/0.54 thf(func_def_17, type, bot_bot: !>[X0: $tType]:(X0)).
% 0.99/0.54 thf(func_def_18, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.99/0.54 thf(func_def_19, type, product_Pair: !>[X0: $tType, X1: $tType]:((X0 > X1 > product_prod @ X0 @ X1))).
% 0.99/0.54 thf(func_def_20, type, produc2004651681e_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 0.99/0.54 thf(func_def_21, type, product_case_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 0.99/0.54 thf(func_def_22, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.99/0.54 thf(func_def_23, type, is_empty: !>[X0: $tType]:((set @ X0 > $o))).
% 0.99/0.54 thf(func_def_24, type, static_FVF: (fml > set @ variable)).
% 0.99/0.54 thf(func_def_25, type, static_FVT: (trm > set @ variable)).
% 0.99/0.54 thf(func_def_26, type, geq: (trm > trm > fml)).
% 0.99/0.54 thf(func_def_27, type, pred: (char > trm > fml)).
% 0.99/0.54 thf(func_def_28, type, const: (char > trm)).
% 0.99/0.54 thf(func_def_29, type, func: (char > trm > trm)).
% 0.99/0.54 thf(func_def_30, type, uSubst1556497037e_Geqo: (option @ trm > option @ trm > option @ fml)).
% 0.99/0.54 thf(func_def_31, type, uSubst969145931substt: (trm > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game))).
% 0.99/0.54 thf(func_def_32, type, uSubst1138577137pconst: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > char > option @ trm)).
% 0.99/0.54 thf(func_def_33, type, uSubst95898978stappf: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > fml > option @ fml)).
% 0.99/0.54 thf(func_def_34, type, uSubst95898992stappt: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > option @ trm)).
% 0.99/0.54 thf(func_def_35, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.99/0.54 thf(func_def_36, type, ua: set @ variable).
% 0.99/0.54 thf(func_def_37, type, va: set @ variable).
% 0.99/0.54 thf(func_def_38, type, sigma: product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game)).
% 0.99/0.54 thf(func_def_39, type, theta: trm).
% 0.99/0.54 thf(func_def_40, type, p: char).
% 0.99/0.54 thf(func_def_41, type, vv: (set @ variable > set @ variable > variable)).
% 0.99/0.54 thf(func_def_42, type, vva: (set @ variable > set @ variable > variable)).
% 0.99/0.54 thf(func_def_44, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.99/0.54 thf(func_def_45, type, vAND: ($o > $o > $o)).
% 0.99/0.54 thf(func_def_46, type, db0: !>[X0: $tType]:(X0)).
% 0.99/0.54 thf(func_def_47, type, db1: !>[X0: $tType]:(X0)).
% 0.99/0.54 thf(func_def_48, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.99/0.54 thf(func_def_49, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.99/0.54 thf(func_def_52, type, db4: !>[X0: $tType]:(X0)).
% 0.99/0.54 thf(func_def_53, type, db2: !>[X0: $tType]:(X0)).
% 0.99/0.54 thf(func_def_54, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.99/0.54 thf(func_def_55, type, vNOT: ($o > $o)).
% 0.99/0.54 thf(func_def_56, type, vIMP: ($o > $o > $o)).
% 0.99/0.54 thf(func_def_57, type, vOR: ($o > $o > $o)).
% 0.99/0.54 thf(func_def_58, type, db3: !>[X0: $tType]:(X0)).
% 0.99/0.54 thf(func_def_59, type, sP0: !>[X0: $tType, X1: $tType]:(((option @ X1 > option @ X0 > $o) > option @ X1 > option @ X0 > $o))).
% 0.99/0.54 thf(func_def_60, type, sP1: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.99/0.54 thf(func_def_61, type, sP2: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.99/0.54 thf(func_def_62, type, sP3: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.99/0.54 thf(func_def_63, type, sP4: (option @ trm > option @ trm > option @ fml > $o)).
% 0.99/0.54 thf(func_def_64, type, sK5: (set @ variable > set @ variable > variable)).
% 0.99/0.54 thf(func_def_65, type, sK6: !>[X0: $tType, X1: $tType]:(((option @ X1 > option @ X0 > $o) > option @ X1 > option @ X0 > X1))).
% 0.99/0.54 thf(func_def_66, type, sK7: !>[X0: $tType, X1: $tType]:(((option @ X1 > option @ X0 > $o) > option @ X1 > option @ X0 > X0))).
% 0.99/0.54 thf(func_def_67, type, sK8: !>[X0: $tType]:(((option @ X0 > $o) > X0))).
% 0.99/0.54 thf(func_def_68, type, sK9: !>[X0: $tType]:((option @ X0 > X0))).
% 0.99/0.54 thf(func_def_69, type, sK10: ((variable > option @ fml > $o) > variable)).
% 0.99/0.54 thf(func_def_70, type, sK11: ((variable > option @ fml > $o) > variable)).
% 0.99/0.54 thf(func_def_71, type, sK12: ((variable > option @ fml > $o) > fml)).
% 0.99/0.54 thf(func_def_72, type, sK13: ((option @ fml > $o) > fml)).
% 0.99/0.54 thf(func_def_73, type, sK14: (option @ fml > fml)).
% 0.99/0.54 thf(func_def_74, type, sK15: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.99/0.54 thf(func_def_75, type, sK16: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.99/0.54 thf(func_def_76, type, sK17: ((option @ fml > option @ fml > $o) > fml)).
% 0.99/0.54 thf(func_def_77, type, sK18: ((option @ fml > option @ fml > $o) > option @ fml)).
% 0.99/0.54 thf(func_def_78, type, sK19: ((option @ fml > option @ fml > $o) > fml)).
% 0.99/0.54 thf(func_def_79, type, sK20: ((option @ fml > option @ fml > $o) > fml)).
% 0.99/0.54 thf(func_def_80, type, sK21: (char > set @ variable > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > fml)).
% 0.99/0.54 thf(func_def_81, type, sK22: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.99/0.54 thf(func_def_82, type, sK23: ((char > option @ trm > $o) > char)).
% 0.99/0.54 thf(func_def_83, type, sK24: ((char > option @ trm > $o) > char)).
% 0.99/0.54 thf(func_def_84, type, sK25: ((char > option @ trm > $o) > trm)).
% 0.99/0.54 thf(func_def_85, type, sK26: ((option @ trm > option @ trm > $o) > trm)).
% 0.99/0.54 thf(func_def_86, type, sK27: ((option @ trm > option @ trm > $o) > option @ trm)).
% 0.99/0.54 thf(func_def_87, type, sK28: ((option @ trm > option @ trm > $o) > trm)).
% 0.99/0.54 thf(func_def_88, type, sK29: ((option @ trm > option @ trm > $o) > trm)).
% 0.99/0.54 thf(func_def_89, type, sK30: ((variable > option @ trm > $o) > variable)).
% 0.99/0.54 thf(func_def_90, type, sK31: ((variable > option @ trm > $o) > variable)).
% 0.99/0.54 thf(func_def_91, type, sK32: ((variable > option @ trm > $o) > trm)).
% 0.99/0.54 thf(func_def_92, type, sK33: (option @ trm > trm)).
% 0.99/0.54 thf(func_def_93, type, sK34: ((option @ trm > $o) > trm)).
% 0.99/0.54 thf(func_def_94, type, sK35: ((option @ game > option @ fml > $o) > game)).
% 0.99/0.54 thf(func_def_95, type, sK36: ((option @ game > option @ fml > $o) > option @ fml)).
% 0.99/0.54 thf(func_def_96, type, sK37: ((option @ game > option @ fml > $o) > game)).
% 0.99/0.54 thf(func_def_97, type, sK38: ((option @ game > option @ fml > $o) > fml)).
% 0.99/0.54 thf(func_def_98, type, sK39: !>[X0: $tType]:((option @ X0 > (X0 > $o) > X0))).
% 0.99/0.54 thf(func_def_99, type, sK40: !>[X0: $tType]:((set @ X0 > X0))).
% 0.99/0.54 thf(func_def_100, type, sK41: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.99/0.54 thf(func_def_101, type, sK42: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.99/0.54 thf(func_def_102, type, sK43: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.99/0.54 thf(func_def_103, type, sK44: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.99/0.54 thf(func_def_104, type, sK45: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.99/0.54 thf(func_def_105, type, sK46: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.99/0.54 thf(func_def_106, type, sK47: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.99/0.54 thf(func_def_107, type, sK48: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.99/0.54 thf(func_def_108, type, sK49: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.99/0.54 thf(func_def_109, type, sK50: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > set @ X0 > X0))).
% 0.99/0.54 thf(func_def_110, type, sK51: !>[X0: $tType]:((set @ X0 > X0))).
% 0.99/0.54 thf(func_def_111, type, sK52: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.99/0.54 thf(func_def_112, type, sK53: (option @ game > game)).
% 0.99/0.54 thf(func_def_113, type, sK54: ((option @ game > $o) > game)).
% 0.99/0.54 thf(func_def_114, type, sK55: ((option @ game > option @ game > $o) > game)).
% 0.99/0.54 thf(func_def_115, type, sK56: ((option @ game > option @ game > $o) > option @ game)).
% 0.99/0.54 thf(func_def_116, type, sK57: ((option @ game > option @ game > $o) > game)).
% 0.99/0.54 thf(func_def_117, type, sK58: ((option @ game > option @ game > $o) > game)).
% 0.99/0.54 thf(func_def_118, type, sK59: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.99/0.54 thf(func_def_119, type, sK60: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.99/0.54 thf(func_def_120, type, sK61: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.99/0.54 thf(func_def_121, type, sK62: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.99/0.54 thf(func_def_122, type, sK63: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.99/0.54 thf(func_def_123, type, sK64: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.99/0.54 thf(func_def_124, type, sK65: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.99/0.54 thf(func_def_125, type, sK66: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.99/0.54 thf(func_def_126, type, sK67: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.99/0.54 thf(func_def_127, type, sK68: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.99/0.54 thf(func_def_128, type, sK69: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.99/0.54 thf(func_def_129, type, sK70: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.99/0.54 thf(func_def_130, type, sK71: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.99/0.54 thf(func_def_131, type, sK72: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X0 > $o) > (X1 > $o) > X1))).
% 0.99/0.54 thf(func_def_132, type, sK73: (option @ trm > option @ trm > option @ fml > trm)).
% 0.99/0.54 thf(func_def_133, type, sK74: (option @ trm > option @ trm > option @ fml > trm)).
% 0.99/0.54 thf(func_def_134, type, sK75: (option @ trm > trm)).
% 0.99/0.54 thf(func_def_135, type, sK76: (char > set @ variable > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > trm)).
% 0.99/0.54 thf(func_def_136, type, sK77: (char > set @ variable > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > trm)).
% 0.99/0.54 thf(func_def_137, type, sK78: (char > set @ variable > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > trm)).
% 0.99/0.54 thf(func_def_138, type, sK79: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > set @ X0 > X0))).
% 0.99/0.54 thf(func_def_139, type, sK80: (product_prod @ option @ game @ option @ fml > game)).
% 0.99/0.54 thf(func_def_140, type, sK81: (product_prod @ option @ game @ option @ fml > option @ fml)).
% 0.99/0.54 thf(func_def_141, type, sK82: (product_prod @ option @ game @ option @ fml > game)).
% 0.99/0.54 thf(func_def_142, type, sK83: (product_prod @ option @ game @ option @ fml > fml)).
% 0.99/0.54 thf(func_def_143, type, sK84: !>[X0: $tType]:(((X0 > $o) > set @ X0 > X0))).
% 0.99/0.54 thf(func_def_144, type, sK85: (option @ game > game)).
% 0.99/0.54 thf(func_def_145, type, sK86: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.99/0.54 thf(func_def_146, type, sK87: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.99/0.54 thf(func_def_147, type, sK88: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.99/0.54 thf(func_def_148, type, sK89: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.99/0.54 thf(func_def_149, type, sK90: !>[X0: $tType]:((set @ X0 > X0))).
% 0.99/0.54 thf(func_def_150, type, sK91: (option @ trm > trm)).
% 0.99/0.54 thf(func_def_151, type, sK92: !>[X0: $tType]:((set @ X0 > X0))).
% 0.99/0.54 thf(func_def_152, type, sK93: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.99/0.54 thf(func_def_153, type, sK94: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.99/0.54 thf(func_def_154, type, sK95: (option @ fml > fml)).
% 0.99/0.54 thf(func_def_155, type, sK96: !>[X0: $tType]:((option @ X0 > X0))).
% 0.99/0.54 thf(func_def_156, type, sK97: !>[X0: $tType]:((option @ X0 > X0))).
% 0.99/0.54 thf(func_def_157, type, sK98: (set @ variable > set @ variable > variable)).
% 0.99/0.54 thf(func_def_158, type, sK99: (set @ variable > set @ variable > variable)).
% 0.99/0.54 thf(func_def_159, type, sK100: (set @ variable > set @ variable > variable)).
% 0.99/0.54 thf(f3,axiom,(
% 0.99/0.54 ~((((inf_inf @ set @ variable @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X0 : (char > option @ trm)] : ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X1 : (char > option @ trm)] : ((product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X2 : (char > option @ fml), X3 : (char > option @ game)] : (X2)))))))) @ sigma @ p))) @ va)) = bot_bot @ set @ variable) => (((uSubst95898978stappf @ (uSubst969145931substt @ (the @ trm @ (uSubst95898992stappt @ sigma @ va @ theta))) @ bot_bot @ set @ variable @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X0 : (char > option @ trm)] : ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X1 : (char > option @ trm)] : ((product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X2 : (char > option @ fml), X3 : (char > option @ game)] : (X2)))))))) @ sigma @ p)))) = none @ fml))),
% 0.99/0.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__092_060open_062_Iif_AFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_A_092_060inter_062_AV_A_061_A_123_125_Athen_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_Aelse_Aundeff_J_A_092_060noteq_062_Aundeff_092_060close_062)).
% 0.99/0.54 thf(f4,axiom,(
% 0.99/0.54 ~(((((inf_inf @ set @ variable @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X0 : (char > option @ trm)] : ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X1 : (char > option @ trm)] : ((product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X2 : (char > option @ fml), X3 : (char > option @ game)] : (X2)))))))) @ sigma @ p))) @ va)) != bot_bot @ set @ variable) => (none @ fml = ((uSubst95898978stappf @ sigma @ va @ (pred @ p @ theta))))) & ((((inf_inf @ set @ variable @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X0 : (char > option @ trm)] : ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X1 : (char > option @ trm)] : ((product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X2 : (char > option @ fml), X3 : (char > option @ game)] : (X2)))))))) @ sigma @ p))) @ va)) = bot_bot @ set @ variable) => (((uSubst95898978stappf @ (uSubst969145931substt @ (the @ trm @ (uSubst95898992stappt @ sigma @ va @ theta))) @ bot_bot @ set @ variable @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X0 : (char > option @ trm)] : ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X1 : (char > option @ trm)] : ((product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X2 : (char > option @ fml), X3 : (char > option @ game)] : (X2)))))))) @ sigma @ p)))) = ((uSubst95898978stappf @ sigma @ va @ (pred @ p @ theta)))))) => (((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X0 : (char > option @ trm)] : ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X1 : (char > option @ trm)] : ((product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X2 : (char > option @ fml), X3 : (char > option @ game)] : (X2)))))))) @ sigma @ p)) = none @ fml)),
% 0.99/0.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3__092_060open_062_Iif_AFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_A_092_060inter_062_AV_A_061_A_123_125_Athen_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_Aelse_Aundeff_J_A_092_060noteq_062_Ausubstappf_A_092_060sigma_062_AV_A_IPred_Ap_A_092_060theta_062_J_A_092_060Longrightarrow_062_ASPreds_A_092_060sigma_062_Ap_A_061_Aundeff_092_060close_062)).
% 0.99/0.54 thf(f7,axiom,(
% 0.99/0.54 (((vv @ va @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X0 : (char > option @ trm)] : ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X1 : (char > option @ trm)] : ((product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X2 : (char > option @ fml), X3 : (char > option @ game)] : (X2)))))))) @ sigma @ p))))) != ((vva @ va @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X0 : (char > option @ trm)] : ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X1 : (char > option @ trm)] : ((product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X2 : (char > option @ fml), X3 : (char > option @ game)] : (X2)))))))) @ sigma @ p)))))) | ~(member @ variable @ (vva @ va @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X0 : (char > option @ trm)] : ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X1 : (char > option @ trm)] : ((product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X2 : (char > option @ fml), X3 : (char > option @ game)] : (X2)))))))) @ sigma @ p)))) @ va) | ~(member @ variable @ (vv @ va @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X0 : (char > option @ trm)] : ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X1 : (char > option @ trm)] : ((product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X2 : (char > option @ fml), X3 : (char > option @ game)] : (X2)))))))) @ sigma @ p)))) @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X0 : (char > option @ trm)] : ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X1 : (char > option @ trm)] : ((product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X2 : (char > option @ fml), X3 : (char > option @ game)] : (X2)))))))) @ sigma @ p))))),
% 0.99/0.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6__092_060open_062vv_AV_A_IFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_J_A_092_060notin_062_AFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_A_092_060or_062_Avva_AV_A_IFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_J_A_092_060notin_062_AV_A_092_060or_062_Avv_AV_A_IFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_J_A_092_060noteq_062_Avva_AV_A_IFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_J_092_060close_062)).
% 0.99/0.54 thf(f12,axiom,(
% 0.99/0.54 (((((vv @ va @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X0 : (char > option @ trm)] : ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X1 : (char > option @ trm)] : ((product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X2 : (char > option @ fml), X3 : (char > option @ game)] : (X2)))))))) @ sigma @ p))))) = ((vva @ va @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X0 : (char > option @ trm)] : ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X1 : (char > option @ trm)] : ((product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X2 : (char > option @ fml), X3 : (char > option @ game)] : (X2)))))))) @ sigma @ p)))))) & (member @ variable @ (vva @ va @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X0 : (char > option @ trm)] : ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X1 : (char > option @ trm)] : ((product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X2 : (char > option @ fml), X3 : (char > option @ game)] : (X2)))))))) @ sigma @ p)))) @ va) & (member @ variable @ (vv @ va @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X0 : (char > option @ trm)] : ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X1 : (char > option @ trm)] : ((product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X2 : (char > option @ fml), X3 : (char > option @ game)] : (X2)))))))) @ sigma @ p)))) @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X0 : (char > option @ trm)] : ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X1 : (char > option @ trm)] : ((product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X2 : (char > option @ fml), X3 : (char > option @ game)] : (X2)))))))) @ sigma @ p))))) | (((inf_inf @ set @ variable @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X0 : (char > option @ trm)] : ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X1 : (char > option @ trm)] : ((product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X2 : (char > option @ fml), X3 : (char > option @ game)] : (X2)))))))) @ sigma @ p))) @ va)) = bot_bot @ set @ variable)) & (! [X4 : variable] : (! [X5 : variable] : ((X4 != X5) | ~(member @ variable @ X5 @ va)) | ~(member @ variable @ X4 @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X0 : (char > option @ trm)] : ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X1 : (char > option @ trm)] : ((product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X2 : (char > option @ fml), X3 : (char > option @ game)] : (X2)))))))) @ sigma @ p))))) | (((inf_inf @ set @ variable @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X0 : (char > option @ trm)] : ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X1 : (char > option @ trm)] : ((product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X2 : (char > option @ fml), X3 : (char > option @ game)] : (X2)))))))) @ sigma @ p))) @ va)) != bot_bot @ set @ variable))),
% 0.99/0.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_f10)).
% 0.99/0.54 thf(f287,conjecture,(
% 0.99/0.54 (((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X0 : (char > option @ trm)] : ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X1 : (char > option @ trm)] : ((product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X2 : (char > option @ fml), X3 : (char > option @ game)] : (X2)))))))) @ sigma @ p)) = none @ fml) | (((uSubst95898978stappf @ sigma @ va @ (pred @ p @ theta))) != none @ fml)),
% 0.99/0.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 0.99/0.54 thf(f288,negated_conjecture,(
% 0.99/0.54 ~((((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X0 : (char > option @ trm)] : ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X1 : (char > option @ trm)] : ((product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X2 : (char > option @ fml), X3 : (char > option @ game)] : (X2)))))))) @ sigma @ p)) = none @ fml) | (((uSubst95898978stappf @ sigma @ va @ (pred @ p @ theta))) != none @ fml))),
% 0.99/0.54 inference(negated_conjecture,[status(cth)],[f287])).
% 0.99/0.54 thf(f291,plain,(
% 0.99/0.54 ~((((inf_inf @ set @ variable @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X0 : (char > option @ trm)] : ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X1 : (char > option @ trm)] : ((product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X2 : (char > option @ fml), X3 : (char > option @ game)] : (X2)))))))) @ sigma @ p))) @ va)) = bot_bot @ set @ variable) => (((uSubst95898978stappf @ (uSubst969145931substt @ (the @ trm @ (uSubst95898992stappt @ sigma @ va @ theta))) @ bot_bot @ set @ variable @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X4 : (char > option @ trm)] : ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X5 : (char > option @ trm)] : ((product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X6 : (char > option @ fml), X7 : (char > option @ game)] : (X6)))))))) @ sigma @ p)))) = none @ fml))),
% 0.99/0.54 inference(rectify,[],[f3])).
% 0.99/0.54 thf(f292,plain,(
% 0.99/0.54 ~((bot_bot @ set @ variable = ((inf_inf @ set @ variable @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))) @ va))) => (none @ fml = ((uSubst95898978stappf @ (uSubst969145931substt @ (the @ trm @ (uSubst95898992stappt @ sigma @ va @ theta))) @ bot_bot @ set @ variable @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))))))),
% 0.99/0.54 inference(fool_elimination,[],[f291])).
% 0.99/0.54 thf(f293,plain,(
% 0.99/0.54 ~(((((inf_inf @ set @ variable @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X0 : (char > option @ trm)] : ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X1 : (char > option @ trm)] : ((product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X2 : (char > option @ fml), X3 : (char > option @ game)] : (X2)))))))) @ sigma @ p))) @ va)) != bot_bot @ set @ variable) => (none @ fml = ((uSubst95898978stappf @ sigma @ va @ (pred @ p @ theta))))) & ((((inf_inf @ set @ variable @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X4 : (char > option @ trm)] : ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X5 : (char > option @ trm)] : ((product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X6 : (char > option @ fml), X7 : (char > option @ game)] : (X6)))))))) @ sigma @ p))) @ va)) = bot_bot @ set @ variable) => (((uSubst95898978stappf @ (uSubst969145931substt @ (the @ trm @ (uSubst95898992stappt @ sigma @ va @ theta))) @ bot_bot @ set @ variable @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X8 : (char > option @ trm)] : ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X9 : (char > option @ trm)] : ((product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X10 : (char > option @ fml), X11 : (char > option @ game)] : (X10)))))))) @ sigma @ p)))) = ((uSubst95898978stappf @ sigma @ va @ (pred @ p @ theta)))))) => (((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X12 : (char > option @ trm)] : ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X13 : (char > option @ trm)] : ((product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X14 : (char > option @ fml), X15 : (char > option @ game)] : (X14)))))))) @ sigma @ p)) = none @ fml)),
% 0.99/0.54 inference(rectify,[],[f4])).
% 0.99/0.54 thf(f294,plain,(
% 0.99/0.54 ~(((bot_bot @ set @ variable != ((inf_inf @ set @ variable @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))) @ va))) => (none @ fml = ((uSubst95898978stappf @ sigma @ va @ (pred @ p @ theta))))) & ((bot_bot @ set @ variable = ((inf_inf @ set @ variable @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))) @ va))) => (((uSubst95898978stappf @ sigma @ va @ (pred @ p @ theta))) = ((uSubst95898978stappf @ (uSubst969145931substt @ (the @ trm @ (uSubst95898992stappt @ sigma @ va @ theta))) @ bot_bot @ set @ variable @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))))))) => (none @ fml = ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p)))),
% 0.99/0.54 inference(fool_elimination,[],[f293])).
% 0.99/0.54 thf(f297,plain,(
% 0.99/0.54 (((vv @ va @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X0 : (char > option @ trm)] : ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X1 : (char > option @ trm)] : ((product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X2 : (char > option @ fml), X3 : (char > option @ game)] : (X2)))))))) @ sigma @ p))))) != ((vva @ va @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X4 : (char > option @ trm)] : ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X5 : (char > option @ trm)] : ((product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X6 : (char > option @ fml), X7 : (char > option @ game)] : (X6)))))))) @ sigma @ p)))))) | ~(member @ variable @ (vva @ va @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X8 : (char > option @ trm)] : ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X9 : (char > option @ trm)] : ((product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X10 : (char > option @ fml), X11 : (char > option @ game)] : (X10)))))))) @ sigma @ p)))) @ va) | ~(member @ variable @ (vv @ va @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X12 : (char > option @ trm)] : ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X13 : (char > option @ trm)] : ((product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X14 : (char > option @ fml), X15 : (char > option @ game)] : (X14)))))))) @ sigma @ p)))) @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X16 : (char > option @ trm)] : ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X17 : (char > option @ trm)] : ((product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X18 : (char > option @ fml), X19 : (char > option @ game)] : (X18)))))))) @ sigma @ p))))),
% 0.99/0.54 inference(rectify,[],[f7])).
% 0.99/0.54 thf(f298,plain,(
% 0.99/0.54 (((vv @ va @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))))) != ((vva @ va @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p)))))) | ~ ($true = ((member @ variable @ (vva @ va @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p)))) @ va))) | ~ (((member @ variable @ (vv @ va @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p)))) @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))))) = $true)),
% 0.99/0.54 inference(fool_elimination,[],[f297])).
% 0.99/0.54 thf(f304,plain,(
% 0.99/0.54 (((((vv @ va @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X0 : (char > option @ trm)] : ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X1 : (char > option @ trm)] : ((product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X2 : (char > option @ fml), X3 : (char > option @ game)] : (X2)))))))) @ sigma @ p))))) = ((vva @ va @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X4 : (char > option @ trm)] : ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X5 : (char > option @ trm)] : ((product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X6 : (char > option @ fml), X7 : (char > option @ game)] : (X6)))))))) @ sigma @ p)))))) & (member @ variable @ (vva @ va @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X8 : (char > option @ trm)] : ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X9 : (char > option @ trm)] : ((product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X10 : (char > option @ fml), X11 : (char > option @ game)] : (X10)))))))) @ sigma @ p)))) @ va) & (member @ variable @ (vv @ va @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X12 : (char > option @ trm)] : ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X13 : (char > option @ trm)] : ((product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X14 : (char > option @ fml), X15 : (char > option @ game)] : (X14)))))))) @ sigma @ p)))) @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X16 : (char > option @ trm)] : ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X17 : (char > option @ trm)] : ((product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X18 : (char > option @ fml), X19 : (char > option @ game)] : (X18)))))))) @ sigma @ p))))) | (((inf_inf @ set @ variable @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X20 : (char > option @ trm)] : ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X21 : (char > option @ trm)] : ((product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X22 : (char > option @ fml), X23 : (char > option @ game)] : (X22)))))))) @ sigma @ p))) @ va)) = bot_bot @ set @ variable)) & (! [X24 : variable] : (! [X25 : variable] : ((X24 != X25) | ~(member @ variable @ X25 @ va)) | ~(member @ variable @ X24 @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X26 : (char > option @ trm)] : ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X27 : (char > option @ trm)] : ((product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X28 : (char > option @ fml), X29 : (char > option @ game)] : (X28)))))))) @ sigma @ p))))) | (((inf_inf @ set @ variable @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X30 : (char > option @ trm)] : ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X31 : (char > option @ trm)] : ((product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X32 : (char > option @ fml), X33 : (char > option @ game)] : (X32)))))))) @ sigma @ p))) @ va)) != bot_bot @ set @ variable))),
% 0.99/0.54 inference(rectify,[],[f12])).
% 0.99/0.54 thf(f305,plain,(
% 0.99/0.54 (((((vv @ va @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))))) = ((vva @ va @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p)))))) & ($true = ((member @ variable @ (vva @ va @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p)))) @ va))) & (((member @ variable @ (vv @ va @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p)))) @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))))) = $true)) | (bot_bot @ set @ variable = ((inf_inf @ set @ variable @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))) @ va)))) & (! [X24 : variable] : (! [X25 : variable] : ((X24 != X25) | ~ ($true = ((member @ variable @ X25 @ va)))) | ~ ($true = ((member @ variable @ X24 @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))))))) | (bot_bot @ set @ variable != ((inf_inf @ set @ variable @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))) @ va))))),
% 0.99/0.54 inference(fool_elimination,[],[f304])).
% 0.99/0.54 thf(f757,plain,(
% 0.99/0.54 ~((((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X0 : (char > option @ trm)] : ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X1 : (char > option @ trm)] : ((product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[X2 : (char > option @ fml), X3 : (char > option @ game)] : (X2)))))))) @ sigma @ p)) = none @ fml) | (((uSubst95898978stappf @ sigma @ va @ (pred @ p @ theta))) != none @ fml))),
% 0.99/0.54 inference(rectify,[],[f288])).
% 0.99/0.54 thf(f758,plain,(
% 0.99/0.54 ~((none @ fml = ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))) | (none @ fml != ((uSubst95898978stappf @ sigma @ va @ (pred @ p @ theta)))))),
% 0.99/0.54 inference(fool_elimination,[],[f757])).
% 0.99/0.54 thf(f759,plain,(
% 0.99/0.54 (((vv @ va @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))))) != ((vva @ va @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p)))))) | ($true != ((member @ variable @ (vva @ va @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p)))) @ va))) | (((member @ variable @ (vv @ va @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p)))) @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))))) != $true)),
% 0.99/0.54 inference(flattening,[],[f298])).
% 0.99/0.54 thf(f761,plain,(
% 0.99/0.54 (((((vv @ va @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))))) = ((vva @ va @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p)))))) & ($true = ((member @ variable @ (vva @ va @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p)))) @ va))) & (((member @ variable @ (vv @ va @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p)))) @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))))) = $true)) | (bot_bot @ set @ variable = ((inf_inf @ set @ variable @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))) @ va)))) & (! [X0 : variable] : (! [X1 : variable] : ((X0 != X1) | ~ ($true = ((member @ variable @ X1 @ va)))) | ~ ($true = ((member @ variable @ X0 @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))))))) | (bot_bot @ set @ variable != ((inf_inf @ set @ variable @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))) @ va))))),
% 0.99/0.54 inference(rectify,[],[f305])).
% 0.99/0.54 thf(f762,plain,(
% 0.99/0.54 (((((vv @ va @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))))) = ((vva @ va @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p)))))) & ($true = ((member @ variable @ (vva @ va @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p)))) @ va))) & (((member @ variable @ (vv @ va @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p)))) @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))))) = $true)) | (bot_bot @ set @ variable = ((inf_inf @ set @ variable @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))) @ va)))) & (! [X0 : variable] : (! [X1 : variable] : ((X0 != X1) | ($true != ((member @ variable @ X1 @ va)))) | ($true != ((member @ variable @ X0 @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))))))) | (bot_bot @ set @ variable != ((inf_inf @ set @ variable @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))) @ va))))),
% 0.99/0.54 inference(flattening,[],[f761])).
% 0.99/0.54 thf(f780,plain,(
% 0.99/0.54 (none @ fml != ((uSubst95898978stappf @ (uSubst969145931substt @ (the @ trm @ (uSubst95898992stappt @ sigma @ va @ theta))) @ bot_bot @ set @ variable @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))))) & (bot_bot @ set @ variable = ((inf_inf @ set @ variable @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))) @ va)))),
% 0.99/0.54 inference(ennf_transformation,[],[f292])).
% 0.99/0.54 thf(f781,plain,(
% 0.99/0.54 (none @ fml = ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))) | (((none @ fml = ((uSubst95898978stappf @ sigma @ va @ (pred @ p @ theta)))) | (bot_bot @ set @ variable = ((inf_inf @ set @ variable @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))) @ va)))) & ((((uSubst95898978stappf @ sigma @ va @ (pred @ p @ theta))) = ((uSubst95898978stappf @ (uSubst969145931substt @ (the @ trm @ (uSubst95898992stappt @ sigma @ va @ theta))) @ bot_bot @ set @ variable @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))))) | (bot_bot @ set @ variable != ((inf_inf @ set @ variable @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))) @ va)))))),
% 0.99/0.54 inference(ennf_transformation,[],[f294])).
% 0.99/0.54 thf(f1013,plain,(
% 0.99/0.54 (none @ fml != ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))) & (none @ fml = ((uSubst95898978stappf @ sigma @ va @ (pred @ p @ theta))))),
% 0.99/0.54 inference(ennf_transformation,[],[f758])).
% 0.99/0.54 thf(f1089,plain,(
% 0.99/0.54 (none @ fml != ((uSubst95898978stappf @ (uSubst969145931substt @ (the @ trm @ (uSubst95898992stappt @ sigma @ va @ theta))) @ bot_bot @ set @ variable @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p)))))),
% 0.99/0.54 inference(cnf_transformation,[],[f780])).
% 0.99/0.54 thf(f1090,plain,(
% 0.99/0.54 (none @ fml = ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))) | (((uSubst95898978stappf @ sigma @ va @ (pred @ p @ theta))) = ((uSubst95898978stappf @ (uSubst969145931substt @ (the @ trm @ (uSubst95898992stappt @ sigma @ va @ theta))) @ bot_bot @ set @ variable @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))))) | (bot_bot @ set @ variable != ((inf_inf @ set @ variable @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))) @ va)))),
% 0.99/0.54 inference(cnf_transformation,[],[f781])).
% 0.99/0.54 thf(f1094,plain,(
% 0.99/0.54 (((vv @ va @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))))) != ((vva @ va @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p)))))) | ($true != ((member @ variable @ (vva @ va @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p)))) @ va))) | (((member @ variable @ (vv @ va @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p)))) @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))))) != $true)),
% 0.99/0.54 inference(cnf_transformation,[],[f759])).
% 0.99/0.54 thf(f1100,plain,(
% 0.99/0.54 (((member @ variable @ (vv @ va @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p)))) @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))))) = $true) | (bot_bot @ set @ variable = ((inf_inf @ set @ variable @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))) @ va)))),
% 0.99/0.54 inference(cnf_transformation,[],[f762])).
% 0.99/0.54 thf(f1101,plain,(
% 0.99/0.54 ($true = ((member @ variable @ (vva @ va @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p)))) @ va))) | (bot_bot @ set @ variable = ((inf_inf @ set @ variable @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))) @ va)))),
% 0.99/0.54 inference(cnf_transformation,[],[f762])).
% 0.99/0.54 thf(f1102,plain,(
% 0.99/0.54 (((vv @ va @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))))) = ((vva @ va @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p)))))) | (bot_bot @ set @ variable = ((inf_inf @ set @ variable @ (static_FVF @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p))) @ va)))),
% 0.99/0.54 inference(cnf_transformation,[],[f762])).
% 0.99/0.54 thf(f1449,plain,(
% 0.99/0.54 (none @ fml = ((uSubst95898978stappf @ sigma @ va @ (pred @ p @ theta))))),
% 0.99/0.54 inference(cnf_transformation,[],[f1013])).
% 0.99/0.54 thf(f1450,plain,(
% 0.99/0.54 (none @ fml != ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p)))),
% 0.99/0.54 inference(cnf_transformation,[],[f1013])).
% 0.99/0.54 thf(f1941,plain,(
% 0.99/0.54 (((uSubst95898978stappf @ sigma @ va @ (pred @ p @ theta))) = ((uSubst95898978stappf @ (uSubst969145931substt @ (the @ trm @ (uSubst95898992stappt @ sigma @ va @ theta))) @ bot_bot @ set @ variable @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p)))))),
% 0.99/0.54 inference(global_subsumption,[],[f1090,f1094,f1102,f1101,f1100,f1450])).
% 0.99/0.54 thf(f2115,plain,(
% 0.99/0.54 (none @ fml = ((uSubst95898978stappf @ (uSubst969145931substt @ (the @ trm @ (uSubst95898992stappt @ sigma @ va @ theta))) @ bot_bot @ set @ variable @ (the @ fml @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ fml) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y2)))))))) @ sigma @ p)))))),
% 0.99/0.54 inference(forward_demodulation,[],[f1941,f1449])).
% 0.99/0.54 thf(f2116,plain,(
% 0.99/0.54 $false),
% 0.99/0.54 inference(forward_subsumption_resolution,[],[f2115,f1089])).
% 0.99/0.54 % SZS output end Proof for theBenchmark
% 0.99/0.54 % (832891)------------------------------
% 0.99/0.54 % (832891)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.99/0.54 % (832891)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.99/0.54 % (832891)CaDiCaL version: 2.1.3
% 0.99/0.54 % (832891)Termination reason: Refutation
% 0.99/0.54 % (832891)Time elapsed: 0.142 s
% 0.99/0.54 % (832891)Peak memory usage: 14 MB
% 0.99/0.54 % (832891)Instructions burned: 178 (million)
% 0.99/0.54 % (832884)Success in time 0.218 s
% 0.99/0.54 % Vampire exiting
%------------------------------------------------------------------------------