%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP204^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 08:08:48 AM UTC 2026
% Result : Theorem 0.33s 0.49s
% Output : Refutation 0.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP204^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.24 % Computer : n013.cluster.edu
% 0.12/0.24 % Model : x86_64 x86_64
% 0.12/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.24 % Memory : 8046.5625MB
% 0.12/0.24 % OS : Linux 6.8.0-71-generic
% 0.12/0.24 % CPULimit : 300
% 0.12/0.24 % WCLimit : 300
% 0.12/0.24 % DateTime : Tue Sep 29 20:10:51 UTC 2026
% 0.12/0.24 % CPUTime :
% 0.12/0.24 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.29 Running higher-order theorem proving
% 0.24/0.36 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.33/0.49 % (2601619)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.33/0.49 % (2601627)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=1504212952:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.33/0.49 % (2601625)lrs+10_16_si=on:nwc=1.5:random_seed=7387801:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.33/0.49 % (2601630)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.33/0.49 % (2601630)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.33/0.49 % (2601625)Instruction limit reached!
% 0.33/0.49 % (2601625)------------------------------
% 0.33/0.49 % (2601625)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.33/0.49 % (2601625)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/0.49 % (2601625)CaDiCaL version: 2.1.3
% 0.33/0.49 % (2601625)Termination reason: Instruction limit
% 0.33/0.49 % (2601625)Termination phase: shuffling
% 0.33/0.49 % (2601625)Time elapsed: 0.010 s
% 0.33/0.49 % (2601625)Peak memory usage: 11 MB
% 0.33/0.49 % (2601625)Instructions burned: 18 (million)
% 0.33/0.49 % (2601626)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3812126862:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.33/0.49 % (2601624)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3795156974:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.33/0.49 % (2601628)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=915730489:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.33/0.49 % (2601629)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1254843394:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.33/0.49 % (2601630)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=1796446793:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.33/0.49 % (2601626)Instruction limit reached!
% 0.33/0.49 % (2601626)------------------------------
% 0.33/0.49 % (2601626)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.33/0.49 % (2601626)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/0.49 % (2601626)CaDiCaL version: 2.1.3
% 0.33/0.49 % (2601626)Termination reason: Instruction limit
% 0.33/0.49 % (2601626)Termination phase: shuffling
% 0.33/0.49 % (2601626)Time elapsed: 0.003 s
% 0.33/0.49 % (2601626)Peak memory usage: 10 MB
% 0.33/0.49 % (2601626)Instructions burned: 3 (million)
% 0.33/0.49 % (2601634)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2049201278:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.33/0.49 % (2601628)Instruction limit reached!
% 0.33/0.49 % (2601628)------------------------------
% 0.33/0.49 % (2601628)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.33/0.49 % (2601628)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/0.49 % (2601628)CaDiCaL version: 2.1.3
% 0.33/0.49 % (2601628)Termination reason: Instruction limit
% 0.33/0.49 % (2601628)Termination phase: shuffling
% 0.33/0.49 % (2601628)Time elapsed: 0.021 s
% 0.33/0.49 % (2601628)Peak memory usage: 11 MB
% 0.33/0.49 % (2601628)Instructions burned: 25 (million)
% 0.33/0.49 % (2601634)Instruction limit reached!
% 0.33/0.49 % (2601634)------------------------------
% 0.33/0.49 % (2601634)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.33/0.49 % (2601634)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/0.49 % (2601634)CaDiCaL version: 2.1.3
% 0.33/0.49 % (2601634)Termination reason: Instruction limit
% 0.33/0.49 % (2601634)Termination phase: shuffling
% 0.33/0.49 % (2601634)Time elapsed: 0.002 s
% 0.33/0.49 % (2601634)Peak memory usage: 10 MB
% 0.33/0.49 % (2601634)Instructions burned: 3 (million)
% 0.33/0.49 % (2601639)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2433165148:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.33/0.49 % (2601641)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.33/0.49 % (2601639)Instruction limit reached!
% 0.33/0.49 % (2601639)------------------------------
% 0.33/0.49 % (2601639)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.33/0.49 % (2601639)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/0.49 % (2601639)CaDiCaL version: 2.1.3
% 0.33/0.49 % (2601639)Termination reason: Instruction limit
% 0.33/0.49 % (2601639)Termination phase: shuffling
% 0.33/0.49 % (2601639)Time elapsed: 0.005 s
% 0.33/0.49 % (2601639)Peak memory usage: 10 MB
% 0.33/0.49 % (2601639)Instructions burned: 5 (million)
% 0.33/0.49 % (2601641)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1910957057:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.33/0.49 % (2601641)Instruction limit reached!
% 0.33/0.49 % (2601641)------------------------------
% 0.33/0.49 % (2601641)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.33/0.49 % (2601641)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/0.49 % (2601641)CaDiCaL version: 2.1.3
% 0.33/0.49 % (2601641)Termination reason: Instruction limit
% 0.33/0.49 % (2601641)Termination phase: shuffling
% 0.33/0.49 % (2601641)Time elapsed: 0.004 s
% 0.33/0.49 % (2601641)Peak memory usage: 10 MB
% 0.33/0.49 % (2601641)Instructions burned: 8 (million)
% 0.33/0.49 % (2601642)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1928594026:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.33/0.49 % (2601627) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2601619-2601627"...
% 0.33/0.49 % (2601645)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.33/0.49 % (2601645)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.33/0.49 % (2601627)...printing done.
% 0.33/0.49 % (2601627)Refutation found. Thanks to Tanya!
% 0.33/0.49 % SZS status Theorem for theBenchmark
% 0.33/0.49 % SZS output start Proof for theBenchmark
% 0.33/0.49 thf(type_def_5, type, produc1418842292n_game: $tType).
% 0.33/0.49 thf(type_def_6, type, produc62062515n_game: $tType).
% 0.33/0.49 thf(type_def_7, type, produc799602994n_game: $tType).
% 0.33/0.49 thf(type_def_8, type, produc1739631244on_fml: $tType).
% 0.33/0.49 thf(type_def_9, type, option_game: $tType).
% 0.33/0.49 thf(type_def_10, type, option_trm: $tType).
% 0.33/0.49 thf(type_def_11, type, option_fml: $tType).
% 0.33/0.49 thf(type_def_12, type, set_variable: $tType).
% 0.33/0.49 thf(type_def_13, type, variable: $tType).
% 0.33/0.49 thf(type_def_14, type, game: $tType).
% 0.33/0.49 thf(type_def_15, type, char: $tType).
% 0.33/0.49 thf(type_def_16, type, trm: $tType).
% 0.33/0.49 thf(type_def_17, type, fml: $tType).
% 0.33/0.49 thf(type_def_18, type, sTfun: ($tType * $tType) > $tType).
% 0.33/0.49 thf(func_def_0, type, if_option_fml: ($o > option_fml > option_fml > option_fml)).
% 0.33/0.49 thf(func_def_1, type, if_option_trm: ($o > option_trm > option_trm > option_trm)).
% 0.33/0.49 thf(func_def_2, type, inf_inf_variable_o: ((variable > $o) > (variable > $o) > variable > $o)).
% 0.33/0.49 thf(func_def_3, type, inf_inf_o: ($o > $o > $o)).
% 0.33/0.49 thf(func_def_4, type, inf_inf_set_variable: (set_variable > set_variable > set_variable)).
% 0.33/0.49 thf(func_def_5, type, none_fml: option_fml).
% 0.33/0.49 thf(func_def_6, type, none_game: option_game).
% 0.33/0.49 thf(func_def_7, type, none_trm: option_trm).
% 0.33/0.49 thf(func_def_8, type, some_fml: (fml > option_fml)).
% 0.33/0.49 thf(func_def_9, type, some_game: (game > option_game)).
% 0.33/0.49 thf(func_def_10, type, some_trm: (trm > option_trm)).
% 0.33/0.49 thf(func_def_11, type, case_option_o_fml: ($o > (fml > $o) > option_fml > $o)).
% 0.33/0.49 thf(func_def_12, type, case_option_o_game: ($o > (game > $o) > option_game > $o)).
% 0.33/0.49 thf(func_def_13, type, case_option_o_trm: ($o > (trm > $o) > option_trm > $o)).
% 0.33/0.49 thf(func_def_14, type, case_o209804997ml_fml: (option_fml > (fml > option_fml) > option_fml > option_fml)).
% 0.33/0.49 thf(func_def_15, type, case_o325794063ml_trm: (option_fml > (trm > option_fml) > option_trm > option_fml)).
% 0.33/0.49 thf(func_def_16, type, case_o487727941rm_trm: (option_trm > (trm > option_trm) > option_trm > option_trm)).
% 0.33/0.49 thf(func_def_17, type, the_fml: (option_fml > fml)).
% 0.33/0.49 thf(func_def_18, type, the_game: (option_game > game)).
% 0.33/0.49 thf(func_def_19, type, the_trm: (option_trm > trm)).
% 0.33/0.49 thf(func_def_20, type, bot_bot_variable_o: (variable > $o)).
% 0.33/0.49 thf(func_def_21, type, bot_bot_set_variable: set_variable).
% 0.33/0.49 thf(func_def_22, type, ord_le1407353162able_o: ((variable > $o) > (variable > $o) > $o)).
% 0.33/0.49 thf(func_def_23, type, ord_le282106107riable: (set_variable > set_variable > $o)).
% 0.33/0.49 thf(func_def_24, type, produc2124676926on_fml: (option_game > option_fml > produc1739631244on_fml)).
% 0.33/0.49 thf(func_def_25, type, produc1598111045on_fml: (((char > option_fml) > (char > option_game) > char > option_fml) > produc799602994n_game > char > option_fml)).
% 0.33/0.49 thf(func_def_26, type, produc1214549391on_trm: (((char > option_fml) > (char > option_game) > char > option_trm) > produc799602994n_game > char > option_trm)).
% 0.33/0.49 thf(func_def_27, type, produc1591622303on_fml: (((char > option_fml) > (char > option_game) > option_fml) > produc799602994n_game > option_fml)).
% 0.33/0.49 thf(func_def_28, type, produc2129367017on_trm: (((char > option_fml) > (char > option_game) > option_trm) > produc799602994n_game > option_trm)).
% 0.33/0.49 thf(func_def_29, type, produc377919108on_fml: (((char > option_trm) > produc799602994n_game > char > option_fml) > produc62062515n_game > char > option_fml)).
% 0.33/0.49 thf(func_def_30, type, produc2141841102on_trm: (((char > option_trm) > produc799602994n_game > char > option_trm) > produc62062515n_game > char > option_trm)).
% 0.33/0.49 thf(func_def_31, type, produc1903410526on_fml: (((char > option_trm) > produc799602994n_game > option_fml) > produc62062515n_game > option_fml)).
% 0.33/0.49 thf(func_def_32, type, produc293671592on_trm: (((char > option_trm) > produc799602994n_game > option_trm) > produc62062515n_game > option_trm)).
% 0.33/0.49 thf(func_def_33, type, produc1278328899on_fml: (((char > option_trm) > produc62062515n_game > char > option_fml) > produc1418842292n_game > char > option_fml)).
% 0.33/0.49 thf(func_def_34, type, produc724717725on_fml: (((char > option_trm) > produc62062515n_game > option_fml) > produc1418842292n_game > option_fml)).
% 0.33/0.49 thf(func_def_35, type, produc1420172399on_fml: (((char > option_fml) > (char > option_game) > char > option_fml) > produc799602994n_game > char > option_fml)).
% 0.33/0.49 thf(func_def_36, type, produc1036610745on_trm: (((char > option_fml) > (char > option_game) > char > option_trm) > produc799602994n_game > char > option_trm)).
% 0.33/0.49 thf(func_def_37, type, produc347802313on_fml: (((char > option_fml) > (char > option_game) > option_fml) > produc799602994n_game > option_fml)).
% 0.33/0.49 thf(func_def_38, type, produc885547027on_trm: (((char > option_fml) > (char > option_game) > option_trm) > produc799602994n_game > option_trm)).
% 0.33/0.49 thf(func_def_39, type, produc1615133358on_fml: (((char > option_trm) > produc799602994n_game > char > option_fml) > produc62062515n_game > char > option_fml)).
% 0.33/0.49 thf(func_def_40, type, produc1231571704on_trm: (((char > option_trm) > produc799602994n_game > char > option_trm) > produc62062515n_game > char > option_trm)).
% 0.33/0.49 thf(func_def_41, type, produc154833544on_fml: (((char > option_trm) > produc799602994n_game > option_fml) > produc62062515n_game > option_fml)).
% 0.33/0.49 thf(func_def_42, type, produc692578258on_trm: (((char > option_trm) > produc799602994n_game > option_trm) > produc62062515n_game > option_trm)).
% 0.33/0.49 thf(func_def_43, type, produc1250175341on_fml: (((char > option_trm) > produc62062515n_game > char > option_fml) > produc1418842292n_game > char > option_fml)).
% 0.33/0.49 thf(func_def_44, type, produc866613687on_trm: (((char > option_trm) > produc62062515n_game > char > option_trm) > produc1418842292n_game > char > option_trm)).
% 0.33/0.49 thf(func_def_45, type, produc1499310791on_fml: (((char > option_trm) > produc62062515n_game > option_fml) > produc1418842292n_game > option_fml)).
% 0.33/0.49 thf(func_def_46, type, collect_variable: ((variable > $o) > set_variable)).
% 0.33/0.49 thf(func_def_47, type, is_empty_variable: (set_variable > $o)).
% 0.33/0.49 thf(func_def_48, type, static_FVF: (fml > set_variable)).
% 0.33/0.49 thf(func_def_49, type, static_FVT: (trm > set_variable)).
% 0.33/0.49 thf(func_def_50, type, geq: (trm > trm > fml)).
% 0.33/0.49 thf(func_def_51, type, pred: (char > trm > fml)).
% 0.33/0.49 thf(func_def_52, type, const: (char > trm)).
% 0.33/0.49 thf(func_def_53, type, func: (char > trm > trm)).
% 0.33/0.49 thf(func_def_54, type, uSubst152838031e_Geqo: (option_trm > option_trm > option_fml)).
% 0.33/0.49 thf(func_def_55, type, uSubst1408967625substt: (trm > produc1418842292n_game)).
% 0.33/0.49 thf(func_def_56, type, uSubst1559070963pconst: (produc1418842292n_game > set_variable > char > option_trm)).
% 0.33/0.49 thf(func_def_57, type, uSubst516392804stappf: (produc1418842292n_game > set_variable > fml > option_fml)).
% 0.33/0.49 thf(func_def_58, type, uSubst516392818stappt: (produc1418842292n_game > set_variable > trm > option_trm)).
% 0.33/0.49 thf(func_def_59, type, member_variable: (variable > set_variable > $o)).
% 0.33/0.49 thf(func_def_60, type, ua: set_variable).
% 0.33/0.49 thf(func_def_61, type, va: set_variable).
% 0.33/0.49 thf(func_def_62, type, sigma: produc1418842292n_game).
% 0.33/0.49 thf(func_def_63, type, theta: trm).
% 0.33/0.49 thf(func_def_64, type, p: char).
% 0.33/0.49 thf(func_def_65, type, vv: (set_variable > set_variable > variable)).
% 0.33/0.49 thf(func_def_66, type, vva: (set_variable > set_variable > variable)).
% 0.33/0.49 thf(func_def_68, type, db0: !>[X0: $tType]:(X0)).
% 0.33/0.49 thf(func_def_69, type, db1: !>[X0: $tType]:(X0)).
% 0.33/0.49 thf(func_def_70, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.33/0.49 thf(func_def_73, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.33/0.49 thf(func_def_74, type, vOR: ($o > $o > $o)).
% 0.33/0.49 thf(func_def_75, type, db3: !>[X0: $tType]:(X0)).
% 0.33/0.49 thf(func_def_76, type, db4: !>[X0: $tType]:(X0)).
% 0.33/0.49 thf(func_def_77, type, db2: !>[X0: $tType]:(X0)).
% 0.33/0.49 thf(func_def_78, type, vAND: ($o > $o > $o)).
% 0.33/0.49 thf(func_def_79, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.33/0.49 thf(func_def_80, type, vIMP: ($o > $o > $o)).
% 0.33/0.49 thf(func_def_81, type, vNOT: ($o > $o)).
% 0.33/0.49 thf(func_def_82, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.33/0.49 thf(func_def_83, type, sP0: (option_fml > option_trm > option_trm > $o)).
% 0.33/0.49 thf(func_def_84, type, sK1: ((variable > $o) > variable)).
% 0.33/0.49 thf(func_def_85, type, sK2: (set_variable > char > produc1418842292n_game > trm)).
% 0.33/0.49 thf(func_def_86, type, sK3: ((option_game > option_fml > $o) > option_game > option_fml > fml)).
% 0.33/0.50 thf(func_def_87, type, sK4: ((option_game > option_fml > $o) > option_game > option_fml > game)).
% 0.33/0.50 thf(func_def_88, type, sK5: (option_game > option_trm > (option_game > option_trm > $o) > game)).
% 0.33/0.50 thf(func_def_89, type, sK6: (option_game > option_trm > (option_game > option_trm > $o) > trm)).
% 0.33/0.50 thf(func_def_90, type, sK7: ((option_trm > $o) > trm)).
% 0.33/0.50 thf(func_def_91, type, sK8: (option_fml > fml)).
% 0.33/0.50 thf(func_def_92, type, sK9: (set_variable > set_variable > variable)).
% 0.33/0.50 thf(func_def_93, type, sK10: (set_variable > set_variable > variable)).
% 0.33/0.50 thf(func_def_94, type, sK11: (set_variable > set_variable > variable)).
% 0.33/0.50 thf(func_def_95, type, sK12: (option_game > option_trm > (option_trm > option_game > $o) > trm)).
% 0.33/0.50 thf(func_def_96, type, sK13: (option_game > option_trm > (option_trm > option_game > $o) > game)).
% 0.33/0.50 thf(func_def_97, type, sK14: (produc1418842292n_game > set_variable > char > trm)).
% 0.33/0.50 thf(func_def_98, type, sK15: ((set_variable > set_variable > set_variable) > set_variable)).
% 0.33/0.50 thf(func_def_99, type, sK16: ((set_variable > set_variable > set_variable) > set_variable)).
% 0.33/0.50 thf(func_def_100, type, sK17: ((set_variable > set_variable > set_variable) > set_variable)).
% 0.33/0.50 thf(func_def_101, type, sK18: ((set_variable > set_variable > set_variable) > set_variable)).
% 0.33/0.50 thf(func_def_102, type, sK19: ((set_variable > set_variable > set_variable) > set_variable)).
% 0.33/0.50 thf(func_def_103, type, sK20: ((set_variable > set_variable > set_variable) > set_variable)).
% 0.33/0.50 thf(func_def_104, type, sK21: ((set_variable > set_variable > set_variable) > set_variable)).
% 0.33/0.50 thf(func_def_105, type, sK22: ((variable > $o) > (variable > $o) > variable)).
% 0.33/0.50 thf(func_def_106, type, sK23: ((variable > option_fml > $o) > variable)).
% 0.33/0.50 thf(func_def_107, type, sK24: ((variable > option_fml > $o) > variable)).
% 0.33/0.50 thf(func_def_108, type, sK25: ((variable > option_fml > $o) > fml)).
% 0.33/0.50 thf(func_def_109, type, sK26: (produc1739631244on_fml > game)).
% 0.33/0.50 thf(func_def_110, type, sK27: (produc1739631244on_fml > option_fml)).
% 0.33/0.50 thf(func_def_111, type, sK28: (produc1739631244on_fml > fml)).
% 0.33/0.50 thf(func_def_112, type, sK29: (produc1739631244on_fml > game)).
% 0.33/0.50 thf(func_def_113, type, sK30: (option_trm > option_fml > (option_trm > option_fml > $o) > trm)).
% 0.33/0.50 thf(func_def_114, type, sK31: (option_trm > option_fml > (option_trm > option_fml > $o) > fml)).
% 0.33/0.50 thf(func_def_115, type, sK32: (option_game > game)).
% 0.33/0.50 thf(func_def_116, type, sK33: (option_trm > trm)).
% 0.33/0.50 thf(func_def_117, type, sK34: (set_variable > variable)).
% 0.33/0.50 thf(func_def_118, type, sK35: (char > produc1418842292n_game > set_variable > fml)).
% 0.33/0.50 thf(func_def_119, type, sK36: (set_variable > set_variable > variable)).
% 0.33/0.50 thf(func_def_120, type, sK37: (set_variable > set_variable > variable)).
% 0.33/0.50 thf(func_def_121, type, sK38: ((set_variable > set_variable) > set_variable)).
% 0.33/0.50 thf(func_def_122, type, sK39: ((set_variable > set_variable) > set_variable)).
% 0.33/0.50 thf(func_def_123, type, sK40: ((option_fml > $o) > fml)).
% 0.33/0.50 thf(func_def_124, type, sK41: (option_fml > fml)).
% 0.33/0.50 thf(func_def_125, type, sK42: ((variable > $o) > (variable > $o) > variable)).
% 0.33/0.50 thf(func_def_126, type, sK43: (option_game > game)).
% 0.33/0.50 thf(func_def_127, type, sK44: ((variable > $o) > (variable > $o) > set_variable > variable)).
% 0.33/0.50 thf(func_def_128, type, sK45: (option_game > option_fml > (option_fml > option_game > $o) > fml)).
% 0.33/0.50 thf(func_def_129, type, sK46: (option_game > option_fml > (option_fml > option_game > $o) > game)).
% 0.33/0.50 thf(func_def_130, type, sK47: ((option_trm > option_trm > $o) > option_trm > option_trm > trm)).
% 0.33/0.50 thf(func_def_131, type, sK48: ((option_trm > option_trm > $o) > option_trm > option_trm > trm)).
% 0.33/0.50 thf(func_def_132, type, sK49: ((option_game > option_fml > $o) > option_fml)).
% 0.33/0.50 thf(func_def_133, type, sK50: ((option_game > option_fml > $o) > game)).
% 0.33/0.50 thf(func_def_134, type, sK51: ((option_game > option_fml > $o) > fml)).
% 0.33/0.50 thf(func_def_135, type, sK52: ((option_game > option_fml > $o) > game)).
% 0.33/0.50 thf(func_def_136, type, sK53: ((set_variable > set_variable) > set_variable)).
% 0.33/0.50 thf(func_def_137, type, sK54: ((set_variable > set_variable) > set_variable)).
% 0.33/0.50 thf(func_def_138, type, sK55: ((option_game > option_game > $o) > option_game > option_game > game)).
% 0.33/0.50 thf(func_def_139, type, sK56: ((option_game > option_game > $o) > option_game > option_game > game)).
% 0.33/0.50 thf(func_def_140, type, sK57: ((fml > $o) > option_fml > fml)).
% 0.33/0.50 thf(func_def_141, type, sK58: ((trm > option_trm) > (option_trm > $o) > (trm > $o) > trm)).
% 0.33/0.50 thf(func_def_142, type, sK59: (option_game > game)).
% 0.33/0.50 thf(func_def_143, type, sK60: ((trm > $o) > option_trm > trm)).
% 0.33/0.50 thf(func_def_144, type, sK61: ((variable > option_trm > $o) > variable)).
% 0.33/0.50 thf(func_def_145, type, sK62: ((variable > option_trm > $o) > trm)).
% 0.33/0.50 thf(func_def_146, type, sK63: ((variable > option_trm > $o) > variable)).
% 0.33/0.50 thf(func_def_147, type, sK64: ((variable > $o) > set_variable > (variable > $o) > variable)).
% 0.33/0.50 thf(func_def_148, type, sK65: (set_variable > variable)).
% 0.33/0.50 thf(func_def_149, type, sK66: ((option_game > $o) > game)).
% 0.33/0.50 thf(func_def_150, type, sK67: ((variable > $o) > (variable > $o) > variable)).
% 0.33/0.50 thf(func_def_151, type, sK68: (option_fml > fml)).
% 0.33/0.50 thf(func_def_152, type, sK69: (option_game > game)).
% 0.33/0.50 thf(func_def_153, type, sK70: ((option_fml > $o) > fml)).
% 0.33/0.50 thf(func_def_154, type, sK71: (option_game > (game > $o) > game)).
% 0.33/0.50 thf(func_def_155, type, sK72: (option_trm > trm)).
% 0.33/0.50 thf(func_def_156, type, sK73: (option_fml > (option_fml > option_trm > $o) > option_trm > fml)).
% 0.33/0.50 thf(func_def_157, type, sK74: (option_fml > (option_fml > option_trm > $o) > option_trm > trm)).
% 0.33/0.50 thf(func_def_158, type, sK75: (set_variable > variable)).
% 0.33/0.50 thf(func_def_159, type, sK76: (set_variable > produc1418842292n_game > char > trm)).
% 0.33/0.50 thf(func_def_160, type, sK77: ((option_game > $o) > game)).
% 0.33/0.50 thf(func_def_161, type, sK78: (set_variable > variable)).
% 0.33/0.50 thf(func_def_162, type, sK79: ((option_trm > $o) > trm)).
% 0.33/0.50 thf(func_def_163, type, sK80: (option_fml > fml)).
% 0.33/0.50 thf(func_def_164, type, sK81: ((option_game > option_game > $o) > option_game)).
% 0.33/0.50 thf(func_def_165, type, sK82: ((option_game > option_game > $o) > game)).
% 0.33/0.50 thf(func_def_166, type, sK83: ((option_game > option_game > $o) > game)).
% 0.33/0.50 thf(func_def_167, type, sK84: ((option_game > option_game > $o) > game)).
% 0.33/0.50 thf(func_def_168, type, sK85: ((option_fml > $o) > (fml > option_fml) > (fml > $o) > fml)).
% 0.33/0.50 thf(func_def_169, type, sK86: ((option_fml > $o) > (trm > option_fml) > (trm > $o) > trm)).
% 0.33/0.50 thf(func_def_170, type, sK87: (set_variable > set_variable > variable)).
% 0.33/0.50 thf(func_def_171, type, sK88: ((option_fml > option_fml > $o) > option_fml > option_fml > fml)).
% 0.33/0.50 thf(func_def_172, type, sK89: ((option_fml > option_fml > $o) > option_fml > option_fml > fml)).
% 0.33/0.50 thf(func_def_173, type, sK90: (option_fml > fml)).
% 0.33/0.50 thf(func_def_174, type, sK91: ((variable > $o) > variable)).
% 0.33/0.50 thf(func_def_175, type, sK92: (option_trm > trm)).
% 0.33/0.50 thf(func_def_176, type, sK93: (option_trm > option_trm > option_fml > trm)).
% 0.33/0.50 thf(func_def_177, type, sK94: (option_trm > option_trm > option_fml > trm)).
% 0.33/0.50 thf(func_def_178, type, sK95: (option_trm > trm)).
% 0.33/0.50 thf(func_def_179, type, sK96: ((set_variable > set_variable) > set_variable)).
% 0.33/0.50 thf(func_def_180, type, sK97: ((set_variable > set_variable) > set_variable)).
% 0.33/0.50 thf(func_def_181, type, sK98: ((char > option_trm > $o) > char)).
% 0.33/0.50 thf(func_def_182, type, sK99: ((char > option_trm > $o) > char)).
% 0.33/0.50 thf(func_def_183, type, sK100: ((char > option_trm > $o) > trm)).
% 0.33/0.50 thf(func_def_184, type, sK101: (set_variable > set_variable > variable)).
% 0.33/0.50 thf(func_def_185, type, sK102: (set_variable > (variable > $o) > variable)).
% 0.33/0.50 thf(func_def_186, type, sK103: ((option_fml > option_fml > $o) > option_fml)).
% 0.33/0.50 thf(func_def_187, type, sK104: ((option_fml > option_fml > $o) > fml)).
% 0.33/0.50 thf(func_def_188, type, sK105: ((option_fml > option_fml > $o) > fml)).
% 0.33/0.50 thf(func_def_189, type, sK106: ((option_fml > option_fml > $o) > fml)).
% 0.33/0.50 thf(func_def_190, type, sK107: (set_variable > set_variable > variable)).
% 0.33/0.50 thf(func_def_191, type, sK108: (option_trm > trm)).
% 0.33/0.50 thf(func_def_192, type, sK109: ((option_trm > option_trm > $o) > trm)).
% 0.33/0.50 thf(func_def_193, type, sK110: ((option_trm > option_trm > $o) > trm)).
% 0.33/0.50 thf(func_def_194, type, sK111: ((option_trm > option_trm > $o) > trm)).
% 0.33/0.50 thf(func_def_195, type, sK112: ((option_trm > option_trm > $o) > option_trm)).
% 0.33/0.50 thf(func_def_196, type, sK113: ((set_variable > set_variable) > set_variable)).
% 0.33/0.50 thf(func_def_197, type, sK114: ((set_variable > set_variable) > set_variable)).
% 0.33/0.50 thf(func_def_198, type, sK115: (option_trm > trm)).
% 0.33/0.50 thf(func_def_199, type, sK116: (set_variable > set_variable > variable)).
% 0.33/0.50 thf(func_def_200, type, sK117: (option_game > game)).
% 0.33/0.50 thf(f3,axiom,(
% 0.33/0.50 ~((((inf_inf_set_variable @ (static_FVF @ (the_fml @ (produc1250175341on_fml @ (^[X0 : (char > option_trm)] : ((produc1615133358on_fml @ (^[X1 : (char > option_trm)] : ((produc1420172399on_fml @ (^[X2 : (char > option_fml), X3 : (char > option_game)] : (X2)))))))) @ sigma @ p))) @ va)) = bot_bot_set_variable) => (none_fml = ((uSubst516392804stappf @ (uSubst1408967625substt @ (the_trm @ (uSubst516392818stappt @ sigma @ va @ theta))) @ bot_bot_set_variable @ (the_fml @ (produc1250175341on_fml @ (^[X0 : (char > option_trm)] : ((produc1615133358on_fml @ (^[X1 : (char > option_trm)] : ((produc1420172399on_fml @ (^[X2 : (char > option_fml), X3 : (char > option_game)] : (X2)))))))) @ sigma @ p))))))),
% 0.33/0.50 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)).
% 0.33/0.50 thf(f4,axiom,(
% 0.33/0.50 ~(((bot_bot_set_variable = ((inf_inf_set_variable @ (static_FVF @ (the_fml @ (produc1250175341on_fml @ (^[X0 : (char > option_trm)] : ((produc1615133358on_fml @ (^[X1 : (char > option_trm)] : ((produc1420172399on_fml @ (^[X2 : (char > option_fml), X3 : (char > option_game)] : (X2)))))))) @ sigma @ p))) @ va))) => (((uSubst516392804stappf @ sigma @ va @ (pred @ p @ theta))) = ((uSubst516392804stappf @ (uSubst1408967625substt @ (the_trm @ (uSubst516392818stappt @ sigma @ va @ theta))) @ bot_bot_set_variable @ (the_fml @ (produc1250175341on_fml @ (^[X0 : (char > option_trm)] : ((produc1615133358on_fml @ (^[X1 : (char > option_trm)] : ((produc1420172399on_fml @ (^[X2 : (char > option_fml), X3 : (char > option_game)] : (X2)))))))) @ sigma @ p)))))) & ((bot_bot_set_variable != ((inf_inf_set_variable @ (static_FVF @ (the_fml @ (produc1250175341on_fml @ (^[X0 : (char > option_trm)] : ((produc1615133358on_fml @ (^[X1 : (char > option_trm)] : ((produc1420172399on_fml @ (^[X2 : (char > option_fml), X3 : (char > option_game)] : (X2)))))))) @ sigma @ p))) @ va))) => (none_fml = ((uSubst516392804stappf @ sigma @ va @ (pred @ p @ theta)))))) => (((produc1250175341on_fml @ (^[X0 : (char > option_trm)] : ((produc1615133358on_fml @ (^[X1 : (char > option_trm)] : ((produc1420172399on_fml @ (^[X2 : (char > option_fml), X3 : (char > option_game)] : (X2)))))))) @ sigma @ p)) = none_fml)),
% 0.33/0.50 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)).
% 0.33/0.50 thf(f358,conjecture,(
% 0.33/0.50 (((uSubst516392804stappf @ sigma @ va @ (pred @ p @ theta))) != none_fml) | (none_fml = ((produc1250175341on_fml @ (^[X0 : (char > option_trm)] : ((produc1615133358on_fml @ (^[X1 : (char > option_trm)] : ((produc1420172399on_fml @ (^[X2 : (char > option_fml), X3 : (char > option_game)] : (X2)))))))) @ sigma @ p)))),
% 0.33/0.50 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 0.33/0.50 thf(f359,negated_conjecture,(
% 0.33/0.50 ~((((uSubst516392804stappf @ sigma @ va @ (pred @ p @ theta))) != none_fml) | (none_fml = ((produc1250175341on_fml @ (^[X0 : (char > option_trm)] : ((produc1615133358on_fml @ (^[X1 : (char > option_trm)] : ((produc1420172399on_fml @ (^[X2 : (char > option_fml), X3 : (char > option_game)] : (X2)))))))) @ sigma @ p))))),
% 0.33/0.50 inference(negated_conjecture,[status(cth)],[f358])).
% 0.33/0.50 thf(f418,plain,(
% 0.33/0.50 ~(((bot_bot_set_variable = ((inf_inf_set_variable @ (static_FVF @ (the_fml @ (produc1250175341on_fml @ (^[X0 : (char > option_trm)] : ((produc1615133358on_fml @ (^[X1 : (char > option_trm)] : ((produc1420172399on_fml @ (^[X2 : (char > option_fml), X3 : (char > option_game)] : (X2)))))))) @ sigma @ p))) @ va))) => (((uSubst516392804stappf @ sigma @ va @ (pred @ p @ theta))) = ((uSubst516392804stappf @ (uSubst1408967625substt @ (the_trm @ (uSubst516392818stappt @ sigma @ va @ theta))) @ bot_bot_set_variable @ (the_fml @ (produc1250175341on_fml @ (^[X4 : (char > option_trm)] : ((produc1615133358on_fml @ (^[X5 : (char > option_trm)] : ((produc1420172399on_fml @ (^[X6 : (char > option_fml), X7 : (char > option_game)] : (X6)))))))) @ sigma @ p)))))) & ((bot_bot_set_variable != ((inf_inf_set_variable @ (static_FVF @ (the_fml @ (produc1250175341on_fml @ (^[X8 : (char > option_trm)] : ((produc1615133358on_fml @ (^[X9 : (char > option_trm)] : ((produc1420172399on_fml @ (^[X10 : (char > option_fml), X11 : (char > option_game)] : (X10)))))))) @ sigma @ p))) @ va))) => (none_fml = ((uSubst516392804stappf @ sigma @ va @ (pred @ p @ theta)))))) => (((produc1250175341on_fml @ (^[X12 : (char > option_trm)] : ((produc1615133358on_fml @ (^[X13 : (char > option_trm)] : ((produc1420172399on_fml @ (^[X14 : (char > option_fml), X15 : (char > option_game)] : (X14)))))))) @ sigma @ p)) = none_fml)),
% 0.33/0.50 inference(rectify,[],[f4])).
% 0.33/0.50 thf(f419,plain,(
% 0.33/0.50 ~(((bot_bot_set_variable = ((inf_inf_set_variable @ (static_FVF @ (the_fml @ (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p))) @ va))) => (((uSubst516392804stappf @ sigma @ va @ (pred @ p @ theta))) = ((uSubst516392804stappf @ (uSubst1408967625substt @ (the_trm @ (uSubst516392818stappt @ sigma @ va @ theta))) @ bot_bot_set_variable @ (the_fml @ (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p)))))) & ((bot_bot_set_variable != ((inf_inf_set_variable @ (static_FVF @ (the_fml @ (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p))) @ va))) => (none_fml = ((uSubst516392804stappf @ sigma @ va @ (pred @ p @ theta)))))) => (none_fml = ((produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p)))),
% 0.33/0.50 inference(fool_elimination,[],[f418])).
% 0.33/0.50 thf(f537,plain,(
% 0.33/0.50 ~((((uSubst516392804stappf @ sigma @ va @ (pred @ p @ theta))) != none_fml) | (none_fml = ((produc1250175341on_fml @ (^[X0 : (char > option_trm)] : ((produc1615133358on_fml @ (^[X1 : (char > option_trm)] : ((produc1420172399on_fml @ (^[X2 : (char > option_fml), X3 : (char > option_game)] : (X2)))))))) @ sigma @ p))))),
% 0.33/0.50 inference(rectify,[],[f359])).
% 0.33/0.50 thf(f538,plain,(
% 0.33/0.50 ~((none_fml != ((uSubst516392804stappf @ sigma @ va @ (pred @ p @ theta)))) | (none_fml = ((produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p))))),
% 0.33/0.50 inference(fool_elimination,[],[f537])).
% 0.33/0.50 thf(f822,plain,(
% 0.33/0.50 ~((((inf_inf_set_variable @ (static_FVF @ (the_fml @ (produc1250175341on_fml @ (^[X0 : (char > option_trm)] : ((produc1615133358on_fml @ (^[X1 : (char > option_trm)] : ((produc1420172399on_fml @ (^[X2 : (char > option_fml), X3 : (char > option_game)] : (X2)))))))) @ sigma @ p))) @ va)) = bot_bot_set_variable) => (none_fml = ((uSubst516392804stappf @ (uSubst1408967625substt @ (the_trm @ (uSubst516392818stappt @ sigma @ va @ theta))) @ bot_bot_set_variable @ (the_fml @ (produc1250175341on_fml @ (^[X4 : (char > option_trm)] : ((produc1615133358on_fml @ (^[X5 : (char > option_trm)] : ((produc1420172399on_fml @ (^[X6 : (char > option_fml), X7 : (char > option_game)] : (X6)))))))) @ sigma @ p))))))),
% 0.33/0.50 inference(rectify,[],[f3])).
% 0.33/0.50 thf(f823,plain,(
% 0.33/0.50 ~((bot_bot_set_variable = ((inf_inf_set_variable @ (static_FVF @ (the_fml @ (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p))) @ va))) => (none_fml = ((uSubst516392804stappf @ (uSubst1408967625substt @ (the_trm @ (uSubst516392818stappt @ sigma @ va @ theta))) @ bot_bot_set_variable @ (the_fml @ (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p))))))),
% 0.33/0.50 inference(fool_elimination,[],[f822])).
% 0.33/0.50 thf(f925,plain,(
% 0.33/0.50 (none_fml != ((produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p))) & (none_fml = ((uSubst516392804stappf @ sigma @ va @ (pred @ p @ theta))))),
% 0.33/0.50 inference(ennf_transformation,[],[f538])).
% 0.33/0.50 thf(f1023,plain,(
% 0.33/0.50 (bot_bot_set_variable = ((inf_inf_set_variable @ (static_FVF @ (the_fml @ (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p))) @ va))) & (none_fml != ((uSubst516392804stappf @ (uSubst1408967625substt @ (the_trm @ (uSubst516392818stappt @ sigma @ va @ theta))) @ bot_bot_set_variable @ (the_fml @ (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p)))))),
% 0.33/0.50 inference(ennf_transformation,[],[f823])).
% 0.33/0.50 thf(f1048,plain,(
% 0.33/0.50 (((bot_bot_set_variable != ((inf_inf_set_variable @ (static_FVF @ (the_fml @ (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p))) @ va))) | (((uSubst516392804stappf @ sigma @ va @ (pred @ p @ theta))) = ((uSubst516392804stappf @ (uSubst1408967625substt @ (the_trm @ (uSubst516392818stappt @ sigma @ va @ theta))) @ bot_bot_set_variable @ (the_fml @ (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p)))))) & ((bot_bot_set_variable = ((inf_inf_set_variable @ (static_FVF @ (the_fml @ (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p))) @ va))) | (none_fml = ((uSubst516392804stappf @ sigma @ va @ (pred @ p @ theta)))))) | (none_fml = ((produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p)))),
% 0.33/0.50 inference(ennf_transformation,[],[f419])).
% 0.33/0.50 thf(f1565,plain,(
% 0.33/0.50 (((uSubst516392804stappf @ sigma @ va @ (pred @ p @ theta))) = ((uSubst516392804stappf @ (uSubst1408967625substt @ (the_trm @ (uSubst516392818stappt @ sigma @ va @ theta))) @ bot_bot_set_variable @ (the_fml @ (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p))))) | (none_fml = ((produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p))) | (bot_bot_set_variable != ((inf_inf_set_variable @ (static_FVF @ (the_fml @ (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p))) @ va)))),
% 0.33/0.50 inference(cnf_transformation,[],[f1048])).
% 0.33/0.50 thf(f1749,plain,(
% 0.33/0.50 (none_fml = ((uSubst516392804stappf @ sigma @ va @ (pred @ p @ theta))))),
% 0.33/0.50 inference(cnf_transformation,[],[f925])).
% 0.33/0.50 thf(f1750,plain,(
% 0.33/0.50 (none_fml != ((produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p)))),
% 0.33/0.50 inference(cnf_transformation,[],[f925])).
% 0.33/0.50 thf(f1900,plain,(
% 0.33/0.50 (none_fml != ((uSubst516392804stappf @ (uSubst1408967625substt @ (the_trm @ (uSubst516392818stappt @ sigma @ va @ theta))) @ bot_bot_set_variable @ (the_fml @ (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p)))))),
% 0.33/0.50 inference(cnf_transformation,[],[f1023])).
% 0.33/0.50 thf(f1901,plain,(
% 0.33/0.50 (bot_bot_set_variable = ((inf_inf_set_variable @ (static_FVF @ (the_fml @ (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p))) @ va)))),
% 0.33/0.50 inference(cnf_transformation,[],[f1023])).
% 0.33/0.50 thf(f2369,definition,(
% 0.33/0.50 spl118_6 <=> (bot_bot_set_variable = ((inf_inf_set_variable @ (static_FVF @ (the_fml @ (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p))) @ va)))),
% 0.33/0.50 introduced(definition,[new_symbols(definition,[spl118_6])],[avatar_definition])).
% 0.33/0.50 thf(f2397,definition,(
% 0.33/0.50 spl118_12 <=> (none_fml = ((produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p)))),
% 0.33/0.50 introduced(definition,[new_symbols(definition,[spl118_12])],[avatar_definition])).
% 0.33/0.50 thf(f2401,definition,(
% 0.33/0.50 spl118_13 <=> (((uSubst516392804stappf @ sigma @ va @ (pred @ p @ theta))) = ((uSubst516392804stappf @ (uSubst1408967625substt @ (the_trm @ (uSubst516392818stappt @ sigma @ va @ theta))) @ bot_bot_set_variable @ (the_fml @ (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p)))))),
% 0.33/0.50 introduced(definition,[new_symbols(definition,[spl118_13])],[avatar_definition])).
% 0.33/0.50 thf(f2404,plain,(
% 0.33/0.50 ~spl118_6 | spl118_12 | spl118_13),
% 0.33/0.50 inference(avatar_split_clause,[],[f1565,f2401,f2397,f2369])).
% 0.33/0.50 thf(f2406,definition,(
% 0.33/0.50 spl118_14 <=> (none_fml = ((uSubst516392804stappf @ (uSubst1408967625substt @ (the_trm @ (uSubst516392818stappt @ sigma @ va @ theta))) @ bot_bot_set_variable @ (the_fml @ (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p)))))),
% 0.33/0.50 introduced(definition,[new_symbols(definition,[spl118_14])],[avatar_definition])).
% 0.33/0.50 thf(f2409,plain,(
% 0.33/0.50 ~spl118_14),
% 0.33/0.50 inference(avatar_split_clause,[],[f1900,f2406])).
% 0.33/0.50 thf(f2520,plain,(
% 0.33/0.50 ~spl118_12),
% 0.33/0.50 inference(avatar_split_clause,[],[f1750,f2397])).
% 0.33/0.50 thf(f2527,definition,(
% 0.33/0.50 spl118_38 <=> (none_fml = ((uSubst516392804stappf @ sigma @ va @ (pred @ p @ theta))))),
% 0.33/0.50 introduced(definition,[new_symbols(definition,[spl118_38])],[avatar_definition])).
% 0.33/0.50 thf(f2530,plain,(
% 0.33/0.50 spl118_38),
% 0.33/0.50 inference(avatar_split_clause,[],[f1749,f2527])).
% 0.33/0.50 thf(f2531,plain,(
% 0.33/0.50 spl118_6),
% 0.33/0.50 inference(avatar_split_clause,[],[f1901,f2369])).
% 0.33/0.50 thf(f2674,definition,(
% 0.33/0.50 (none_fml != ((uSubst516392804stappf @ sigma @ va @ (pred @ p @ theta)))) | (((uSubst516392804stappf @ sigma @ va @ (pred @ p @ theta))) != ((uSubst516392804stappf @ (uSubst1408967625substt @ (the_trm @ (uSubst516392818stappt @ sigma @ va @ theta))) @ bot_bot_set_variable @ (the_fml @ (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p))))) | (none_fml = ((uSubst516392804stappf @ (uSubst1408967625substt @ (the_trm @ (uSubst516392818stappt @ sigma @ va @ theta))) @ bot_bot_set_variable @ (the_fml @ (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p)))))),
% 0.33/0.50 introduced(theory,[theory_tautology_sat_conflict])).
% 0.33/0.50 cnf(s11, plain, ~spl118_6 | spl118_12 | spl118_13, inference(sat_conversion,[],[f2404])).
% 0.33/0.50 cnf(s12, plain, ~spl118_14, inference(sat_conversion,[],[f2409])).
% 0.33/0.50 cnf(s37, plain, ~spl118_12, inference(sat_conversion,[],[f2520])).
% 0.33/0.50 cnf(s39, plain, spl118_38, inference(sat_conversion,[],[f2530])).
% 0.33/0.50 cnf(s40, plain, spl118_6, inference(sat_conversion,[],[f2531])).
% 0.33/0.50 cnf(s80, plain, ~spl118_13 | spl118_14 | ~spl118_38, inference(sat_conversion,[],[f2674])).
% 0.33/0.50 cnf(s81, plain, ~spl118_13, inference(rat,[],[s80,s39,s12])).
% 0.33/0.50 cnf(s82, plain, $false, inference(rat,[],[s11,s81,s37,s40])).
% 0.33/0.50 thf(f2675,plain,(
% 0.33/0.50 $false),
% 0.33/0.50 inference(avatar_sat_refutation,[],[s82])).
% 0.33/0.50 % SZS output end Proof for theBenchmark
% 0.33/0.50 % (2601627)------------------------------
% 0.33/0.50 % (2601627)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.33/0.50 % (2601627)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/0.50 % (2601627)CaDiCaL version: 2.1.3
% 0.33/0.50 % (2601627)Termination reason: Refutation
% 0.33/0.50 % (2601627)Time elapsed: 0.076 s
% 0.33/0.50 % (2601627)Peak memory usage: 15 MB
% 0.33/0.50 % (2601627)Instructions burned: 169 (million)
% 0.33/0.50 % (2601619)Success in time 0.122 s
% 0.33/0.50 % Vampire exiting
%------------------------------------------------------------------------------