%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n015.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 0.62s 0.44s
% Output : Refutation 0.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP204^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n015.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 20:14:49 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.23/0.30 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
% 0.62/0.44 % (4060811)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.62/0.44 % (4060818)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=4257123834:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.62/0.44 % (4060818)Instruction limit reached!
% 0.62/0.44 % (4060818)------------------------------
% 0.62/0.44 % (4060818)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.62/0.44 % (4060818)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.44 % (4060818)CaDiCaL version: 2.1.3
% 0.62/0.44 % (4060818)Termination reason: Instruction limit
% 0.62/0.44 % (4060818)Termination phase: shuffling
% 0.62/0.44 % (4060818)Time elapsed: 0.002 s
% 0.62/0.44 % (4060818)Peak memory usage: 10 MB
% 0.62/0.44 % (4060818)Instructions burned: 5 (million)
% 0.62/0.44 % (4060816)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2171720370:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.62/0.44 % (4060817)lrs+10_16_si=on:nwc=1.5:random_seed=1535979662:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.62/0.44 % (4060819)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=2063761693: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)
% 0.62/0.44 % (4060824)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2299317462:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.62/0.44 % (4060824)Instruction limit reached!
% 0.62/0.44 % (4060824)------------------------------
% 0.62/0.44 % (4060824)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.62/0.44 % (4060824)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.44 % (4060824)CaDiCaL version: 2.1.3
% 0.62/0.44 % (4060824)Termination reason: Instruction limit
% 0.62/0.44 % (4060824)Termination phase: shuffling
% 0.62/0.44 % (4060824)Time elapsed: 0.002 s
% 0.62/0.44 % (4060824)Peak memory usage: 10 MB
% 0.62/0.44 % (4060824)Instructions burned: 7 (million)
% 0.62/0.44 % (4060817)Instruction limit reached!
% 0.62/0.44 % (4060817)------------------------------
% 0.62/0.44 % (4060817)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.62/0.44 % (4060817)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.44 % (4060817)CaDiCaL version: 2.1.3
% 0.62/0.44 % (4060817)Termination reason: Instruction limit
% 0.62/0.44 % (4060817)Termination phase: shuffling
% 0.62/0.44 % (4060817)Time elapsed: 0.009 s
% 0.62/0.44 % (4060817)Peak memory usage: 10 MB
% 0.62/0.44 % (4060817)Instructions burned: 20 (million)
% 0.62/0.44 % (4060820)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2058696115:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.62/0.44 % (4060822)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.62/0.44 % (4060822)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
% 0.62/0.44 % (4060821)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=270451029:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.62/0.44 % (4060829)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1542911019:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.62/0.44 % (4060822)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=3702569680:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.62/0.44 % (4060829)Instruction limit reached!
% 0.62/0.44 % (4060829)------------------------------
% 0.62/0.44 % (4060829)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.62/0.44 % (4060829)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.44 % (4060829)CaDiCaL version: 2.1.3
% 0.62/0.44 % (4060829)Termination reason: Instruction limit
% 0.62/0.44 % (4060829)Termination phase: shuffling
% 0.62/0.44 % (4060829)Time elapsed: 0.002 s
% 0.62/0.44 % (4060829)Peak memory usage: 10 MB
% 0.62/0.44 % (4060829)Instructions burned: 9 (million)
% 0.62/0.44 % (4060830)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.62/0.44 % (4060830)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1541719160:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.62/0.44 % (4060820)Instruction limit reached!
% 0.62/0.44 % (4060820)------------------------------
% 0.62/0.44 % (4060820)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.62/0.44 % (4060820)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.44 % (4060820)CaDiCaL version: 2.1.3
% 0.62/0.44 % (4060820)Termination reason: Instruction limit
% 0.62/0.44 % (4060820)Termination phase: shuffling
% 0.62/0.44 % (4060820)Time elapsed: 0.019 s
% 0.62/0.44 % (4060820)Peak memory usage: 10 MB
% 0.62/0.44 % (4060820)Instructions burned: 24 (million)
% 0.62/0.44 % (4060830)Instruction limit reached!
% 0.62/0.44 % (4060830)------------------------------
% 0.62/0.44 % (4060830)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.62/0.44 % (4060830)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.44 % (4060835)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1898400442:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.62/0.44 % (4060830)CaDiCaL version: 2.1.3
% 0.62/0.44 % (4060830)Termination reason: Instruction limit
% 0.62/0.44 % (4060830)Termination phase: shuffling
% 0.62/0.44 % (4060830)Time elapsed: 0.004 s
% 0.62/0.44 % (4060830)Peak memory usage: 10 MB
% 0.62/0.44 % (4060830)Instructions burned: 8 (million)
% 0.62/0.44 % (4060835)Instruction limit reached!
% 0.62/0.44 % (4060835)------------------------------
% 0.62/0.44 % (4060835)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.62/0.44 % (4060835)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.44 % (4060835)CaDiCaL version: 2.1.3
% 0.62/0.44 % (4060835)Termination reason: Instruction limit
% 0.62/0.44 % (4060835)Termination phase: shuffling
% 0.62/0.44 % (4060835)Time elapsed: 0.004 s
% 0.62/0.44 % (4060835)Peak memory usage: 10 MB
% 0.62/0.44 % (4060835)Instructions burned: 15 (million)
% 0.62/0.44 % (4060816)Instruction limit reached!
% 0.62/0.44 % (4060816)------------------------------
% 0.62/0.44 % (4060816)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.62/0.44 % (4060816)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.44 % (4060816)CaDiCaL version: 2.1.3
% 0.62/0.44 % (4060816)Termination reason: Instruction limit
% 0.62/0.44 % (4060816)Termination phase: Property scanning
% 0.62/0.44 % (4060816)Time elapsed: 0.041 s
% 0.62/0.44 % (4060816)Peak memory usage: 12 MB
% 0.62/0.44 % (4060816)Instructions burned: 89 (million)
% 0.62/0.44 % (4060840)lrs+10_1_si=on:cs=on:random_seed=3892415214:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.62/0.44 % (4060840)Instruction limit reached!
% 0.62/0.44 % (4060840)------------------------------
% 0.62/0.44 % (4060840)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.62/0.44 % (4060840)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.44 % (4060840)CaDiCaL version: 2.1.3
% 0.62/0.44 % (4060840)Termination reason: Instruction limit
% 0.62/0.44 % (4060840)Termination phase: shuffling
% 0.62/0.44 % (4060840)Time elapsed: 0.002 s
% 0.62/0.44 % (4060840)Peak memory usage: 10 MB
% 0.62/0.44 % (4060840)Instructions burned: 8 (million)
% 0.62/0.44 % (4060839)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=2448000497:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.62/0.44 % (4060837)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
% 0.62/0.44 % (4060837)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.62/0.44 % (4060841)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.62/0.44 % (4060837)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1818941430:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.62/0.44 % (4060841)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=3537503039:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.62/0.44 % (4060841)Instruction limit reached!
% 0.62/0.44 % (4060841)------------------------------
% 0.62/0.44 % (4060841)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.62/0.44 % (4060841)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.44 % (4060841)CaDiCaL version: 2.1.3
% 0.62/0.44 % (4060841)Termination reason: Instruction limit
% 0.62/0.44 % (4060841)Termination phase: shuffling
% 0.62/0.44 % (4060841)Time elapsed: 0.002 s
% 0.62/0.44 % (4060841)Peak memory usage: 10 MB
% 0.62/0.44 % (4060841)Instructions burned: 3 (million)
% 0.62/0.44 % (4060837)Instruction limit reached!
% 0.62/0.44 % (4060837)------------------------------
% 0.62/0.44 % (4060837)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.62/0.44 % (4060837)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.44 % (4060837)CaDiCaL version: 2.1.3
% 0.62/0.44 % (4060837)Termination reason: Instruction limit
% 0.62/0.44 % (4060837)Termination phase: shuffling
% 0.62/0.44 % (4060837)Time elapsed: 0.014 s
% 0.62/0.44 % (4060837)Peak memory usage: 10 MB
% 0.62/0.44 % (4060837)Instructions burned: 28 (million)
% 0.62/0.44 % (4060819) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4060811-4060819"...
% 0.62/0.44 % (4060819)...printing done.
% 0.62/0.44 % (4060819)Refutation found. Thanks to Tanya!
% 0.62/0.44 % SZS status Theorem for theBenchmark
% 0.62/0.44 % SZS output start Proof for theBenchmark
% 0.62/0.44 thf(type_def_5, type, product_prod: ($tType * $tType) > $tType).
% 0.62/0.44 thf(type_def_6, type, variable: $tType).
% 0.62/0.44 thf(type_def_7, type, option: $tType > $tType).
% 0.62/0.44 thf(type_def_8, type, game: $tType).
% 0.62/0.44 thf(type_def_9, type, char: $tType).
% 0.62/0.44 thf(type_def_10, type, trm: $tType).
% 0.62/0.44 thf(type_def_11, type, fml: $tType).
% 0.62/0.44 thf(type_def_12, type, set: $tType > $tType).
% 0.62/0.44 thf(type_def_13, type, sTfun: ($tType * $tType) > $tType).
% 0.62/0.44 thf(func_def_0, type, bounded_lattice: !>[X0: $tType]:($o)).
% 0.62/0.44 thf(func_def_1, type, type: !>[X0: $tType]:($o)).
% 0.62/0.44 thf(func_def_2, type, bot: !>[X0: $tType]:($o)).
% 0.62/0.44 thf(func_def_3, type, ord: !>[X0: $tType]:($o)).
% 0.62/0.44 thf(func_def_4, type, order: !>[X0: $tType]:($o)).
% 0.62/0.44 thf(func_def_5, type, lattice: !>[X0: $tType]:($o)).
% 0.62/0.44 thf(func_def_6, type, linorder: !>[X0: $tType]:($o)).
% 0.62/0.44 thf(func_def_7, type, preorder: !>[X0: $tType]:($o)).
% 0.62/0.44 thf(func_def_8, type, order_bot: !>[X0: $tType]:($o)).
% 0.62/0.44 thf(func_def_9, type, semilattice_inf: !>[X0: $tType]:($o)).
% 0.62/0.44 thf(func_def_10, type, bounded_lattice_bot: !>[X0: $tType]:($o)).
% 0.62/0.44 thf(func_def_11, type, if: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 0.62/0.44 thf(func_def_12, type, inf_inf: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.62/0.44 thf(func_def_13, type, none: !>[X0: $tType]:(option @ X0)).
% 0.62/0.44 thf(func_def_14, type, some: !>[X0: $tType]:((X0 > option @ X0))).
% 0.62/0.44 thf(func_def_15, type, case_option: !>[X0: $tType, X1: $tType]:((X0 > (X1 > X0) > option @ X1 > X0))).
% 0.62/0.44 thf(func_def_16, type, the: !>[X0: $tType]:((option @ X0 > X0))).
% 0.62/0.44 thf(func_def_17, type, bot_bot: !>[X0: $tType]:(X0)).
% 0.62/0.44 thf(func_def_18, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.62/0.44 thf(func_def_19, type, product_Pair: !>[X0: $tType, X1: $tType]:((X0 > X1 > product_prod @ X0 @ X1))).
% 0.62/0.44 thf(func_def_20, type, produc2004651681e_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 0.62/0.44 thf(func_def_21, type, product_case_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 0.62/0.44 thf(func_def_22, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.62/0.44 thf(func_def_23, type, is_empty: !>[X0: $tType]:((set @ X0 > $o))).
% 0.62/0.44 thf(func_def_24, type, static_FVF: (fml > set @ variable)).
% 0.62/0.44 thf(func_def_25, type, static_FVT: (trm > set @ variable)).
% 0.62/0.44 thf(func_def_26, type, geq: (trm > trm > fml)).
% 0.62/0.44 thf(func_def_27, type, pred: (char > trm > fml)).
% 0.62/0.44 thf(func_def_28, type, const: (char > trm)).
% 0.62/0.44 thf(func_def_29, type, func: (char > trm > trm)).
% 0.62/0.44 thf(func_def_30, type, uSubst1556497037e_Geqo: (option @ trm > option @ trm > option @ fml)).
% 0.62/0.44 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))).
% 0.62/0.44 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)).
% 0.62/0.44 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)).
% 0.62/0.44 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)).
% 0.62/0.44 thf(func_def_35, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.62/0.44 thf(func_def_36, type, ua: set @ variable).
% 0.62/0.44 thf(func_def_37, type, va: set @ variable).
% 0.62/0.44 thf(func_def_38, type, sigma: product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game)).
% 0.62/0.44 thf(func_def_39, type, theta: trm).
% 0.62/0.44 thf(func_def_40, type, p: char).
% 0.62/0.44 thf(func_def_41, type, vv: (set @ variable > set @ variable > variable)).
% 0.62/0.44 thf(func_def_42, type, vva: (set @ variable > set @ variable > variable)).
% 0.62/0.44 thf(func_def_46, type, db1: !>[X0: $tType]:(X0)).
% 0.62/0.44 thf(func_def_47, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.62/0.44 thf(func_def_48, type, db0: !>[X0: $tType]:(X0)).
% 0.62/0.44 thf(func_def_49, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.62/0.44 thf(func_def_50, type, vAND: ($o > $o > $o)).
% 0.62/0.44 thf(func_def_51, type, db2: !>[X0: $tType]:(X0)).
% 0.62/0.44 thf(func_def_52, type, db3: !>[X0: $tType]:(X0)).
% 0.62/0.44 thf(func_def_53, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.62/0.44 thf(func_def_54, type, vIMP: ($o > $o > $o)).
% 0.62/0.44 thf(func_def_55, type, db4: !>[X0: $tType]:(X0)).
% 0.62/0.44 thf(func_def_56, type, vOR: ($o > $o > $o)).
% 0.62/0.44 thf(func_def_57, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.62/0.45 thf(func_def_58, type, sP0: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.62/0.45 thf(func_def_59, type, sP1: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.62/0.45 thf(func_def_60, type, sP2: (option @ trm > option @ trm > option @ fml > $o)).
% 0.62/0.45 thf(func_def_61, type, sK3: !>[X0: $tType]:((option @ X0 > X0))).
% 0.62/0.45 thf(func_def_62, type, sK4: ((option @ game > option @ game > $o) > game)).
% 0.62/0.45 thf(func_def_63, type, sK5: ((option @ game > option @ game > $o) > game)).
% 0.62/0.45 thf(func_def_64, type, sK6: ((option @ game > option @ game > $o) > game)).
% 0.62/0.45 thf(func_def_65, type, sK7: ((option @ game > option @ game > $o) > option @ game)).
% 0.62/0.45 thf(func_def_66, type, sK8: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.62/0.45 thf(func_def_67, type, sK9: ((option @ trm > $o) > trm)).
% 0.62/0.45 thf(func_def_68, type, sK10: !>[X0: $tType]:((set @ X0 > X0))).
% 0.62/0.45 thf(func_def_69, type, sK11: (set @ variable > set @ variable > variable)).
% 0.62/0.45 thf(func_def_70, type, sK12: (set @ variable > set @ variable > variable)).
% 0.62/0.45 thf(func_def_71, type, sK13: (set @ variable > set @ variable > variable)).
% 0.62/0.45 thf(func_def_72, type, sK14: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.62/0.45 thf(func_def_73, type, sK15: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.62/0.45 thf(func_def_74, type, sK16: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.62/0.45 thf(func_def_75, type, sK17: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.62/0.45 thf(func_def_76, type, sK18: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.62/0.45 thf(func_def_77, type, sK19: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.62/0.45 thf(func_def_78, type, sK20: (set @ variable > char > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > trm)).
% 0.62/0.45 thf(func_def_79, type, sK21: ((option @ trm > option @ trm > $o) > trm)).
% 0.62/0.45 thf(func_def_80, type, sK22: ((option @ trm > option @ trm > $o) > trm)).
% 0.62/0.45 thf(func_def_81, type, sK23: ((option @ trm > option @ trm > $o) > trm)).
% 0.62/0.45 thf(func_def_82, type, sK24: ((option @ trm > option @ trm > $o) > option @ trm)).
% 0.62/0.45 thf(func_def_83, type, sK25: (product_prod @ option @ game @ option @ fml > option @ fml)).
% 0.62/0.45 thf(func_def_84, type, sK26: (product_prod @ option @ game @ option @ fml > game)).
% 0.62/0.45 thf(func_def_85, type, sK27: (product_prod @ option @ game @ option @ fml > fml)).
% 0.62/0.45 thf(func_def_86, type, sK28: (product_prod @ option @ game @ option @ fml > game)).
% 0.62/0.45 thf(func_def_87, type, sK29: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > char > set @ variable > fml)).
% 0.62/0.45 thf(func_def_88, type, sK30: !>[X0: $tType]:(((X0 > $o) > set @ X0 > X0))).
% 0.62/0.45 thf(func_def_89, type, sK31: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > X0))).
% 0.62/0.45 thf(func_def_90, type, sK32: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.62/0.45 thf(func_def_91, type, sK33: !>[X0: $tType]:((set @ X0 > X0))).
% 0.62/0.45 thf(func_def_92, type, sK34: ((option @ game > $o) > game)).
% 0.62/0.45 thf(func_def_93, type, sK35: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.62/0.45 thf(func_def_94, type, sK36: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.62/0.45 thf(func_def_95, type, sK37: (option @ fml > fml)).
% 0.62/0.45 thf(func_def_96, type, sK38: (option @ trm > trm)).
% 0.62/0.45 thf(func_def_97, type, sK39: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.62/0.45 thf(func_def_98, type, sK40: (option @ fml > fml)).
% 0.62/0.45 thf(func_def_99, type, sK41: !>[X0: $tType]:((set @ X0 > X0))).
% 0.62/0.45 thf(func_def_100, type, sK42: ((option @ fml > $o) > fml)).
% 0.62/0.45 thf(func_def_101, type, sK43: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.62/0.45 thf(func_def_102, type, sK44: ((char > option @ trm > $o) > char)).
% 0.62/0.45 thf(func_def_103, type, sK45: ((char > option @ trm > $o) > trm)).
% 0.62/0.45 thf(func_def_104, type, sK46: ((char > option @ trm > $o) > char)).
% 0.62/0.45 thf(func_def_105, type, sK47: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.62/0.45 thf(func_def_106, type, sK48: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.62/0.45 thf(func_def_107, type, sK49: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.62/0.45 thf(func_def_108, type, sK50: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.62/0.45 thf(func_def_109, type, sK51: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.62/0.45 thf(func_def_110, type, sK52: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.62/0.45 thf(func_def_111, type, sK53: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.62/0.45 thf(func_def_112, type, sK54: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.62/0.45 thf(func_def_113, type, sK55: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.62/0.45 thf(func_def_114, type, sK56: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.62/0.45 thf(func_def_115, type, sK57: ((option @ game > option @ fml > $o) > game)).
% 0.62/0.45 thf(func_def_116, type, sK58: ((option @ game > option @ fml > $o) > fml)).
% 0.62/0.45 thf(func_def_117, type, sK59: ((option @ game > option @ fml > $o) > game)).
% 0.62/0.45 thf(func_def_118, type, sK60: ((option @ game > option @ fml > $o) > option @ fml)).
% 0.62/0.45 thf(func_def_119, type, sK61: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.62/0.45 thf(func_def_120, type, sK62: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.62/0.45 thf(func_def_121, type, sK63: (option @ trm > trm)).
% 0.62/0.45 thf(func_def_122, type, sK64: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.62/0.45 thf(func_def_123, type, sK65: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.62/0.45 thf(func_def_124, type, sK66: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.62/0.45 thf(func_def_125, type, sK67: !>[X0: $tType]:((option @ X0 > (X0 > $o) > X0))).
% 0.62/0.45 thf(func_def_126, type, sK68: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.62/0.45 thf(func_def_127, type, sK69: (option @ game > game)).
% 0.62/0.45 thf(func_def_128, type, sK70: !>[X0: $tType, X1: $tType]:((option @ X1 > option @ X0 > (option @ X1 > option @ X0 > $o) > X1))).
% 0.62/0.45 thf(func_def_129, type, sK71: !>[X0: $tType, X1: $tType]:((option @ X1 > option @ X0 > (option @ X1 > option @ X0 > $o) > X0))).
% 0.62/0.45 thf(func_def_130, type, sK72: !>[X0: $tType]:(((X0 > $o) > set @ X0 > (X0 > $o) > X0))).
% 0.62/0.45 thf(func_def_131, type, sK73: !>[X0: $tType]:(((option @ X0 > $o) > X0))).
% 0.62/0.45 thf(func_def_132, type, sK74: !>[X0: $tType]:((set @ X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.62/0.45 thf(func_def_133, type, sK75: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > char > trm)).
% 0.62/0.45 thf(func_def_134, type, sK76: (option @ trm > trm)).
% 0.62/0.45 thf(func_def_135, type, sK77: (option @ trm > option @ trm > option @ fml > trm)).
% 0.62/0.45 thf(func_def_136, type, sK78: (option @ trm > option @ trm > option @ fml > trm)).
% 0.62/0.45 thf(func_def_137, type, sK79: !>[X0: $tType]:((option @ X0 > X0))).
% 0.62/0.45 thf(func_def_138, type, sK80: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.62/0.45 thf(func_def_139, type, sK81: ((variable > option @ trm > $o) > trm)).
% 0.62/0.45 thf(func_def_140, type, sK82: ((variable > option @ trm > $o) > variable)).
% 0.62/0.45 thf(func_def_141, type, sK83: ((variable > option @ trm > $o) > variable)).
% 0.62/0.45 thf(func_def_142, type, sK84: (set @ variable > set @ variable > variable)).
% 0.62/0.45 thf(func_def_143, type, sK85: !>[X0: $tType, X1: $tType]:(((X0 > $o) > (X1 > $o) > (X0 > X1) > X0))).
% 0.62/0.45 thf(func_def_144, type, sK86: (set @ variable > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > char > trm)).
% 0.62/0.45 thf(func_def_145, type, sK87: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.62/0.45 thf(func_def_146, type, sK88: ((variable > option @ fml > $o) > variable)).
% 0.62/0.45 thf(func_def_147, type, sK89: ((variable > option @ fml > $o) > fml)).
% 0.62/0.45 thf(func_def_148, type, sK90: ((variable > option @ fml > $o) > variable)).
% 0.62/0.45 thf(func_def_149, type, sK91: ((option @ fml > option @ fml > $o) > fml)).
% 0.62/0.45 thf(func_def_150, type, sK92: ((option @ fml > option @ fml > $o) > fml)).
% 0.62/0.45 thf(func_def_151, type, sK93: ((option @ fml > option @ fml > $o) > fml)).
% 0.62/0.45 thf(func_def_152, type, sK94: ((option @ fml > option @ fml > $o) > option @ fml)).
% 0.62/0.45 thf(func_def_153, type, sK95: (option @ game > game)).
% 0.62/0.45 thf(func_def_154, type, sK96: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > X0))).
% 0.62/0.45 thf(func_def_155, type, sK97: !>[X0: $tType]:((set @ X0 > X0))).
% 0.62/0.45 thf(func_def_156, type, sK98: !>[X0: $tType]:((option @ X0 > X0))).
% 0.62/0.45 thf(func_def_157, type, vNOT: ($o > $o)).
% 0.62/0.45 thf(f3,axiom,(
% 0.62/0.45 ~((((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 @ (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))))))),
% 0.62/0.45 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)).
% 0.62/0.45 thf(f4,axiom,(
% 0.62/0.45 ~(((((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 @ 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) @ (^[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 = ((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)))),
% 0.62/0.45 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)).
% 0.62/0.45 thf(f287,conjecture,(
% 0.62/0.45 (((uSubst95898978stappf @ sigma @ va @ (pred @ p @ theta))) != none @ 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)),
% 0.62/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 0.62/0.45 thf(f288,negated_conjecture,(
% 0.62/0.45 ~((((uSubst95898978stappf @ sigma @ va @ (pred @ p @ theta))) != none @ 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))),
% 0.62/0.45 inference(negated_conjecture,[status(cth)],[f287])).
% 0.62/0.45 thf(f296,plain,(
% 0.62/0.45 ~((((uSubst95898978stappf @ sigma @ va @ (pred @ p @ theta))) != none @ 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))),
% 0.62/0.45 inference(rectify,[],[f288])).
% 0.62/0.45 thf(f297,plain,(
% 0.62/0.45 ~((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)))))),
% 0.62/0.45 inference(fool_elimination,[],[f296])).
% 0.62/0.45 thf(f550,plain,(
% 0.62/0.45 ~(((((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 @ 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) @ (^[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))))))) => (none @ 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)))),
% 0.62/0.45 inference(rectify,[],[f4])).
% 0.62/0.45 thf(f551,plain,(
% 0.62/0.45 ~(((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)))),
% 0.62/0.45 inference(fool_elimination,[],[f550])).
% 0.62/0.45 thf(f683,plain,(
% 0.62/0.45 ~((((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 @ (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))))))),
% 0.62/0.45 inference(rectify,[],[f3])).
% 0.62/0.45 thf(f684,plain,(
% 0.62/0.45 ~((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))))))),
% 0.62/0.45 inference(fool_elimination,[],[f683])).
% 0.62/0.45 thf(f915,plain,(
% 0.62/0.45 (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)))),
% 0.62/0.45 inference(ennf_transformation,[],[f684])).
% 0.62/0.45 thf(f1023,plain,(
% 0.62/0.45 (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)))) & ((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)))))))),
% 0.62/0.45 inference(ennf_transformation,[],[f551])).
% 0.62/0.45 thf(f1034,plain,(
% 0.62/0.45 (none @ fml = ((uSubst95898978stappf @ sigma @ va @ (pred @ p @ theta)))) & (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)))),
% 0.62/0.45 inference(ennf_transformation,[],[f297])).
% 0.62/0.45 thf(f1321,plain,(
% 0.62/0.45 (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)))),
% 0.62/0.45 inference(cnf_transformation,[],[f915])).
% 0.62/0.45 thf(f1322,plain,(
% 0.62/0.45 (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)))))),
% 0.62/0.45 inference(cnf_transformation,[],[f915])).
% 0.62/0.45 thf(f1444,plain,(
% 0.62/0.45 (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))) | (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)))))),
% 0.62/0.45 inference(cnf_transformation,[],[f1023])).
% 0.62/0.45 thf(f1562,plain,(
% 0.62/0.45 (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)))),
% 0.62/0.45 inference(cnf_transformation,[],[f1034])).
% 0.62/0.45 thf(f1563,plain,(
% 0.62/0.45 (none @ fml = ((uSubst95898978stappf @ sigma @ va @ (pred @ p @ theta))))),
% 0.62/0.45 inference(cnf_transformation,[],[f1034])).
% 0.62/0.45 thf(f1854,definition,(
% 0.62/0.45 spl99_2 <=> (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)))),
% 0.62/0.45 introduced(definition,[new_symbols(definition,[spl99_2])],[avatar_definition])).
% 0.62/0.45 thf(f1872,definition,(
% 0.62/0.45 spl99_6 <=> (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)))),
% 0.62/0.45 introduced(definition,[new_symbols(definition,[spl99_6])],[avatar_definition])).
% 0.62/0.45 thf(f1877,definition,(
% 0.62/0.45 spl99_7 <=> (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)))))),
% 0.62/0.45 introduced(definition,[new_symbols(definition,[spl99_7])],[avatar_definition])).
% 0.62/0.45 thf(f1880,plain,(
% 0.62/0.45 ~spl99_7),
% 0.62/0.45 inference(avatar_split_clause,[],[f1322,f1877])).
% 0.62/0.45 thf(f1886,plain,(
% 0.62/0.45 spl99_6),
% 0.62/0.45 inference(avatar_split_clause,[],[f1321,f1872])).
% 0.62/0.45 thf(f1888,definition,(
% 0.62/0.45 spl99_9 <=> (none @ fml = ((uSubst95898978stappf @ sigma @ va @ (pred @ p @ theta))))),
% 0.62/0.45 introduced(definition,[new_symbols(definition,[spl99_9])],[avatar_definition])).
% 0.62/0.45 thf(f1962,plain,(
% 0.62/0.45 spl99_9),
% 0.62/0.45 inference(avatar_split_clause,[],[f1563,f1888])).
% 0.62/0.45 thf(f1963,plain,(
% 0.62/0.45 ~spl99_2),
% 0.62/0.45 inference(avatar_split_clause,[],[f1562,f1854])).
% 0.62/0.45 thf(f1975,definition,(
% 0.62/0.45 spl99_26 <=> (((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)))))),
% 0.62/0.45 introduced(definition,[new_symbols(definition,[spl99_26])],[avatar_definition])).
% 0.62/0.45 thf(f1978,plain,(
% 0.62/0.45 spl99_2 | spl99_26 | ~spl99_6),
% 0.62/0.45 inference(avatar_split_clause,[],[f1444,f1872,f1975,f1854])).
% 0.62/0.45 thf(f1984,definition,(
% 0.62/0.45 (none @ fml != ((uSubst95898978stappf @ sigma @ va @ (pred @ p @ theta)))) | (((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 = ((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)))))),
% 0.62/0.45 introduced(theory,[theory_tautology_sat_conflict])).
% 0.62/0.45 cnf(s5, plain, ~spl99_7, inference(sat_conversion,[],[f1880])).
% 0.62/0.45 cnf(s7, plain, spl99_6, inference(sat_conversion,[],[f1886])).
% 0.62/0.45 cnf(s24, plain, spl99_9, inference(sat_conversion,[],[f1962])).
% 0.62/0.45 cnf(s25, plain, ~spl99_2, inference(sat_conversion,[],[f1963])).
% 0.62/0.45 cnf(s28, plain, spl99_2 | ~spl99_6 | spl99_26, inference(sat_conversion,[],[f1978])).
% 0.62/0.45 cnf(s30, plain, spl99_7 | ~spl99_9 | ~spl99_26, inference(sat_conversion,[],[f1984])).
% 0.62/0.45 cnf(s31, plain, spl99_26, inference(rat,[],[s28,s25,s7])).
% 0.62/0.45 cnf(s33, plain, spl99_7, inference(rat,[],[s30,s24,s31])).
% 0.62/0.45 cnf(s34, plain, $false, inference(rat,[],[s5,s33])).
% 0.62/0.45 thf(f1985,plain,(
% 0.62/0.45 $false),
% 0.62/0.45 inference(avatar_sat_refutation,[],[s34])).
% 0.62/0.45 % SZS output end Proof for theBenchmark
% 0.62/0.45 % (4060819)------------------------------
% 0.62/0.45 % (4060819)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.62/0.45 % (4060819)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.45 % (4060819)CaDiCaL version: 2.1.3
% 0.62/0.45 % (4060819)Termination reason: Refutation
% 0.62/0.45 % (4060819)Time elapsed: 0.078 s
% 0.62/0.45 % (4060819)Peak memory usage: 14 MB
% 0.62/0.45 % (4060819)Instructions burned: 164 (million)
% 0.62/0.45 % (4060811)Success in time 0.134 s
% 0.62/0.45 % Vampire exiting
%------------------------------------------------------------------------------