%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP200^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:08:47 AM UTC 2026
% Result : Theorem 0.65s 0.44s
% Output : Refutation 0.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP200^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n017.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 20:06:22 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.23/0.27 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.65/0.44 % (831386)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.65/0.44 % (831396)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3726898969:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.65/0.44 % (831397)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.65/0.44 % (831397)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
% 0.65/0.44 % (831391)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3236852806:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.65/0.44 % (831393)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2449068050:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.65/0.44 % (831394)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=4122992120: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)
% 0.65/0.44 % (831395)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=4046581377:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.65/0.44 % (831397)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=3130157197:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.65/0.44 % (831393)Instruction limit reached!
% 0.65/0.44 % (831393)------------------------------
% 0.65/0.44 % (831393)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.44 % (831393)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.44 % (831393)CaDiCaL version: 2.1.3
% 0.65/0.44 % (831393)Termination reason: Instruction limit
% 0.65/0.44 % (831393)Termination phase: shuffling
% 0.65/0.44 % (831393)Time elapsed: 0.003 s
% 0.65/0.44 % (831393)Peak memory usage: 10 MB
% 0.65/0.44 % (831393)Instructions burned: 5 (million)
% 0.65/0.44 % (831395)Instruction limit reached!
% 0.65/0.44 % (831395)------------------------------
% 0.65/0.44 % (831395)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.44 % (831395)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.44 % (831395)CaDiCaL version: 2.1.3
% 0.65/0.44 % (831395)Termination reason: Instruction limit
% 0.65/0.44 % (831395)Termination phase: Property scanning
% 0.65/0.44 % (831395)Time elapsed: 0.012 s
% 0.65/0.44 % (831395)Peak memory usage: 10 MB
% 0.65/0.44 % (831395)Instructions burned: 24 (million)
% 0.65/0.44 % (831396)Instruction limit reached!
% 0.65/0.44 % (831396)------------------------------
% 0.65/0.44 % (831396)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.44 % (831396)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.44 % (831396)CaDiCaL version: 2.1.3
% 0.65/0.44 % (831396)Termination reason: Instruction limit
% 0.65/0.44 % (831396)Termination phase: Property scanning
% 0.65/0.44 % (831396)Time elapsed: 0.021 s
% 0.65/0.44 % (831396)Peak memory usage: 12 MB
% 0.65/0.44 % (831396)Instructions burned: 77 (million)
% 0.65/0.44 % (831406)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.65/0.44 % (831392)lrs+10_16_si=on:nwc=1.5:random_seed=457139221:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.65/0.44 % (831406)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2536042929:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.65/0.44 % (831404)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1176144667:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.65/0.44 % (831406)Instruction limit reached!
% 0.65/0.44 % (831406)------------------------------
% 0.65/0.44 % (831406)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.44 % (831406)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.44 % (831406)CaDiCaL version: 2.1.3
% 0.65/0.44 % (831406)Termination reason: Instruction limit
% 0.65/0.44 % (831406)Termination phase: shuffling
% 0.65/0.44 % (831406)Time elapsed: 0.002 s
% 0.65/0.44 % (831406)Peak memory usage: 10 MB
% 0.65/0.44 % (831406)Instructions burned: 9 (million)
% 0.65/0.44 % (831404)Instruction limit reached!
% 0.65/0.44 % (831404)------------------------------
% 0.65/0.44 % (831404)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.44 % (831404)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.44 % (831404)CaDiCaL version: 2.1.3
% 0.65/0.44 % (831404)Termination reason: Instruction limit
% 0.65/0.44 % (831404)Termination phase: shuffling
% 0.65/0.44 % (831404)Time elapsed: 0.002 s
% 0.65/0.44 % (831404)Peak memory usage: 10 MB
% 0.65/0.44 % (831404)Instructions burned: 3 (million)
% 0.65/0.44 % (831405)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3324683122:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.65/0.44 % (831405)Instruction limit reached!
% 0.65/0.44 % (831405)------------------------------
% 0.65/0.44 % (831405)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.44 % (831405)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.44 % (831405)CaDiCaL version: 2.1.3
% 0.65/0.44 % (831405)Termination reason: Instruction limit
% 0.65/0.44 % (831405)Termination phase: shuffling
% 0.65/0.44 % (831405)Time elapsed: 0.004 s
% 0.65/0.44 % (831405)Peak memory usage: 10 MB
% 0.65/0.44 % (831405)Instructions burned: 6 (million)
% 0.65/0.44 % (831410)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2824855166:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.65/0.44 % (831391)Instruction limit reached!
% 0.65/0.44 % (831391)------------------------------
% 0.65/0.44 % (831391)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.44 % (831391)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.44 % (831391)CaDiCaL version: 2.1.3
% 0.65/0.44 % (831391)Termination reason: Instruction limit
% 0.65/0.44 % (831391)Termination phase: Function definition elimination
% 0.65/0.44 % (831391)Time elapsed: 0.043 s
% 0.65/0.44 % (831391)Peak memory usage: 12 MB
% 0.65/0.44 % (831391)Instructions burned: 87 (million)
% 0.65/0.44 % (831392)Instruction limit reached!
% 0.65/0.44 % (831392)------------------------------
% 0.65/0.44 % (831392)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.44 % (831392)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.44 % (831392)CaDiCaL version: 2.1.3
% 0.65/0.44 % (831392)Termination reason: Instruction limit
% 0.65/0.44 % (831392)Termination phase: Property scanning
% 0.65/0.44 % (831392)Time elapsed: 0.019 s
% 0.65/0.44 % (831392)Peak memory usage: 10 MB
% 0.65/0.44 % (831392)Instructions burned: 23 (million)
% 0.65/0.44 % (831411)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
% 0.65/0.44 % (831411)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.65/0.44 % (831410)Instruction limit reached!
% 0.65/0.44 % (831410)------------------------------
% 0.65/0.44 % (831410)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.44 % (831410)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.44 % (831410)CaDiCaL version: 2.1.3
% 0.65/0.44 % (831410)Termination reason: Instruction limit
% 0.65/0.44 % (831410)Termination phase: shuffling
% 0.65/0.44 % (831410)Time elapsed: 0.004 s
% 0.65/0.44 % (831410)Peak memory usage: 10 MB
% 0.65/0.44 % (831410)Instructions burned: 13 (million)
% 0.65/0.44 % (831411)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=833798699:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.65/0.44 % (831416)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.65/0.44 % (831416)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=3335251154:i=2:add=on:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 0.65/0.44 % (831416)Instruction limit reached!
% 0.65/0.44 % (831416)------------------------------
% 0.65/0.44 % (831416)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.44 % (831416)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.44 % (831416)CaDiCaL version: 2.1.3
% 0.65/0.44 % (831416)Termination reason: Instruction limit
% 0.65/0.44 % (831416)Termination phase: shuffling
% 0.65/0.44 % (831416)Time elapsed: 0.001 s
% 0.65/0.44 % (831416)Peak memory usage: 10 MB
% 0.65/0.44 % (831416)Instructions burned: 3 (million)
% 0.65/0.44 % (831413)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=3363015321:i=86:piset=equals:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/86Mi)
% 0.65/0.44 % (831411)Instruction limit reached!
% 0.65/0.44 % (831411)------------------------------
% 0.65/0.44 % (831411)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.44 % (831411)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.44 % (831411)CaDiCaL version: 2.1.3
% 0.65/0.44 % (831411)Termination reason: Instruction limit
% 0.65/0.44 % (831411)Termination phase: shuffling
% 0.65/0.44 % (831411)Time elapsed: 0.014 s
% 0.65/0.44 % (831411)Peak memory usage: 10 MB
% 0.65/0.44 % (831411)Instructions burned: 30 (million)
% 0.65/0.44 % (831420)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=3305008669:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.65/0.44 % (831415)lrs+10_1_si=on:cs=on:random_seed=2529355603:i=8:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/8Mi)
% 0.65/0.44 % (831397)Instruction limit reached!
% 0.65/0.44 % (831397)------------------------------
% 0.65/0.44 % (831397)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.44 % (831397)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.44 % (831397)CaDiCaL version: 2.1.3
% 0.65/0.44 % (831397)Termination reason: Instruction limit
% 0.65/0.44 % (831397)Termination phase: Saturation
% 0.65/0.44 % (831397)Time elapsed: 0.083 s
% 0.65/0.44 % (831397)Peak memory usage: 14 MB
% 0.65/0.44 % (831397)Instructions burned: 158 (million)
% 0.65/0.44 % (831422)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=1805551553:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.65/0.44 % (831394) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-831386-831394"...
% 0.65/0.44 % (831417)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2238932042:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 0.65/0.44 % (831415)Instruction limit reached!
% 0.65/0.44 % (831415)------------------------------
% 0.65/0.44 % (831415)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.44 % (831415)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.44 % (831415)CaDiCaL version: 2.1.3
% 0.65/0.44 % (831415)Termination reason: Instruction limit
% 0.65/0.44 % (831415)Termination phase: shuffling
% 0.65/0.44 % (831415)Time elapsed: 0.006 s
% 0.65/0.44 % (831415)Peak memory usage: 10 MB
% 0.65/0.44 % (831415)Instructions burned: 12 (million)
% 0.65/0.44 % (831394)...printing done.
% 0.65/0.44 % (831394)Refutation found. Thanks to Tanya!
% 0.65/0.44 % SZS status Theorem for theBenchmark
% 0.65/0.44 % SZS output start Proof for theBenchmark
% 0.65/0.44 thf(type_def_5, type, denotational_interp: $tType).
% 0.65/0.44 thf(type_def_6, type, product_prod: ($tType * $tType) > $tType).
% 0.65/0.44 thf(type_def_7, type, variable: $tType).
% 0.65/0.44 thf(type_def_8, type, option: $tType > $tType).
% 0.65/0.44 thf(type_def_9, type, game: $tType).
% 0.65/0.44 thf(type_def_10, type, char: $tType).
% 0.65/0.44 thf(type_def_11, type, trm: $tType).
% 0.65/0.44 thf(type_def_12, type, fml: $tType).
% 0.65/0.44 thf(type_def_13, type, real: $tType).
% 0.65/0.44 thf(type_def_14, type, set: $tType > $tType).
% 0.65/0.44 thf(type_def_15, type, sTfun: ($tType * $tType) > $tType).
% 0.65/0.44 thf(func_def_0, type, type: !>[X0: $tType]:($o)).
% 0.65/0.44 thf(func_def_1, type, ord: !>[X0: $tType]:($o)).
% 0.65/0.44 thf(func_def_2, type, top: !>[X0: $tType]:($o)).
% 0.65/0.44 thf(func_def_3, type, order: !>[X0: $tType]:($o)).
% 0.65/0.44 thf(func_def_4, type, linorder: !>[X0: $tType]:($o)).
% 0.65/0.44 thf(func_def_5, type, preorder: !>[X0: $tType]:($o)).
% 0.65/0.44 thf(func_def_6, type, order_top: !>[X0: $tType]:($o)).
% 0.65/0.44 thf(func_def_7, type, bNF_Greatest_image2: !>[X0: $tType, X1: $tType, X2: $tType]:((set @ X0 > (X0 > X1) > (X0 > X2) > set @ product_prod @ X1 @ X2))).
% 0.65/0.44 thf(func_def_8, type, bNF_Gr1317331620lImage: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X0 > (X0 > X1) > set @ product_prod @ X1 @ X1))).
% 0.65/0.44 thf(func_def_9, type, bNF_Gr2107612801vImage: !>[X0: $tType, X1: $tType]:((set @ X0 > set @ product_prod @ X1 @ X1 > (X0 > X1) > set @ product_prod @ X0 @ X0))).
% 0.65/0.44 thf(func_def_10, type, denota1419872369iation: ((variable > real) > (variable > real) > set @ variable > $o)).
% 0.65/0.44 thf(func_def_11, type, if: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 0.65/0.44 thf(func_def_12, type, none: !>[X0: $tType]:(option @ X0)).
% 0.65/0.44 thf(func_def_13, type, some: !>[X0: $tType]:((X0 > option @ X0))).
% 0.65/0.44 thf(func_def_14, type, case_option: !>[X0: $tType, X1: $tType]:((X0 > (X1 > X0) > option @ X1 > X0))).
% 0.65/0.44 thf(func_def_15, type, the: !>[X0: $tType]:((option @ X0 > X0))).
% 0.65/0.44 thf(func_def_16, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.65/0.44 thf(func_def_17, type, order_Greatest: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.65/0.44 thf(func_def_18, type, top_top: !>[X0: $tType]:(X0)).
% 0.65/0.44 thf(func_def_19, type, product_Pair: !>[X0: $tType, X1: $tType]:((X0 > X1 > product_prod @ X0 @ X1))).
% 0.65/0.44 thf(func_def_20, type, powp: !>[X0: $tType]:(((X0 > $o) > set @ X0 > $o))).
% 0.65/0.44 thf(func_def_21, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.65/0.44 thf(func_def_22, type, geq: (trm > trm > fml)).
% 0.65/0.44 thf(func_def_23, type, assign: (variable > trm > game)).
% 0.65/0.44 thf(func_def_24, type, ode: (char > trm > game)).
% 0.65/0.44 thf(func_def_25, type, test: (fml > game)).
% 0.65/0.44 thf(func_def_26, type, const: (char > trm)).
% 0.65/0.44 thf(func_def_27, type, differential: (trm > trm)).
% 0.65/0.44 thf(func_def_28, type, func: (char > trm > trm)).
% 0.65/0.44 thf(func_def_29, type, number: (real > trm)).
% 0.65/0.44 thf(func_def_30, type, plus: (trm > trm > trm)).
% 0.65/0.44 thf(func_def_31, type, times: (trm > trm > trm)).
% 0.65/0.44 thf(func_def_32, type, var: (variable > trm)).
% 0.65/0.44 thf(func_def_33, type, uSubst1326326671ssigno: (variable > option @ trm > option @ game)).
% 0.65/0.44 thf(func_def_34, type, uSubst1741596714no_rel: (product_prod @ variable @ option @ trm > product_prod @ variable @ option @ trm > $o)).
% 0.65/0.44 thf(func_def_35, type, uSubst259074819ntialo: (option @ trm > option @ trm)).
% 0.65/0.44 thf(func_def_36, type, uSubst99643830lo_rel: (option @ trm > option @ trm > $o)).
% 0.65/0.44 thf(func_def_37, type, uSubst1556497037e_Geqo: (option @ trm > option @ trm > option @ fml)).
% 0.65/0.44 thf(func_def_38, type, uSubst864323244qo_rel: (product_prod @ option @ trm @ option @ trm > product_prod @ option @ trm @ option @ trm > $o)).
% 0.65/0.44 thf(func_def_39, type, uSubst1083227664e_ODEo: (char > option @ trm > option @ game)).
% 0.65/0.44 thf(func_def_40, type, uSubst2007600873Eo_rel: (product_prod @ char @ option @ trm > product_prod @ char @ option @ trm > $o)).
% 0.65/0.44 thf(func_def_41, type, uSubst1112714340_Pluso: (option @ trm > option @ trm > option @ trm)).
% 0.65/0.44 thf(func_def_42, type, uSubst270600597so_rel: (product_prod @ option @ trm @ option @ trm > product_prod @ option @ trm @ option @ trm > $o)).
% 0.65/0.44 thf(func_def_43, type, uSubst190403692_Testo: (option @ fml > option @ game)).
% 0.65/0.44 thf(func_def_44, type, uSubst533687181to_rel: (option @ fml > option @ fml > $o)).
% 0.65/0.44 thf(func_def_45, type, uSubst277968634Timeso: (option @ trm > option @ trm > option @ trm)).
% 0.65/0.44 thf(func_def_46, type, uSubst1377811071so_rel: (product_prod @ option @ trm @ option @ trm > product_prod @ option @ trm @ option @ trm > $o)).
% 0.65/0.44 thf(func_def_47, 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)).
% 0.65/0.44 thf(func_def_48, 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)).
% 0.65/0.44 thf(func_def_49, 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)).
% 0.65/0.44 thf(func_def_50, type, uSubst2096773001pt_rel: (product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > $o)).
% 0.65/0.44 thf(func_def_51, type, accp: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > $o))).
% 0.65/0.44 thf(func_def_52, type, lex_prod: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X0 > set @ product_prod @ X1 @ X1 > set @ product_prod @ product_prod @ X0 @ X1 @ product_prod @ X0 @ X1))).
% 0.65/0.44 thf(func_def_53, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.65/0.44 thf(func_def_54, type, u: set @ variable).
% 0.65/0.44 thf(func_def_55, type, ua: set @ variable).
% 0.65/0.44 thf(func_def_56, type, eta: trm).
% 0.65/0.44 thf(func_def_57, type, nu: (variable > real)).
% 0.65/0.44 thf(func_def_58, type, nu2: (variable > real)).
% 0.65/0.44 thf(func_def_59, type, omega: (variable > real)).
% 0.65/0.44 thf(func_def_60, type, omega2: (variable > real)).
% 0.65/0.44 thf(func_def_61, type, sigma: product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game)).
% 0.65/0.44 thf(func_def_62, type, theta: trm).
% 0.65/0.44 thf(func_def_64, type, db0: !>[X0: $tType]:(X0)).
% 0.65/0.44 thf(func_def_65, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.65/0.44 thf(func_def_66, type, db2: !>[X0: $tType]:(X0)).
% 0.65/0.44 thf(func_def_67, type, db1: !>[X0: $tType]:(X0)).
% 0.65/0.44 thf(func_def_68, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.65/0.44 thf(func_def_71, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.65/0.44 thf(func_def_72, type, vAND: ($o > $o > $o)).
% 0.65/0.44 thf(func_def_73, type, db4: !>[X0: $tType]:(X0)).
% 0.65/0.44 thf(func_def_74, type, db3: !>[X0: $tType]:(X0)).
% 0.65/0.44 thf(func_def_75, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.65/0.44 thf(func_def_76, type, vIMP: ($o > $o > $o)).
% 0.65/0.44 thf(func_def_77, type, vNOT: ($o > $o)).
% 0.65/0.44 thf(func_def_78, type, vOR: ($o > $o > $o)).
% 0.65/0.44 thf(func_def_79, type, db5: !>[X0: $tType]:(X0)).
% 0.65/0.44 thf(func_def_80, type, sP0: ((denotational_interp > trm > $o) > $o)).
% 0.65/0.44 thf(func_def_81, type, sP1: (option @ fml > option @ trm > option @ trm > $o)).
% 0.65/0.44 thf(func_def_82, type, sP2: (option @ trm > option @ trm > option @ trm > $o)).
% 0.65/0.44 thf(func_def_83, type, sP3: ((trm > $o) > $o)).
% 0.65/0.44 thf(func_def_84, type, sP4: (option @ trm > option @ trm > option @ fml > $o)).
% 0.65/0.44 thf(func_def_85, type, sP5: (option @ trm > option @ trm > option @ trm > $o)).
% 0.65/0.44 thf(func_def_86, type, sP6: (option @ trm > option @ trm > option @ trm > $o)).
% 0.65/0.44 thf(func_def_87, type, sP7: (option @ trm > option @ trm > option @ trm > $o)).
% 0.65/0.44 thf(func_def_88, type, sP8: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.65/0.44 thf(func_def_89, type, sP9: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.65/0.44 thf(func_def_90, type, sK10: ((denotational_interp > trm > $o) > trm)).
% 0.65/0.44 thf(func_def_91, type, sK11: ((denotational_interp > trm > $o) > denotational_interp)).
% 0.65/0.44 thf(func_def_92, type, sK12: ((denotational_interp > trm > $o) > trm)).
% 0.65/0.44 thf(func_def_93, type, sK13: ((denotational_interp > trm > $o) > denotational_interp)).
% 0.65/0.44 thf(func_def_94, type, sK14: ((denotational_interp > trm > $o) > real)).
% 0.65/0.44 thf(func_def_95, type, sK15: ((denotational_interp > trm > $o) > variable)).
% 0.65/0.44 thf(func_def_96, type, sK16: ((denotational_interp > trm > $o) > denotational_interp)).
% 0.65/0.44 thf(func_def_97, type, sK17: ((denotational_interp > trm > $o) > denotational_interp)).
% 0.65/0.44 thf(func_def_98, type, sK18: ((denotational_interp > trm > $o) > trm)).
% 0.65/0.44 thf(func_def_99, type, sK19: ((denotational_interp > trm > $o) > trm)).
% 0.65/0.44 thf(func_def_100, type, sK20: ((denotational_interp > trm > $o) > char)).
% 0.65/0.44 thf(func_def_101, type, sK21: ((denotational_interp > trm > $o) > denotational_interp)).
% 0.65/0.44 thf(func_def_102, type, sK22: ((denotational_interp > trm > $o) > denotational_interp)).
% 0.65/0.44 thf(func_def_103, type, sK23: ((denotational_interp > trm > $o) > trm)).
% 0.65/0.44 thf(func_def_104, type, sK24: ((denotational_interp > trm > $o) > char)).
% 0.65/0.44 thf(func_def_105, type, sK25: ((denotational_interp > trm > $o) > trm)).
% 0.65/0.44 thf(func_def_106, type, sK26: ((denotational_interp > trm > $o) > denotational_interp)).
% 0.65/0.44 thf(func_def_107, type, sK27: !>[X0: $tType]:(((X0 > $o) > X0 > X0))).
% 0.65/0.44 thf(func_def_108, type, sK28: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.65/0.44 thf(func_def_109, type, sK29: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.65/0.44 thf(func_def_110, type, sK30: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.65/0.44 thf(func_def_111, type, sK31: (trm > variable)).
% 0.65/0.44 thf(func_def_112, type, sK32: (trm > char)).
% 0.65/0.44 thf(func_def_113, type, sK33: (trm > trm)).
% 0.65/0.44 thf(func_def_114, type, sK34: (trm > trm)).
% 0.65/0.44 thf(func_def_115, type, sK35: (trm > char)).
% 0.65/0.44 thf(func_def_116, type, sK36: (trm > real)).
% 0.65/0.44 thf(func_def_117, type, sK37: (trm > trm)).
% 0.65/0.44 thf(func_def_118, type, sK38: (trm > trm)).
% 0.65/0.44 thf(func_def_119, type, sK39: (trm > trm)).
% 0.65/0.44 thf(func_def_120, type, sK40: (trm > trm)).
% 0.65/0.44 thf(func_def_121, type, sK41: (option @ trm > trm)).
% 0.65/0.44 thf(func_def_122, type, sK42: (option @ fml > option @ trm > option @ trm > trm)).
% 0.65/0.44 thf(func_def_123, type, sK43: (option @ fml > option @ trm > option @ trm > trm)).
% 0.65/0.44 thf(func_def_124, type, sK44: !>[X0: $tType]:(((option @ X0 > $o) > X0))).
% 0.65/0.44 thf(func_def_125, type, sK45: ((option @ game > option @ game > $o) > game)).
% 0.65/0.44 thf(func_def_126, type, sK46: ((option @ game > option @ game > $o) > game)).
% 0.65/0.44 thf(func_def_127, type, sK47: ((option @ game > option @ game > $o) > option @ game)).
% 0.65/0.44 thf(func_def_128, type, sK48: ((option @ game > option @ game > $o) > game)).
% 0.65/0.44 thf(func_def_129, type, sK49: ((option @ game > option @ fml > $o) > game)).
% 0.65/0.44 thf(func_def_130, type, sK50: ((option @ game > option @ fml > $o) > fml)).
% 0.65/0.44 thf(func_def_131, type, sK51: ((option @ game > option @ fml > $o) > game)).
% 0.65/0.44 thf(func_def_132, type, sK52: ((option @ game > option @ fml > $o) > option @ fml)).
% 0.65/0.44 thf(func_def_133, type, sK53: !>[X0: $tType]:(((X0 > $o) > (X0 > X0 > $o) > X0))).
% 0.65/0.44 thf(func_def_134, type, sK54: (option @ fml > fml)).
% 0.65/0.44 thf(func_def_135, type, sK55: (option @ trm > option @ trm > option @ trm > trm)).
% 0.65/0.44 thf(func_def_136, type, sK56: (option @ trm > option @ trm > option @ trm > trm)).
% 0.65/0.44 thf(func_def_137, type, sK57: (option @ trm > option @ trm > option @ trm > trm)).
% 0.65/0.44 thf(func_def_138, type, sK58: !>[X0: $tType]:((X0 > (X0 > $o) > X0))).
% 0.65/0.44 thf(func_def_139, type, sK59: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.65/0.44 thf(func_def_140, type, sK60: !>[X0: $tType]:((option @ X0 > X0))).
% 0.65/0.44 thf(func_def_141, type, sK61: !>[X0: $tType]:(((X0 > $o) > (X0 > X0 > $o) > X0))).
% 0.65/0.44 thf(func_def_142, type, sK62: (option @ trm > trm)).
% 0.65/0.44 thf(func_def_143, type, sK63: ((trm > $o) > trm)).
% 0.65/0.44 thf(func_def_144, type, sK64: ((trm > $o) > trm)).
% 0.65/0.44 thf(func_def_145, type, sK65: ((trm > $o) > trm)).
% 0.65/0.44 thf(func_def_146, type, sK66: ((trm > $o) > trm)).
% 0.65/0.44 thf(func_def_147, type, sK67: ((trm > $o) > trm)).
% 0.65/0.44 thf(func_def_148, type, sK68: ((trm > $o) > char)).
% 0.65/0.44 thf(func_def_149, type, sK69: ((trm > $o) > trm)).
% 0.65/0.44 thf(func_def_150, type, sK70: ((trm > $o) > variable)).
% 0.65/0.44 thf(func_def_151, type, sK71: ((trm > $o) > real)).
% 0.65/0.44 thf(func_def_152, type, sK72: ((trm > $o) > char)).
% 0.65/0.44 thf(func_def_153, type, sK73: !>[X0: $tType]:(X0)).
% 0.65/0.44 thf(func_def_154, type, sK74: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > X0))).
% 0.65/0.44 thf(func_def_155, type, sK75: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.65/0.44 thf(func_def_156, type, sK76: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > X0))).
% 0.65/0.44 thf(func_def_157, type, sK77: (product_prod @ char @ option @ trm > char)).
% 0.65/0.44 thf(func_def_158, type, sK78: (product_prod @ char @ option @ trm > char)).
% 0.65/0.44 thf(func_def_159, type, sK79: (product_prod @ char @ option @ trm > trm)).
% 0.65/0.44 thf(func_def_160, type, sK80: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.65/0.44 thf(func_def_161, type, sK81: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.65/0.44 thf(func_def_162, type, sK82: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.65/0.44 thf(func_def_163, type, sK83: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.65/0.44 thf(func_def_164, type, sK84: (option @ trm > option @ trm > option @ fml > trm)).
% 0.65/0.44 thf(func_def_165, type, sK85: (option @ trm > option @ trm > option @ fml > trm)).
% 0.65/0.44 thf(func_def_166, type, sK86: (option @ trm > option @ trm > option @ fml > trm)).
% 0.65/0.44 thf(func_def_167, type, sK87: (option @ game > option @ fml > fml)).
% 0.65/0.44 thf(func_def_168, type, sK88: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.65/0.44 thf(func_def_169, type, sK89: (char > option @ trm > option @ game > trm)).
% 0.65/0.44 thf(func_def_170, type, sK90: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.65/0.44 thf(func_def_171, type, sK91: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.65/0.44 thf(func_def_172, type, sK92: !>[X0: $tType]:((option @ X0 > X0))).
% 0.65/0.44 thf(func_def_173, type, sK93: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > (X1 > X0 > $o) > X1))).
% 0.65/0.44 thf(func_def_174, type, sK94: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > (X1 > X0 > $o) > X0))).
% 0.65/0.44 thf(func_def_175, type, sK95: (option @ trm > option @ trm > trm)).
% 0.65/0.44 thf(func_def_176, type, sK96: (option @ trm > trm)).
% 0.65/0.44 thf(func_def_177, type, sK97: (option @ trm > option @ trm > option @ trm > trm)).
% 0.65/0.44 thf(func_def_178, type, sK98: (option @ trm > option @ trm > option @ trm > trm)).
% 0.65/0.44 thf(func_def_179, type, sK99: !>[X0: $tType]:((X0 > (X0 > X0 > $o) > X0))).
% 0.65/0.44 thf(func_def_180, type, sK100: ((option @ trm > option @ trm > $o) > trm)).
% 0.65/0.44 thf(func_def_181, type, sK101: ((option @ trm > option @ trm > $o) > option @ trm)).
% 0.65/0.44 thf(func_def_182, type, sK102: ((option @ trm > option @ trm > $o) > trm)).
% 0.65/0.44 thf(func_def_183, type, sK103: ((option @ trm > option @ trm > $o) > trm)).
% 0.65/0.44 thf(func_def_184, type, sK104: (product_prod @ variable @ option @ fml > fml)).
% 0.65/0.44 thf(func_def_185, type, sK105: (product_prod @ variable @ option @ fml > variable)).
% 0.65/0.44 thf(func_def_186, type, sK106: (product_prod @ variable @ option @ fml > variable)).
% 0.65/0.44 thf(func_def_187, type, sK107: ((option @ game > $o) > game)).
% 0.65/0.44 thf(func_def_188, type, sK108: ((char > option @ trm > $o) > char)).
% 0.65/0.44 thf(func_def_189, type, sK109: ((char > option @ trm > $o) > char)).
% 0.65/0.44 thf(func_def_190, type, sK110: ((char > option @ trm > $o) > trm)).
% 0.65/0.44 thf(func_def_191, type, sK111: !>[X0: $tType]:((set @ X0 > X0))).
% 0.65/0.44 thf(func_def_192, type, sK112: ((option @ fml > $o) > fml)).
% 0.65/0.44 thf(func_def_193, type, sK113: (product_prod @ option @ fml @ option @ fml > option @ fml)).
% 0.65/0.44 thf(func_def_194, type, sK114: (product_prod @ option @ fml @ option @ fml > fml)).
% 0.65/0.44 thf(func_def_195, type, sK115: (product_prod @ option @ fml @ option @ fml > fml)).
% 0.65/0.44 thf(func_def_196, type, sK116: (product_prod @ option @ fml @ option @ fml > fml)).
% 0.65/0.44 thf(func_def_197, type, sK117: (option @ trm > option @ trm > option @ trm > trm)).
% 0.65/0.44 thf(func_def_198, type, sK118: (option @ trm > option @ trm > option @ trm > trm)).
% 0.65/0.44 thf(func_def_199, type, sK119: (option @ trm > trm)).
% 0.65/0.44 thf(func_def_200, type, sK120: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.65/0.44 thf(func_def_201, type, sK121: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.65/0.44 thf(func_def_202, type, sK122: !>[X0: $tType]:((option @ X0 > X0))).
% 0.65/0.44 thf(func_def_203, type, sK123: (variable > option @ game > option @ trm > trm)).
% 0.65/0.44 thf(func_def_204, type, sK124: ((variable > option @ trm > $o) > variable)).
% 0.65/0.44 thf(func_def_205, type, sK125: ((variable > option @ trm > $o) > trm)).
% 0.65/0.44 thf(func_def_206, type, sK126: ((variable > option @ trm > $o) > variable)).
% 0.65/0.44 thf(func_def_207, type, sK127: !>[X0: $tType]:(((X0 > X0 > $o) > (X0 > $o) > X0))).
% 0.65/0.44 thf(func_def_208, type, sK128: (option @ trm > option @ game > variable > trm)).
% 0.65/0.44 thf(func_def_209, type, sK129: (product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game))).
% 0.65/0.44 thf(func_def_210, type, sK130: (product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > set @ variable)).
% 0.65/0.44 thf(func_def_211, type, sK131: (product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > trm)).
% 0.65/0.44 thf(func_def_212, type, sK132: (product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > set @ variable)).
% 0.65/0.44 thf(func_def_213, type, sK133: (product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game))).
% 0.65/0.44 thf(func_def_214, type, sK134: (product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > trm)).
% 0.65/0.44 thf(func_def_215, type, sK135: (product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > trm)).
% 0.65/0.44 thf(func_def_216, type, sK136: (product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > set @ variable)).
% 0.65/0.44 thf(func_def_217, type, sK137: (product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > char)).
% 0.65/0.44 thf(func_def_218, type, sK138: (product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game))).
% 0.65/0.44 thf(func_def_219, type, sK139: (product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > trm)).
% 0.65/0.44 thf(func_def_220, type, sK140: (product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > set @ variable)).
% 0.65/0.44 thf(func_def_221, type, sK141: (product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > trm)).
% 0.65/0.44 thf(func_def_222, type, sK142: (product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > trm)).
% 0.65/0.44 thf(func_def_223, type, sK143: (product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game))).
% 0.65/0.44 thf(func_def_224, type, sK144: (product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game))).
% 0.65/0.44 thf(func_def_225, type, sK145: (product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > variable)).
% 0.65/0.44 thf(func_def_226, type, sK146: (product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > set @ variable)).
% 0.65/0.44 thf(func_def_227, type, sK147: (product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > set @ variable)).
% 0.65/0.44 thf(func_def_228, type, sK148: (product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > char)).
% 0.65/0.44 thf(func_def_229, type, sK149: (product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game))).
% 0.65/0.44 thf(func_def_230, type, sK150: (product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > real)).
% 0.65/0.44 thf(func_def_231, type, sK151: (product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > set @ variable)).
% 0.65/0.44 thf(func_def_232, type, sK152: (product_prod @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ product_prod @ set @ variable @ trm > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game))).
% 0.65/0.44 thf(func_def_233, type, sK153: !>[X0: $tType]:((option @ X0 > (X0 > $o) > X0))).
% 0.65/0.44 thf(func_def_234, type, sK154: (product_prod @ denotational_interp @ trm > denotational_interp)).
% 0.65/0.44 thf(func_def_235, type, sK155: (product_prod @ denotational_interp @ trm > trm)).
% 0.65/0.44 thf(func_def_236, type, sK156: (product_prod @ denotational_interp @ trm > char)).
% 0.65/0.44 thf(func_def_237, type, sK157: (product_prod @ denotational_interp @ trm > variable)).
% 0.65/0.44 thf(func_def_238, type, sK158: (product_prod @ denotational_interp @ trm > denotational_interp)).
% 0.65/0.44 thf(func_def_239, type, sK159: (product_prod @ denotational_interp @ trm > real)).
% 0.65/0.44 thf(func_def_240, type, sK160: (product_prod @ denotational_interp @ trm > denotational_interp)).
% 0.65/0.44 thf(func_def_241, type, sK161: (product_prod @ denotational_interp @ trm > trm)).
% 0.65/0.44 thf(func_def_242, type, sK162: (product_prod @ denotational_interp @ trm > denotational_interp)).
% 0.65/0.44 thf(func_def_243, type, sK163: (product_prod @ denotational_interp @ trm > trm)).
% 0.65/0.44 thf(func_def_244, type, sK164: (product_prod @ denotational_interp @ trm > char)).
% 0.65/0.44 thf(func_def_245, type, sK165: (product_prod @ denotational_interp @ trm > denotational_interp)).
% 0.65/0.44 thf(func_def_246, type, sK166: (product_prod @ denotational_interp @ trm > denotational_interp)).
% 0.65/0.44 thf(func_def_247, type, sK167: (product_prod @ denotational_interp @ trm > trm)).
% 0.65/0.44 thf(func_def_248, type, sK168: (product_prod @ denotational_interp @ trm > trm)).
% 0.65/0.44 thf(func_def_249, type, sK169: (product_prod @ denotational_interp @ trm > trm)).
% 0.65/0.44 thf(func_def_250, type, sK170: (product_prod @ denotational_interp @ trm > denotational_interp)).
% 0.65/0.44 thf(func_def_251, type, sK171: ((option @ fml > option @ fml > $o) > fml)).
% 0.65/0.44 thf(func_def_252, type, sK172: ((option @ fml > option @ fml > $o) > fml)).
% 0.65/0.44 thf(func_def_253, type, sK173: ((option @ fml > option @ fml > $o) > fml)).
% 0.65/0.44 thf(func_def_254, type, sK174: ((option @ fml > option @ fml > $o) > option @ fml)).
% 0.65/0.44 thf(func_def_255, type, sK175: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > X0 > $o) > X0))).
% 0.65/0.44 thf(func_def_256, type, sK176: !>[X0: $tType]:(((X0 > $o) > (X0 > X0 > $o) > X0))).
% 0.65/0.44 thf(func_def_257, type, sK177: !>[X0: $tType]:(((X0 > $o) > (X0 > X0 > $o) > X0))).
% 0.65/0.44 thf(func_def_258, type, sK178: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.65/0.44 thf(func_def_259, type, sK179: (product_prod @ option @ trm @ option @ trm > trm)).
% 0.65/0.44 thf(func_def_260, type, sK180: (product_prod @ option @ trm @ option @ trm > option @ trm)).
% 0.65/0.44 thf(func_def_261, type, sK181: (product_prod @ option @ trm @ option @ trm > trm)).
% 0.65/0.44 thf(func_def_262, type, sK182: (product_prod @ option @ trm @ option @ trm > trm)).
% 0.65/0.44 thf(func_def_263, type, sK183: (option @ trm > option @ game > char > trm)).
% 0.65/0.44 thf(func_def_264, type, sK184: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X1 > set @ product_prod @ X0 @ X1 > X0))).
% 0.65/0.44 thf(func_def_265, type, sK185: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X1 > set @ product_prod @ X0 @ X1 > X1))).
% 0.65/0.44 thf(func_def_266, type, sK186: !>[X0: $tType]:(((X0 > $o) > set @ X0 > (X0 > $o) > X0))).
% 0.65/0.44 thf(func_def_267, type, sK187: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > $o) > (X1 > $o) > X0))).
% 0.65/0.44 thf(func_def_268, type, sK188: (product_prod @ option @ game @ option @ game > option @ game)).
% 0.65/0.44 thf(func_def_269, type, sK189: (product_prod @ option @ game @ option @ game > game)).
% 0.65/0.44 thf(func_def_270, type, sK190: (product_prod @ option @ game @ option @ game > game)).
% 0.65/0.44 thf(func_def_271, type, sK191: (product_prod @ option @ game @ option @ game > game)).
% 0.65/0.44 thf(func_def_272, type, sK192: !>[X0: $tType]:(((X0 > $o) > set @ X0 > X0))).
% 0.65/0.44 thf(func_def_273, type, sK193: (option @ game > option @ fml > fml)).
% 0.65/0.44 thf(func_def_274, type, sK194: (product_prod @ option @ game @ option @ fml > option @ fml)).
% 0.65/0.44 thf(func_def_275, type, sK195: (product_prod @ option @ game @ option @ fml > fml)).
% 0.65/0.44 thf(func_def_276, type, sK196: (product_prod @ option @ game @ option @ fml > game)).
% 0.65/0.44 thf(func_def_277, type, sK197: (product_prod @ option @ game @ option @ fml > game)).
% 0.65/0.44 thf(func_def_278, type, sK198: (option @ trm > option @ trm > option @ trm > trm)).
% 0.65/0.44 thf(func_def_279, type, sK199: (option @ trm > option @ trm > option @ trm > trm)).
% 0.65/0.44 thf(func_def_280, type, sK200: (option @ trm > option @ trm > option @ trm > trm)).
% 0.65/0.44 thf(func_def_281, type, sK201: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.65/0.44 thf(func_def_282, type, sK202: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.65/0.44 thf(func_def_283, type, sK203: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.65/0.44 thf(func_def_284, type, sK204: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.65/0.44 thf(func_def_285, type, sK205: (product_prod @ variable @ option @ trm > trm)).
% 0.65/0.44 thf(func_def_286, type, sK206: (product_prod @ variable @ option @ trm > variable)).
% 0.65/0.44 thf(func_def_287, type, sK207: (product_prod @ variable @ option @ trm > variable)).
% 0.65/0.44 thf(func_def_288, type, sK208: (option @ game > game)).
% 0.65/0.44 thf(func_def_289, type, sK209: !>[X0: $tType, X1: $tType]:((option @ X1 > (option @ X0 > option @ X1 > $o) > option @ X0 > X0))).
% 0.65/0.44 thf(func_def_290, type, sK210: !>[X0: $tType, X1: $tType]:((option @ X1 > (option @ X0 > option @ X1 > $o) > option @ X0 > X1))).
% 0.65/0.44 thf(func_def_291, type, sK211: (option @ trm > option @ trm > trm)).
% 0.65/0.44 thf(func_def_292, type, sK212: (option @ trm > trm)).
% 0.65/0.44 thf(func_def_293, type, sK213: ((option @ trm > $o) > trm)).
% 0.65/0.44 thf(func_def_294, type, sK214: (option @ game > game)).
% 0.65/0.44 thf(func_def_295, type, sK215: ((variable > option @ fml > $o) > variable)).
% 0.65/0.44 thf(func_def_296, type, sK216: ((variable > option @ fml > $o) > variable)).
% 0.65/0.44 thf(func_def_297, type, sK217: ((variable > option @ fml > $o) > fml)).
% 0.65/0.44 thf(func_def_298, type, sK218: (option @ fml > fml)).
% 0.65/0.44 thf(f2,axiom,(
% 0.65/0.44 ! [X0 : product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game),X3 : trm,X1 : set @ variable,X2 : trm] : ((((uSubst95898978stappf @ X0 @ X1 @ (geq @ X2 @ X3))) != none @ fml) => ((((uSubst95898992stappt @ X0 @ X1 @ X3)) != none @ trm) & (((uSubst95898992stappt @ X0 @ X1 @ X2)) != none @ trm)))),
% 0.65/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_usubstappf__geq__conv)).
% 0.65/0.44 thf(f3,axiom,(
% 0.65/0.44 (((uSubst95898978stappf @ sigma @ ua @ (geq @ theta @ eta))) != none @ fml)),
% 0.65/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_Geq_Oprems_I1_J)).
% 0.65/0.44 thf(f279,conjecture,(
% 0.65/0.44 (((uSubst95898992stappt @ sigma @ ua @ theta)) != none @ trm)),
% 0.65/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 0.65/0.44 thf(f280,negated_conjecture,(
% 0.65/0.44 ~ (((uSubst95898992stappt @ sigma @ ua @ theta)) != none @ trm)),
% 0.65/0.44 inference(negated_conjecture,[status(cth)],[f279])).
% 0.65/0.44 thf(f648,plain,(
% 0.65/0.44 ! [X3 : trm,X2 : set @ variable,X0 : product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game),X1 : trm] : ((none @ fml != ((uSubst95898978stappf @ X0 @ X2 @ (geq @ X3 @ X1)))) => ((none @ trm != ((uSubst95898992stappt @ X0 @ X2 @ X1))) & (none @ trm != ((uSubst95898992stappt @ X0 @ X2 @ X3)))))),
% 0.65/0.44 inference(rectify,[],[f2])).
% 0.65/0.44 thf(f650,plain,(
% 0.65/0.44 (none @ trm = ((uSubst95898992stappt @ sigma @ ua @ theta)))),
% 0.65/0.44 inference(flattening,[],[f280])).
% 0.65/0.44 thf(f876,plain,(
% 0.65/0.44 ! [X0 : product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game),X3 : trm,X2 : set @ variable,X1 : trm] : (((none @ trm != ((uSubst95898992stappt @ X0 @ X2 @ X1))) & (none @ trm != ((uSubst95898992stappt @ X0 @ X2 @ X3)))) | (none @ fml = ((uSubst95898978stappf @ X0 @ X2 @ (geq @ X3 @ X1)))))),
% 0.65/0.44 inference(ennf_transformation,[],[f648])).
% 0.65/0.44 thf(f1065,plain,(
% 0.65/0.44 ! [X0 : product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game),X1 : trm,X2 : set @ variable,X3 : trm] : (((none @ trm != ((uSubst95898992stappt @ X0 @ X2 @ X3))) & (none @ trm != ((uSubst95898992stappt @ X0 @ X2 @ X1)))) | (none @ fml = ((uSubst95898978stappf @ X0 @ X2 @ (geq @ X1 @ X3)))))),
% 0.65/0.44 inference(rectify,[],[f876])).
% 0.65/0.44 thf(f1464,plain,(
% 0.65/0.44 ( ! [X2 : set @ variable,X3 : trm,X0 : product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game),X1 : trm] : ((none @ fml = ((uSubst95898978stappf @ X0 @ X2 @ (geq @ X1 @ X3)))) | (none @ trm != ((uSubst95898992stappt @ X0 @ X2 @ X1)))) )),
% 0.65/0.44 inference(cnf_transformation,[],[f1065])).
% 0.65/0.44 thf(f1507,plain,(
% 0.65/0.44 (none @ fml != ((uSubst95898978stappf @ sigma @ ua @ (geq @ theta @ eta))))),
% 0.65/0.44 inference(cnf_transformation,[],[f3])).
% 0.65/0.44 thf(f1727,plain,(
% 0.65/0.44 (none @ trm = ((uSubst95898992stappt @ sigma @ ua @ theta)))),
% 0.65/0.44 inference(cnf_transformation,[],[f650])).
% 0.65/0.44 thf(f2096,definition,(
% 0.65/0.44 spl219_17 <=> (none @ trm = ((uSubst95898992stappt @ sigma @ ua @ theta)))),
% 0.65/0.44 introduced(definition,[new_symbols(definition,[spl219_17])],[avatar_definition])).
% 0.65/0.44 thf(f2098,plain,(
% 0.65/0.44 (none @ trm = ((uSubst95898992stappt @ sigma @ ua @ theta))) | ~spl219_17),
% 0.65/0.44 inference(avatar_component_clause,[],[f2096])).
% 0.65/0.44 thf(f2099,plain,(
% 0.65/0.44 spl219_17),
% 0.65/0.44 inference(avatar_split_clause,[],[f1727,f2096])).
% 0.65/0.44 thf(f2152,definition,(
% 0.65/0.44 spl219_29 <=> (none @ fml = ((uSubst95898978stappf @ sigma @ ua @ (geq @ theta @ eta))))),
% 0.65/0.44 introduced(definition,[new_symbols(definition,[spl219_29])],[avatar_definition])).
% 0.65/0.44 thf(f2154,plain,(
% 0.65/0.44 (none @ fml != ((uSubst95898978stappf @ sigma @ ua @ (geq @ theta @ eta)))) | spl219_29),
% 0.65/0.44 inference(avatar_component_clause,[],[f2152])).
% 0.65/0.44 thf(f2155,plain,(
% 0.65/0.44 ~spl219_29),
% 0.65/0.44 inference(avatar_split_clause,[],[f1507,f2152])).
% 0.65/0.44 thf(f2181,plain,(
% 0.65/0.44 (none @ trm != ((uSubst95898992stappt @ sigma @ ua @ theta))) | (none @ fml != none @ fml) | spl219_29),
% 0.65/0.44 inference(superposition,[],[f2154,f1464])).
% 0.65/0.44 thf(f2182,plain,(
% 0.65/0.44 (none @ trm != ((uSubst95898992stappt @ sigma @ ua @ theta))) | spl219_29),
% 0.65/0.44 inference(trivial_inequality_removal,[],[f2181])).
% 0.65/0.44 thf(f2183,plain,(
% 0.65/0.44 $false | (~spl219_17 | spl219_29)),
% 0.65/0.44 inference(forward_subsumption_resolution,[],[f2182,f2098])).
% 0.65/0.44 thf(f2184,plain,(
% 0.65/0.44 ~spl219_17 | spl219_29),
% 0.65/0.44 inference(avatar_contradiction_clause,[],[f2183])).
% 0.65/0.44 cnf(s15, plain, spl219_17, inference(sat_conversion,[],[f2099])).
% 0.65/0.44 cnf(s28, plain, ~spl219_29, inference(sat_conversion,[],[f2155])).
% 0.65/0.44 cnf(s33, plain, ~spl219_17 | spl219_29, inference(sat_conversion,[],[f2184])).
% 0.65/0.44 cnf(s34, plain, ~spl219_17, inference(rat,[],[s33,s28])).
% 0.65/0.44 cnf(s35, plain, $false, inference(rat,[],[s15,s34])).
% 0.65/0.44 thf(f2185,plain,(
% 0.65/0.44 $false),
% 0.65/0.44 inference(avatar_sat_refutation,[],[s35])).
% 0.65/0.44 % SZS output end Proof for theBenchmark
% 0.65/0.44 % (831394)------------------------------
% 0.65/0.44 % (831394)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.44 % (831394)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.44 % (831394)CaDiCaL version: 2.1.3
% 0.65/0.44 % (831394)Termination reason: Refutation
% 0.65/0.44 % (831394)Time elapsed: 0.088 s
% 0.65/0.44 % (831394)Peak memory usage: 15 MB
% 0.65/0.44 % (831394)Instructions burned: 176 (million)
% 0.65/0.44 % (831386)Success in time 0.154 s
% 0.65/0.44 % Vampire exiting
%------------------------------------------------------------------------------