%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP202^2 : 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 : n016.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 1.73s 0.62s
% Output : Refutation 1.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP202^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n016.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 20:16:20 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 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
% 0.95/0.48 % (852767)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.95/0.48 % (852774)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2617558375:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.95/0.48 % (852774)Instruction limit reached!
% 0.95/0.48 % (852774)------------------------------
% 0.95/0.48 % (852774)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.48 % (852774)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.48 % (852774)CaDiCaL version: 2.1.3
% 0.95/0.48 % (852774)Termination reason: Instruction limit
% 0.95/0.48 % (852774)Termination phase: shuffling
% 0.95/0.48 % (852774)Time elapsed: 0.002 s
% 0.95/0.48 % (852774)Peak memory usage: 10 MB
% 0.95/0.48 % (852774)Instructions burned: 7 (million)
% 0.95/0.48 % (852773)lrs+10_16_si=on:nwc=1.5:random_seed=111053559:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.95/0.48 % (852772)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1935588981:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.95/0.48 % (852775)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=1413373390: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)
% 0.95/0.48 % (852780)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2404826977:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.95/0.48 % (852780)Instruction limit reached!
% 0.95/0.48 % (852780)------------------------------
% 0.95/0.48 % (852780)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.48 % (852780)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.48 % (852780)CaDiCaL version: 2.1.3
% 0.95/0.48 % (852780)Termination reason: Instruction limit
% 0.95/0.48 % (852780)Termination phase: shuffling
% 0.95/0.48 % (852780)Time elapsed: 0.001 s
% 0.95/0.48 % (852780)Peak memory usage: 10 MB
% 0.95/0.48 % (852780)Instructions burned: 3 (million)
% 0.95/0.48 % (852773)Instruction limit reached!
% 0.95/0.48 % (852773)------------------------------
% 0.95/0.48 % (852773)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.48 % (852773)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.48 % (852773)CaDiCaL version: 2.1.3
% 0.95/0.48 % (852773)Termination reason: Instruction limit
% 0.95/0.48 % (852773)Termination phase: shuffling
% 0.95/0.48 % (852773)Time elapsed: 0.008 s
% 0.95/0.48 % (852773)Peak memory usage: 10 MB
% 0.95/0.48 % (852773)Instructions burned: 18 (million)
% 0.95/0.48 % (852776)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=261330547:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.95/0.48 % (852778)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.95/0.48 % (852778)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
% 0.95/0.48 % (852785)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1806999219:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.95/0.48 % (852785)Instruction limit reached!
% 0.95/0.48 % (852785)------------------------------
% 0.95/0.48 % (852785)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.48 % (852785)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.48 % (852785)CaDiCaL version: 2.1.3
% 0.95/0.48 % (852785)Termination reason: Instruction limit
% 0.95/0.48 % (852785)Termination phase: shuffling
% 0.95/0.48 % (852785)Time elapsed: 0.002 s
% 0.95/0.48 % (852785)Peak memory usage: 10 MB
% 0.95/0.48 % (852785)Instructions burned: 8 (million)
% 0.95/0.48 % (852778)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=1105497329:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.95/0.48 % (852786)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.95/0.48 % (852777)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=510827313:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.95/0.52 % (852786)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1816286925:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.95/0.52 % (852789)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2476146962:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.95/0.52 % (852776)Instruction limit reached!
% 0.95/0.52 % (852776)------------------------------
% 0.95/0.52 % (852776)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.52 % (852776)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.52 % (852776)CaDiCaL version: 2.1.3
% 0.95/0.52 % (852776)Termination reason: Instruction limit
% 0.95/0.52 % (852776)Termination phase: shuffling
% 0.95/0.52 % (852776)Time elapsed: 0.019 s
% 0.95/0.52 % (852776)Peak memory usage: 10 MB
% 0.95/0.52 % (852776)Instructions burned: 24 (million)
% 0.95/0.52 % (852786)Instruction limit reached!
% 0.95/0.52 % (852786)------------------------------
% 0.95/0.52 % (852786)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.52 % (852786)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.52 % (852786)CaDiCaL version: 2.1.3
% 0.95/0.52 % (852786)Termination reason: Instruction limit
% 0.95/0.52 % (852786)Termination phase: shuffling
% 0.95/0.52 % (852786)Time elapsed: 0.004 s
% 0.95/0.52 % (852786)Peak memory usage: 10 MB
% 0.95/0.52 % (852786)Instructions burned: 8 (million)
% 0.95/0.52 % (852789)Instruction limit reached!
% 0.95/0.52 % (852789)------------------------------
% 0.95/0.52 % (852789)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.52 % (852789)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.52 % (852789)CaDiCaL version: 2.1.3
% 0.95/0.52 % (852789)Termination reason: Instruction limit
% 0.95/0.52 % (852789)Termination phase: shuffling
% 0.95/0.52 % (852789)Time elapsed: 0.003 s
% 0.95/0.52 % (852789)Peak memory usage: 10 MB
% 0.95/0.52 % (852789)Instructions burned: 14 (million)
% 0.95/0.52 % (852772)Instruction limit reached!
% 0.95/0.52 % (852772)------------------------------
% 0.95/0.52 % (852772)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.52 % (852772)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.52 % (852772)CaDiCaL version: 2.1.3
% 0.95/0.52 % (852772)Termination reason: Instruction limit
% 0.95/0.52 % (852772)Termination phase: Preprocessing 3
% 0.95/0.52 % (852772)Time elapsed: 0.039 s
% 0.95/0.52 % (852772)Peak memory usage: 12 MB
% 0.95/0.52 % (852772)Instructions burned: 87 (million)
% 0.95/0.52 % (852796)lrs+10_1_si=on:cs=on:random_seed=3568244747:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.95/0.52 % (852796)Instruction limit reached!
% 0.95/0.52 % (852796)------------------------------
% 0.95/0.52 % (852796)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.52 % (852796)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.52 % (852796)CaDiCaL version: 2.1.3
% 0.95/0.52 % (852796)Termination reason: Instruction limit
% 0.95/0.52 % (852796)Termination phase: shuffling
% 0.95/0.52 % (852796)Time elapsed: 0.003 s
% 0.95/0.52 % (852796)Peak memory usage: 10 MB
% 0.95/0.52 % (852796)Instructions burned: 12 (million)
% 0.95/0.52 % (852794)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
% 0.95/0.52 % (852794)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.95/0.52 % (852795)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=1204446711:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.95/0.52 % (852794)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1016301573:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.95/0.52 % (852797)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.95/0.56 % (852797)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=4094457701:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.95/0.56 % (852794)Instruction limit reached!
% 0.95/0.56 % (852794)------------------------------
% 0.95/0.56 % (852794)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.56 % (852794)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.56 % (852794)CaDiCaL version: 2.1.3
% 0.95/0.56 % (852794)Termination reason: Instruction limit
% 0.95/0.56 % (852794)Termination phase: shuffling
% 0.95/0.56 % (852794)Time elapsed: 0.007 s
% 0.95/0.56 % (852794)Peak memory usage: 10 MB
% 0.95/0.56 % (852794)Instructions burned: 28 (million)
% 0.95/0.56 % (852797)Instruction limit reached!
% 0.95/0.56 % (852797)------------------------------
% 0.95/0.56 % (852797)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.56 % (852797)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.56 % (852797)CaDiCaL version: 2.1.3
% 0.95/0.56 % (852797)Termination reason: Instruction limit
% 0.95/0.56 % (852797)Termination phase: shuffling
% 0.95/0.56 % (852797)Time elapsed: 0.003 s
% 0.95/0.56 % (852797)Peak memory usage: 10 MB
% 0.95/0.56 % (852797)Instructions burned: 5 (million)
% 0.95/0.56 % (852799)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1273399607:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 0.95/0.56 % (852803)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=2273181428:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.95/0.56 % (852777)Instruction limit reached!
% 0.95/0.56 % (852777)------------------------------
% 0.95/0.56 % (852777)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.56 % (852777)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.56 % (852777)CaDiCaL version: 2.1.3
% 0.95/0.56 % (852777)Termination reason: Instruction limit
% 0.95/0.56 % (852777)Termination phase: Preprocessing 1
% 0.95/0.56 % (852777)Time elapsed: 0.050 s
% 0.95/0.56 % (852777)Peak memory usage: 11 MB
% 0.95/0.56 % (852777)Instructions burned: 75 (million)
% 0.95/0.56 % (852804)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=1089383337:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.95/0.56 % (852799)Instruction limit reached!
% 0.95/0.56 % (852799)------------------------------
% 0.95/0.56 % (852799)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.56 % (852799)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.56 % (852799)CaDiCaL version: 2.1.3
% 0.95/0.56 % (852799)Termination reason: Instruction limit
% 0.95/0.56 % (852799)Termination phase: shuffling
% 0.95/0.56 % (852799)Time elapsed: 0.017 s
% 0.95/0.56 % (852799)Peak memory usage: 10 MB
% 0.95/0.56 % (852799)Instructions burned: 39 (million)
% 0.95/0.56 % (852795)Instruction limit reached!
% 0.95/0.56 % (852795)------------------------------
% 0.95/0.56 % (852795)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.56 % (852795)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.56 % (852795)CaDiCaL version: 2.1.3
% 0.95/0.56 % (852795)Termination reason: Instruction limit
% 0.95/0.56 % (852795)Termination phase: Preprocessing 1
% 0.95/0.56 % (852795)Time elapsed: 0.039 s
% 0.95/0.56 % (852795)Peak memory usage: 11 MB
% 0.95/0.56 % (852795)Instructions burned: 88 (million)
% 0.95/0.56 % (852804)Instruction limit reached!
% 0.95/0.56 % (852804)------------------------------
% 0.95/0.56 % (852804)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.56 % (852804)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.56 % (852804)CaDiCaL version: 2.1.3
% 0.95/0.56 % (852804)Termination reason: Instruction limit
% 0.95/0.56 % (852804)Termination phase: shuffling
% 0.95/0.56 % (852804)Time elapsed: 0.011 s
% 0.95/0.56 % (852804)Peak memory usage: 10 MB
% 0.95/0.56 % (852804)Instructions burned: 27 (million)
% 0.95/0.56 % (852809)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1811514344:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.95/0.56 % (852810)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=3182531789:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.73/0.62 % (852807)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=2961983873:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.73/0.62 % (852811)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=455558174:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.73/0.62 % (852810)Instruction limit reached!
% 1.73/0.62 % (852810)------------------------------
% 1.73/0.62 % (852810)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.73/0.62 % (852810)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.73/0.62 % (852810)CaDiCaL version: 2.1.3
% 1.73/0.62 % (852810)Termination reason: Instruction limit
% 1.73/0.62 % (852810)Termination phase: shuffling
% 1.73/0.62 % (852810)Time elapsed: 0.006 s
% 1.73/0.62 % (852810)Peak memory usage: 10 MB
% 1.73/0.62 % (852810)Instructions burned: 14 (million)
% 1.73/0.62 % (852811)Instruction limit reached!
% 1.73/0.62 % (852811)------------------------------
% 1.73/0.62 % (852811)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.73/0.62 % (852811)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.73/0.62 % (852811)CaDiCaL version: 2.1.3
% 1.73/0.62 % (852811)Termination reason: Instruction limit
% 1.73/0.62 % (852811)Termination phase: shuffling
% 1.73/0.62 % (852811)Time elapsed: 0.002 s
% 1.73/0.62 % (852811)Peak memory usage: 10 MB
% 1.73/0.62 % (852811)Instructions burned: 2 (million)
% 1.73/0.62 % (852807)Instruction limit reached!
% 1.73/0.62 % (852807)------------------------------
% 1.73/0.62 % (852807)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.73/0.62 % (852807)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.73/0.62 % (852807)CaDiCaL version: 2.1.3
% 1.73/0.62 % (852807)Termination reason: Instruction limit
% 1.73/0.62 % (852807)Termination phase: shuffling
% 1.73/0.62 % (852807)Time elapsed: 0.010 s
% 1.73/0.62 % (852807)Peak memory usage: 10 MB
% 1.73/0.62 % (852807)Instructions burned: 24 (million)
% 1.73/0.62 % (852803)Instruction limit reached!
% 1.73/0.62 % (852803)------------------------------
% 1.73/0.62 % (852803)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.73/0.62 % (852803)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.73/0.62 % (852803)CaDiCaL version: 2.1.3
% 1.73/0.62 % (852803)Termination reason: Instruction limit
% 1.73/0.62 % (852803)Termination phase: Saturation
% 1.73/0.62 % (852803)Time elapsed: 0.063 s
% 1.73/0.62 % (852803)Peak memory usage: 15 MB
% 1.73/0.62 % (852803)Instructions burned: 250 (million)
% 1.73/0.62 % (852816)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=3299185623:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.73/0.62 % (852817)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=962370621:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.73/0.62 % (852778)Instruction limit reached!
% 1.73/0.62 % (852778)------------------------------
% 1.73/0.62 % (852778)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.73/0.62 % (852778)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.73/0.62 % (852778)CaDiCaL version: 2.1.3
% 1.73/0.62 % (852778)Termination reason: Instruction limit
% 1.73/0.62 % (852778)Termination phase: Property scanning
% 1.73/0.62 % (852778)Time elapsed: 0.111 s
% 1.73/0.62 % (852778)Peak memory usage: 13 MB
% 1.73/0.62 % (852778)Instructions burned: 158 (million)
% 1.73/0.62 % (852818)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=419739121:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.73/0.62 % (852822)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.73/0.62 % (852817)Instruction limit reached!
% 1.73/0.62 % (852817)------------------------------
% 1.73/0.62 % (852817)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.73/0.62 % (852817)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.73/0.62 % (852817)CaDiCaL version: 2.1.3
% 1.73/0.62 % (852817)Termination reason: Instruction limit
% 1.73/0.62 % (852817)Termination phase: shuffling
% 1.73/0.62 % (852817)Time elapsed: 0.011 s
% 1.73/0.62 % (852817)Peak memory usage: 10 MB
% 1.73/0.62 % (852817)Instructions burned: 25 (million)
% 1.73/0.62 % (852822)lrs+1010_4:1_slsqr=8,1:to=kbo:cha=on:drc=off:si=on:sp=arity:lcm=predicate:uwa=off:fd=preordered:gs=on:nwc=5:s2agt=32:slsqc=1:kmz=on:updr=off:chr=on:pe=on:slsq=on:random_seed=3243781065:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.73/0.62 % (852816)Instruction limit reached!
% 1.73/0.62 % (852816)------------------------------
% 1.73/0.62 % (852816)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.73/0.62 % (852816)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.73/0.62 % (852816)CaDiCaL version: 2.1.3
% 1.73/0.62 % (852816)Termination reason: Instruction limit
% 1.73/0.62 % (852816)Termination phase: shuffling
% 1.73/0.62 % (852816)Time elapsed: 0.013 s
% 1.73/0.62 % (852816)Peak memory usage: 10 MB
% 1.73/0.62 % (852816)Instructions burned: 28 (million)
% 1.73/0.62 % (852822)Instruction limit reached!
% 1.73/0.62 % (852822)------------------------------
% 1.73/0.62 % (852822)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.73/0.62 % (852822)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.73/0.62 % (852822)CaDiCaL version: 2.1.3
% 1.73/0.62 % (852822)Termination reason: Instruction limit
% 1.73/0.62 % (852822)Termination phase: shuffling
% 1.73/0.62 % (852822)Time elapsed: 0.003 s
% 1.73/0.62 % (852822)Peak memory usage: 10 MB
% 1.73/0.62 % (852822)Instructions burned: 12 (million)
% 1.73/0.62 % (852819)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) 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
% 1.73/0.62 % (852819)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.73/0.62 % (852819)ott+21_1_to=kbo:sil=128000:cnfonf=lazy_gen:bsd=on:si=on:sp=const_frequency:lma=off:uwa=off:foolp=on:s2agt=10:lwlo=on:random_seed=2492679793:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.73/0.62 % (852818)Instruction limit reached!
% 1.73/0.62 % (852818)------------------------------
% 1.73/0.62 % (852818)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.73/0.62 % (852818)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.73/0.62 % (852818)CaDiCaL version: 2.1.3
% 1.73/0.62 % (852818)Termination reason: Instruction limit
% 1.73/0.62 % (852818)Termination phase: Preprocessing 1
% 1.73/0.62 % (852818)Time elapsed: 0.027 s
% 1.73/0.62 % (852818)Peak memory usage: 10 MB
% 1.73/0.62 % (852818)Instructions burned: 61 (million)
% 1.73/0.62 % (852827)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=2336558895:i=23:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/23Mi)
% 1.73/0.62 % (852819)Instruction limit reached!
% 1.73/0.62 % (852819)------------------------------
% 1.73/0.62 % (852819)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.73/0.62 % (852819)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.73/0.62 % (852819)CaDiCaL version: 2.1.3
% 1.73/0.62 % (852819)Termination reason: Instruction limit
% 1.73/0.62 % (852819)Termination phase: shuffling
% 1.73/0.62 % (852819)Time elapsed: 0.013 s
% 1.73/0.62 % (852819)Peak memory usage: 10 MB
% 1.73/0.62 % (852819)Instructions burned: 14 (million)
% 1.73/0.62 % (852827)Instruction limit reached!
% 1.73/0.62 % (852827)------------------------------
% 1.73/0.62 % (852827)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.73/0.62 % (852827)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.73/0.62 % (852827)CaDiCaL version: 2.1.3
% 1.73/0.62 % (852827)Termination reason: Instruction limit
% 1.73/0.62 % (852827)Termination phase: shuffling
% 1.73/0.62 % (852827)Time elapsed: 0.012 s
% 1.73/0.62 % (852827)Peak memory usage: 11 MB
% 1.73/0.62 % (852827)Instructions burned: 25 (million)
% 1.73/0.62 % (852831)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=1789785655:i=1240:rtra=on:ixr=off_2997 on theBenchmark for (2997ds/1240Mi)
% 1.73/0.62 % (852824)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=2955835181:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2997 on theBenchmark for (2997ds/31Mi)
% 1.73/0.62 % (852826)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=903192764:i=7:hud=5:bd=preordered:rtra=on:bet=on_2997 on theBenchmark for (2997ds/7Mi)
% 1.73/0.62 % (852826)Instruction limit reached!
% 1.73/0.62 % (852826)------------------------------
% 1.73/0.62 % (852826)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.73/0.62 % (852826)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.73/0.62 % (852826)CaDiCaL version: 2.1.3
% 1.73/0.62 % (852826)Termination reason: Instruction limit
% 1.73/0.62 % (852826)Termination phase: shuffling
% 1.73/0.62 % (852826)Time elapsed: 0.007 s
% 1.73/0.62 % (852826)Peak memory usage: 10 MB
% 1.73/0.62 % (852826)Instructions burned: 8 (million)
% 1.73/0.62 % (852824)Instruction limit reached!
% 1.73/0.62 % (852824)------------------------------
% 1.73/0.62 % (852824)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.73/0.62 % (852824)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.73/0.62 % (852824)CaDiCaL version: 2.1.3
% 1.73/0.62 % (852824)Termination reason: Instruction limit
% 1.73/0.62 % (852824)Termination phase: shuffling
% 1.73/0.62 % (852824)Time elapsed: 0.015 s
% 1.73/0.62 % (852824)Peak memory usage: 11 MB
% 1.73/0.62 % (852824)Instructions burned: 32 (million)
% 1.73/0.62 % (852829)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=3669050357:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2997 on theBenchmark for (2997ds/20Mi)
% 1.73/0.62 % (852833)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=4222130785:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/143Mi)
% 1.73/0.62 % (852836)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=1786315455:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 1.73/0.62 % (852839)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=4118792703:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 1.73/0.62 % (852829)Instruction limit reached!
% 1.73/0.62 % (852829)------------------------------
% 1.73/0.62 % (852829)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.73/0.62 % (852829)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.73/0.62 % (852829)CaDiCaL version: 2.1.3
% 1.73/0.62 % (852829)Termination reason: Instruction limit
% 1.73/0.62 % (852829)Termination phase: shuffling
% 1.73/0.62 % (852829)Time elapsed: 0.019 s
% 1.73/0.62 % (852829)Peak memory usage: 10 MB
% 1.73/0.62 % (852829)Instructions burned: 21 (million)
% 1.73/0.62 % (852839)Instruction limit reached!
% 1.73/0.62 % (852839)------------------------------
% 1.73/0.62 % (852839)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.73/0.62 % (852839)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.73/0.62 % (852839)CaDiCaL version: 2.1.3
% 1.73/0.62 % (852839)Termination reason: Instruction limit
% 1.73/0.62 % (852839)Termination phase: Property scanning
% 1.73/0.62 % (852839)Time elapsed: 0.019 s
% 1.73/0.62 % (852839)Peak memory usage: 10 MB
% 1.73/0.62 % (852839)Instructions burned: 43 (million)
% 1.73/0.62 % (852809) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-852767-852809"...
% 1.73/0.62 % (852842)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.73/0.62 % (852842)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=703939287:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 1.73/0.62 % (852809)...printing done.
% 1.73/0.62 % (852809)Refutation found. Thanks to Tanya!
% 1.73/0.62 % SZS status Theorem for theBenchmark
% 1.73/0.62 % SZS output start Proof for theBenchmark
% 1.73/0.62 thf(type_def_5, type, denotational_interp: $tType).
% 1.73/0.62 thf(type_def_6, type, product_prod: ($tType * $tType) > $tType).
% 1.73/0.62 thf(type_def_7, type, variable: $tType).
% 1.73/0.62 thf(type_def_8, type, option: $tType > $tType).
% 1.73/0.62 thf(type_def_9, type, game: $tType).
% 1.73/0.62 thf(type_def_10, type, char: $tType).
% 1.73/0.62 thf(type_def_11, type, trm: $tType).
% 1.73/0.62 thf(type_def_12, type, fml: $tType).
% 1.73/0.62 thf(type_def_13, type, real: $tType).
% 1.73/0.62 thf(type_def_14, type, set: $tType > $tType).
% 1.73/0.62 thf(type_def_15, type, sTfun: ($tType * $tType) > $tType).
% 1.73/0.62 thf(func_def_0, type, bounded_lattice: !>[X0: $tType]:($o)).
% 1.73/0.62 thf(func_def_1, type, type: !>[X0: $tType]:($o)).
% 1.73/0.62 thf(func_def_2, type, bot: !>[X0: $tType]:($o)).
% 1.73/0.62 thf(func_def_3, type, lattice: !>[X0: $tType]:($o)).
% 1.73/0.62 thf(func_def_4, type, semilattice_inf: !>[X0: $tType]:($o)).
% 1.73/0.62 thf(func_def_5, type, bounded_lattice_bot: !>[X0: $tType]:($o)).
% 1.73/0.62 thf(func_def_6, type, if: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 1.73/0.62 thf(func_def_7, type, inf_inf: !>[X0: $tType]:((X0 > X0 > X0))).
% 1.73/0.62 thf(func_def_8, type, combine_options: !>[X0: $tType]:(((X0 > X0 > X0) > option @ X0 > option @ X0 > option @ X0))).
% 1.73/0.62 thf(func_def_9, type, none: !>[X0: $tType]:(option @ X0)).
% 1.73/0.62 thf(func_def_10, type, some: !>[X0: $tType]:((X0 > option @ X0))).
% 1.73/0.62 thf(func_def_11, type, case_option: !>[X0: $tType, X1: $tType]:((X0 > (X1 > X0) > option @ X1 > X0))).
% 1.73/0.62 thf(func_def_12, type, the: !>[X0: $tType]:((option @ X0 > X0))).
% 1.73/0.62 thf(func_def_13, type, bot_bot: !>[X0: $tType]:(X0)).
% 1.73/0.62 thf(func_def_14, type, product_Pair: !>[X0: $tType, X1: $tType]:((X0 > X1 > product_prod @ X0 @ X1))).
% 1.73/0.62 thf(func_def_15, type, produc2004651681e_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 1.73/0.62 thf(func_def_16, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 1.73/0.62 thf(func_def_17, type, product_case_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 1.73/0.62 thf(func_def_18, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 1.73/0.62 thf(func_def_19, type, is_empty: !>[X0: $tType]:((set @ X0 > $o))).
% 1.73/0.62 thf(func_def_20, type, static_FVF: (fml > set @ variable)).
% 1.73/0.62 thf(func_def_21, type, static_FVT: (trm > set @ variable)).
% 1.73/0.62 thf(func_def_22, type, char2: ($o > $o > $o > $o > $o > $o > $o > $o > char)).
% 1.73/0.62 thf(func_def_23, type, geq: (trm > trm > fml)).
% 1.73/0.62 thf(func_def_24, type, pred: (char > trm > fml)).
% 1.73/0.62 thf(func_def_25, type, const: (char > trm)).
% 1.73/0.62 thf(func_def_26, type, differential: (trm > trm)).
% 1.73/0.62 thf(func_def_27, type, func: (char > trm > trm)).
% 1.73/0.62 thf(func_def_28, type, number: (real > trm)).
% 1.73/0.62 thf(func_def_29, type, plus: (trm > trm > trm)).
% 1.73/0.62 thf(func_def_30, type, times: (trm > trm > trm)).
% 1.73/0.62 thf(func_def_31, type, var: (variable > trm)).
% 1.73/0.62 thf(func_def_32, type, uSubst259074819ntialo: (option @ trm > option @ trm)).
% 1.73/0.62 thf(func_def_33, type, uSubst1556497037e_Geqo: (option @ trm > option @ trm > option @ fml)).
% 1.73/0.62 thf(func_def_34, type, uSubst864323244qo_rel: (product_prod @ option @ trm @ option @ trm > product_prod @ option @ trm @ option @ trm > $o)).
% 1.73/0.62 thf(func_def_35, type, uSubst1112714340_Pluso: (option @ trm > option @ trm > option @ trm)).
% 1.73/0.62 thf(func_def_36, type, uSubst270600597so_rel: (product_prod @ option @ trm @ option @ trm > product_prod @ option @ trm @ option @ trm > $o)).
% 1.73/0.62 thf(func_def_37, type, uSubst277968634Timeso: (option @ trm > option @ trm > option @ trm)).
% 1.73/0.62 thf(func_def_38, type, uSubst1377811071so_rel: (product_prod @ option @ trm @ option @ trm > product_prod @ option @ trm @ option @ trm > $o)).
% 1.73/0.62 thf(func_def_39, type, uSubst_Mirabelle_dot: trm).
% 1.73/0.62 thf(func_def_40, type, uSubst969145931substt: (trm > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game))).
% 1.73/0.62 thf(func_def_41, 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)).
% 1.73/0.62 thf(func_def_42, 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)).
% 1.73/0.62 thf(func_def_43, 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)).
% 1.73/0.62 thf(func_def_44, 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)).
% 1.73/0.62 thf(func_def_45, type, accp: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > $o))).
% 1.73/0.62 thf(func_def_46, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 1.73/0.62 thf(func_def_47, type, u: set @ variable).
% 1.73/0.62 thf(func_def_48, type, v: set @ variable).
% 1.73/0.62 thf(func_def_49, type, sigma: product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game)).
% 1.73/0.62 thf(func_def_50, type, f: char).
% 1.73/0.62 thf(func_def_52, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 1.73/0.62 thf(func_def_55, type, vAND: ($o > $o > $o)).
% 1.73/0.62 thf(func_def_56, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 1.73/0.62 thf(func_def_57, type, db0: !>[X0: $tType]:(X0)).
% 1.73/0.62 thf(func_def_58, type, db3: !>[X0: $tType]:(X0)).
% 1.73/0.62 thf(func_def_59, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 1.73/0.62 thf(func_def_60, type, db1: !>[X0: $tType]:(X0)).
% 1.73/0.62 thf(func_def_61, type, vNOT: ($o > $o)).
% 1.73/0.62 thf(func_def_62, type, db2: !>[X0: $tType]:(X0)).
% 1.73/0.62 thf(func_def_63, type, vOR: ($o > $o > $o)).
% 1.73/0.62 thf(func_def_64, type, vIMP: ($o > $o > $o)).
% 1.73/0.62 thf(func_def_65, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 1.73/0.62 thf(func_def_66, type, db4: !>[X0: $tType]:(X0)).
% 1.73/0.62 thf(func_def_67, type, sP0: (option @ trm > option @ trm > option @ fml > $o)).
% 1.73/0.62 thf(func_def_68, type, sP1: ((product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > $o)).
% 1.73/0.62 thf(func_def_69, type, sP2: ((product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > $o)).
% 1.73/0.62 thf(func_def_70, type, sP3: ((product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > $o)).
% 1.73/0.62 thf(func_def_71, type, sP4: ((product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > $o)).
% 1.73/0.62 thf(func_def_72, type, sP5: ((product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > $o)).
% 1.73/0.62 thf(func_def_73, type, sP6: ((product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > $o)).
% 1.73/0.62 thf(func_def_74, type, sP7: (trm > option @ trm > $o)).
% 1.73/0.62 thf(func_def_75, type, sP8: (trm > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > option @ trm > $o)).
% 1.73/0.62 thf(func_def_76, type, sP9: (option @ trm > trm > $o)).
% 1.73/0.62 thf(func_def_77, type, sP10: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > option @ trm > trm > $o)).
% 1.73/0.62 thf(func_def_78, type, sP11: ((trm > $o) > $o)).
% 1.73/0.62 thf(func_def_79, type, sP12: ((trm > $o) > $o)).
% 1.73/0.62 thf(func_def_80, type, sP13: (option @ trm > option @ trm > option @ trm > $o)).
% 1.73/0.62 thf(func_def_81, type, sP14: (trm > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > option @ trm > $o)).
% 1.73/0.62 thf(func_def_82, type, sP15: (trm > set @ variable > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > option @ trm > $o)).
% 1.73/0.62 thf(func_def_83, type, sP16: (trm > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > option @ trm > $o)).
% 1.73/0.62 thf(func_def_84, type, sP17: (trm > option @ trm > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > $o)).
% 1.73/0.62 thf(func_def_85, type, sP18: (trm > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > option @ trm > $o)).
% 1.73/0.62 thf(func_def_86, type, sP19: (trm > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > option @ trm > $o)).
% 1.73/0.62 thf(func_def_87, type, sP20: !>[X0: $tType, X1: $tType]:(((option @ X0 > option @ X1 > $o) > option @ X1 > option @ X0 > $o))).
% 1.73/0.62 thf(func_def_88, type, sP21: (option @ trm > option @ trm > option @ trm > $o)).
% 1.73/0.62 thf(func_def_89, type, sK22: (option @ trm > trm)).
% 1.73/0.62 thf(func_def_90, type, sK23: (option @ fml > option @ trm > option @ trm > trm)).
% 1.73/0.62 thf(func_def_91, type, sK24: (option @ fml > option @ trm > option @ trm > trm)).
% 1.73/0.62 thf(func_def_92, type, sK25: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ product_prod @ X4 @ product_prod @ X5 @ product_prod @ X0 @ X3 > $o) > X0))).
% 1.73/0.62 thf(func_def_93, type, sK26: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ product_prod @ X4 @ product_prod @ X5 @ product_prod @ X0 @ X3 > $o) > X4))).
% 1.73/0.62 thf(func_def_94, type, sK27: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ product_prod @ X4 @ product_prod @ X5 @ product_prod @ X0 @ X3 > $o) > X3))).
% 1.73/0.62 thf(func_def_95, type, sK28: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ product_prod @ X4 @ product_prod @ X5 @ product_prod @ X0 @ X3 > $o) > X1))).
% 1.73/0.62 thf(func_def_96, type, sK29: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ product_prod @ X4 @ product_prod @ X5 @ product_prod @ X0 @ X3 > $o) > X5))).
% 1.73/0.62 thf(func_def_97, type, sK30: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ product_prod @ X4 @ product_prod @ X5 @ product_prod @ X0 @ X3 > $o) > X2))).
% 1.73/0.62 thf(func_def_98, type, sK31: ((product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > trm)).
% 1.73/0.62 thf(func_def_99, type, sK32: ((product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game))).
% 1.73/0.62 thf(func_def_100, type, sK33: ((product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > set @ variable)).
% 1.73/0.62 thf(func_def_101, type, sK34: ((product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > char)).
% 1.73/0.62 thf(func_def_102, type, sK35: ((product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > set @ variable)).
% 1.73/0.62 thf(func_def_103, type, sK36: ((product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > trm)).
% 1.73/0.62 thf(func_def_104, type, sK37: ((product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game))).
% 1.73/0.62 thf(func_def_105, type, sK38: ((product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > trm)).
% 1.73/0.62 thf(func_def_106, type, sK39: ((product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > set @ variable)).
% 1.73/0.62 thf(func_def_107, type, sK40: ((product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > char)).
% 1.73/0.62 thf(func_def_108, type, sK41: ((product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game))).
% 1.73/0.62 thf(func_def_109, type, sK42: ((product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game))).
% 1.73/0.62 thf(func_def_110, type, sK43: ((product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > set @ variable)).
% 1.73/0.62 thf(func_def_111, type, sK44: ((product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > variable)).
% 1.73/0.62 thf(func_def_112, type, sK45: ((product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game))).
% 1.73/0.62 thf(func_def_113, type, sK46: ((product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > set @ variable)).
% 1.73/0.62 thf(func_def_114, type, sK47: ((product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > trm)).
% 1.73/0.62 thf(func_def_115, type, sK48: ((product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > trm)).
% 1.73/0.62 thf(func_def_116, type, sK49: ((product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > real)).
% 1.73/0.62 thf(func_def_117, type, sK50: ((product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game))).
% 1.73/0.62 thf(func_def_118, type, sK51: ((product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > set @ variable)).
% 1.73/0.62 thf(func_def_119, type, sK52: ((product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > trm)).
% 1.73/0.62 thf(func_def_120, type, sK53: ((product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > set @ variable)).
% 1.73/0.62 thf(func_def_121, type, sK54: ((product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game))).
% 1.73/0.62 thf(func_def_122, type, sK55: (trm > trm)).
% 1.73/0.62 thf(func_def_123, type, sK56: (trm > char)).
% 1.73/0.62 thf(func_def_124, type, sK57: (trm > variable)).
% 1.73/0.62 thf(func_def_125, type, sK58: (trm > real)).
% 1.73/0.62 thf(func_def_126, type, sK59: (trm > char)).
% 1.73/0.62 thf(func_def_127, type, sK60: (trm > trm)).
% 1.73/0.62 thf(func_def_128, type, sK61: (trm > trm)).
% 1.73/0.62 thf(func_def_129, type, sK62: (trm > trm)).
% 1.73/0.62 thf(func_def_130, type, sK63: (trm > trm)).
% 1.73/0.62 thf(func_def_131, type, sK64: (trm > trm)).
% 1.73/0.62 thf(func_def_132, type, sK65: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > (X0 > X1 > X2 > $o) > product_prod @ X0 @ X1 > X0))).
% 1.73/0.62 thf(func_def_133, type, sK66: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > (X0 > X1 > X2 > $o) > product_prod @ X0 @ X1 > X1))).
% 1.73/0.62 thf(func_def_134, type, sK67: ((product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > set @ variable)).
% 1.73/0.62 thf(func_def_135, type, sK68: ((product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game))).
% 1.73/0.62 thf(func_def_136, type, sK69: ((product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > trm)).
% 1.73/0.62 thf(func_def_137, type, sK70: ((product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > set @ variable)).
% 1.73/0.62 thf(func_def_138, type, sK71: ((product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > trm)).
% 1.73/0.62 thf(func_def_139, type, sK72: ((product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > trm)).
% 1.73/0.63 thf(func_def_140, type, sK73: ((product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game))).
% 1.73/0.63 thf(func_def_141, type, sK74: ((product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game))).
% 1.73/0.63 thf(func_def_142, type, sK75: ((product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > trm)).
% 1.73/0.63 thf(func_def_143, type, sK76: ((product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > set @ variable)).
% 1.73/0.63 thf(func_def_144, type, sK77: ((product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > trm)).
% 1.73/0.63 thf(func_def_145, type, sK78: ((product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > char)).
% 1.73/0.63 thf(func_def_146, type, sK79: ((product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game))).
% 1.73/0.63 thf(func_def_147, type, sK80: ((product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > set @ variable)).
% 1.73/0.63 thf(func_def_148, type, sK81: ((product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > trm)).
% 1.73/0.63 thf(func_def_149, type, sK82: ((product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > variable)).
% 1.73/0.63 thf(func_def_150, type, sK83: ((product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game))).
% 1.73/0.63 thf(func_def_151, type, sK84: ((product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > set @ variable)).
% 1.73/0.63 thf(func_def_152, type, sK85: ((product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > char)).
% 1.73/0.63 thf(func_def_153, type, sK86: ((product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game))).
% 1.73/0.63 thf(func_def_154, type, sK87: ((product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > set @ variable)).
% 1.73/0.63 thf(func_def_155, type, sK88: ((product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > set @ variable)).
% 1.73/0.63 thf(func_def_156, type, sK89: ((product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game))).
% 1.73/0.63 thf(func_def_157, type, sK90: ((product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > trm > $o) > real)).
% 1.73/0.63 thf(func_def_158, type, sK91: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > char > trm)).
% 1.73/0.63 thf(func_def_159, type, sK92: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > product_prod @ X0 @ X1 > X1))).
% 1.73/0.63 thf(func_def_160, type, sK93: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > product_prod @ X0 @ X1 > X0))).
% 1.73/0.63 thf(func_def_161, type, sK94: ((variable > option @ trm > $o) > trm)).
% 1.73/0.63 thf(func_def_162, type, sK95: ((variable > option @ trm > $o) > variable)).
% 1.73/0.63 thf(func_def_163, type, sK96: ((variable > option @ trm > $o) > variable)).
% 1.73/0.63 thf(func_def_164, type, sK97: !>[X0: $tType, X1: $tType]:(((product_prod @ X0 @ X1 > $o) > X1))).
% 1.73/0.63 thf(func_def_165, type, sK98: !>[X0: $tType, X1: $tType]:(((product_prod @ X0 @ X1 > $o) > X0))).
% 1.73/0.63 thf(func_def_166, type, sK99: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X1 @ X3 > X3))).
% 1.73/0.63 thf(func_def_167, type, sK100: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X1 @ X3 > X0))).
% 1.73/0.63 thf(func_def_168, type, sK101: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X1 @ X3 > X4))).
% 1.73/0.63 thf(func_def_169, type, sK102: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X1 @ X3 > X1))).
% 1.73/0.63 thf(func_def_170, type, sK103: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X1 @ X3 > X2))).
% 1.73/0.63 thf(func_def_171, type, sK104: !>[X0: $tType]:(((X0 > $o) > option @ X0 > X0))).
% 1.73/0.63 thf(func_def_172, type, sK105: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X0 @ product_prod @ X1 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ X2 > X4))).
% 1.73/0.63 thf(func_def_173, type, sK106: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X0 @ product_prod @ X1 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ X2 > X0))).
% 1.73/0.63 thf(func_def_174, type, sK107: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X0 @ product_prod @ X1 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ X2 > X1))).
% 1.73/0.63 thf(func_def_175, type, sK108: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X0 @ product_prod @ X1 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ X2 > X5))).
% 1.73/0.63 thf(func_def_176, type, sK109: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X0 @ product_prod @ X1 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ X2 > X2))).
% 1.73/0.63 thf(func_def_177, type, sK110: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X0 @ product_prod @ X1 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ X2 > X6))).
% 1.73/0.63 thf(func_def_178, type, sK111: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X0 @ product_prod @ X1 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ X2 > X3))).
% 1.73/0.63 thf(func_def_179, type, sK112: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > X0))).
% 1.73/0.63 thf(func_def_180, type, sK113: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X0))).
% 1.73/0.63 thf(func_def_181, type, sK114: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X1))).
% 1.73/0.63 thf(func_def_182, type, sK115: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X1 @ product_prod @ X2 @ X0 > X1))).
% 1.73/0.63 thf(func_def_183, type, sK116: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X1 @ product_prod @ X2 @ X0 > X2))).
% 1.73/0.63 thf(func_def_184, type, sK117: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X1 @ product_prod @ X2 @ X0 > X3))).
% 1.73/0.63 thf(func_def_185, type, sK118: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X1 @ product_prod @ X2 @ X0 > X0))).
% 1.73/0.63 thf(func_def_186, type, sK119: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > option @ trm > trm > trm)).
% 1.73/0.63 thf(func_def_187, type, sK120: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > option @ trm > trm > trm)).
% 1.73/0.63 thf(func_def_188, type, sK121: (option @ trm > trm > real)).
% 1.73/0.63 thf(func_def_189, type, sK122: (trm > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > option @ trm > trm)).
% 1.73/0.63 thf(func_def_190, type, sK123: (trm > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > option @ trm > char)).
% 1.73/0.63 thf(func_def_191, type, sK124: (trm > option @ trm > variable)).
% 1.73/0.63 thf(func_def_192, type, sK125: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > option @ trm > trm > trm)).
% 1.73/0.63 thf(func_def_193, type, sK126: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > option @ trm > trm > trm)).
% 1.73/0.63 thf(func_def_194, type, sK127: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > option @ trm > trm > trm)).
% 1.73/0.63 thf(func_def_195, type, sK128: (product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > option @ trm > trm > char)).
% 1.73/0.63 thf(func_def_196, type, sK129: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > product_prod @ X1 @ X0 > (X1 > X0 > set @ X2) > X1))).
% 1.73/0.63 thf(func_def_197, type, sK130: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > product_prod @ X1 @ X0 > (X1 > X0 > set @ X2) > X0))).
% 1.73/0.63 thf(func_def_198, type, sK131: (product_prod @ variable @ option @ fml > variable)).
% 1.73/0.63 thf(func_def_199, type, sK132: (product_prod @ variable @ option @ fml > fml)).
% 1.73/0.63 thf(func_def_200, type, sK133: (product_prod @ variable @ option @ fml > variable)).
% 1.73/0.63 thf(func_def_201, type, sK134: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 1.73/0.63 thf(func_def_202, type, sK135: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 1.73/0.63 thf(func_def_203, type, sK136: (char > set @ variable > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > trm)).
% 1.73/0.63 thf(func_def_204, type, sK137: ((trm > $o) > trm)).
% 1.73/0.63 thf(func_def_205, type, sK138: ((trm > $o) > trm)).
% 1.73/0.63 thf(func_def_206, type, sK139: ((trm > $o) > trm)).
% 1.73/0.63 thf(func_def_207, type, sK140: ((trm > $o) > trm)).
% 1.73/0.63 thf(func_def_208, type, sK141: ((trm > $o) > real)).
% 1.73/0.63 thf(func_def_209, type, sK142: ((trm > $o) > trm)).
% 1.73/0.63 thf(func_def_210, type, sK143: ((trm > $o) > char)).
% 1.73/0.63 thf(func_def_211, type, sK144: ((trm > $o) > trm)).
% 1.73/0.63 thf(func_def_212, type, sK145: ((trm > $o) > char)).
% 1.73/0.63 thf(func_def_213, type, sK146: ((trm > $o) > variable)).
% 1.73/0.63 thf(func_def_214, type, sK147: ((char > option @ trm > $o) > trm)).
% 1.73/0.63 thf(func_def_215, type, sK148: ((char > option @ trm > $o) > char)).
% 1.73/0.63 thf(func_def_216, type, sK149: ((char > option @ trm > $o) > char)).
% 1.73/0.63 thf(func_def_217, type, sK150: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X1 @ product_prod @ X3 @ X0 > $o) > X1))).
% 1.73/0.63 thf(func_def_218, type, sK151: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X1 @ product_prod @ X3 @ X0 > $o) > X2))).
% 1.73/0.63 thf(func_def_219, type, sK152: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X1 @ product_prod @ X3 @ X0 > $o) > X3))).
% 1.73/0.63 thf(func_def_220, type, sK153: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X1 @ product_prod @ X3 @ X0 > $o) > X6))).
% 1.73/0.63 thf(func_def_221, type, sK154: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X1 @ product_prod @ X3 @ X0 > $o) > X4))).
% 1.73/0.63 thf(func_def_222, type, sK155: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X1 @ product_prod @ X3 @ X0 > $o) > X5))).
% 1.73/0.63 thf(func_def_223, type, sK156: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X1 @ product_prod @ X3 @ X0 > $o) > X0))).
% 1.73/0.63 thf(func_def_224, type, sK157: !>[X0: $tType]:((option @ X0 > X0))).
% 1.73/0.63 thf(func_def_225, type, sK158: (option @ trm > option @ trm > trm)).
% 1.73/0.63 thf(func_def_226, type, sK159: (product_prod @ option @ fml @ option @ fml > fml)).
% 1.73/0.63 thf(func_def_227, type, sK160: (product_prod @ option @ fml @ option @ fml > fml)).
% 1.73/0.63 thf(func_def_228, type, sK161: (product_prod @ option @ fml @ option @ fml > fml)).
% 1.73/0.63 thf(func_def_229, type, sK162: (product_prod @ option @ fml @ option @ fml > option @ fml)).
% 1.73/0.63 thf(func_def_230, type, sK163: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > (X0 > X1 > $o) > X1))).
% 1.73/0.63 thf(func_def_231, type, sK164: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > (X0 > X1 > $o) > X0))).
% 1.73/0.63 thf(func_def_232, type, sK165: ((option @ trm > option @ trm > $o) > trm)).
% 1.73/0.63 thf(func_def_233, type, sK166: ((option @ trm > option @ trm > $o) > trm)).
% 1.73/0.63 thf(func_def_234, type, sK167: ((option @ trm > option @ trm > $o) > trm)).
% 1.73/0.63 thf(func_def_235, type, sK168: ((option @ trm > option @ trm > $o) > option @ trm)).
% 1.73/0.63 thf(func_def_236, type, sK169: !>[X0: $tType, X1: $tType]:(((X1 > $o) > (X0 > X1) > (X0 > $o) > X0))).
% 1.73/0.63 thf(func_def_237, type, sK170: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > product_prod @ X1 @ X2 > (X1 > X2 > set @ X0) > X1))).
% 1.73/0.63 thf(func_def_238, type, sK171: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > product_prod @ X1 @ X2 > (X1 > X2 > set @ X0) > X2))).
% 1.73/0.63 thf(func_def_239, type, sK172: ((option @ trm > $o) > trm)).
% 1.73/0.63 thf(func_def_240, type, sK173: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > $o) > product_prod @ X1 @ X0 > (X1 > X0 > X2) > X0))).
% 1.73/0.63 thf(func_def_241, type, sK174: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > $o) > product_prod @ X1 @ X0 > (X1 > X0 > X2) > X1))).
% 1.73/0.63 thf(func_def_242, type, sK175: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X2 @ product_prod @ X0 @ product_prod @ X1 @ X3 > $o) > X2))).
% 1.73/0.63 thf(func_def_243, type, sK176: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X2 @ product_prod @ X0 @ product_prod @ X1 @ X3 > $o) > X0))).
% 1.73/0.63 thf(func_def_244, type, sK177: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X2 @ product_prod @ X0 @ product_prod @ X1 @ X3 > $o) > X1))).
% 1.73/0.63 thf(func_def_245, type, sK178: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X2 @ product_prod @ X0 @ product_prod @ X1 @ X3 > $o) > X3))).
% 1.73/0.63 thf(func_def_246, type, sK179: (product_prod @ char @ option @ trm > trm)).
% 1.73/0.63 thf(func_def_247, type, sK180: (product_prod @ char @ option @ trm > char)).
% 1.73/0.63 thf(func_def_248, type, sK181: (product_prod @ char @ option @ trm > char)).
% 1.73/0.63 thf(func_def_249, type, sK182: (product_prod @ variable @ option @ trm > trm)).
% 1.73/0.63 thf(func_def_250, type, sK183: (product_prod @ variable @ option @ trm > variable)).
% 1.73/0.63 thf(func_def_251, type, sK184: (product_prod @ variable @ option @ trm > variable)).
% 1.73/0.63 thf(func_def_252, type, sK185: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X0 @ product_prod @ X1 @ X2 > $o) > X2))).
% 1.73/0.63 thf(func_def_253, type, sK186: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X0 @ product_prod @ X1 @ X2 > $o) > X0))).
% 1.73/0.63 thf(func_def_254, type, sK187: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X0 @ product_prod @ X1 @ X2 > $o) > X1))).
% 1.73/0.63 thf(func_def_255, type, sK188: !>[X0: $tType]:(((option @ X0 > $o) > X0))).
% 1.73/0.63 thf(func_def_256, type, sK189: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > X0 > X1) > (product_prod @ X2 @ X0 > X1) > X2))).
% 1.73/0.63 thf(func_def_257, type, sK190: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > X0 > X1) > (product_prod @ X2 @ X0 > X1) > X0))).
% 1.73/0.63 thf(func_def_258, type, sK191: !>[X0: $tType, X1: $tType]:(((product_prod @ X0 @ X1 > $o) > X1))).
% 1.73/0.63 thf(func_def_259, type, sK192: !>[X0: $tType, X1: $tType]:(((product_prod @ X0 @ X1 > $o) > X0))).
% 1.73/0.63 thf(func_def_260, type, sK193: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X1 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X3 @ X2 > $o) > X3))).
% 1.73/0.63 thf(func_def_261, type, sK194: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X1 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X3 @ X2 > $o) > X2))).
% 1.73/0.63 thf(func_def_262, type, sK195: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X1 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X3 @ X2 > $o) > X1))).
% 1.73/0.63 thf(func_def_263, type, sK196: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X1 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X3 @ X2 > $o) > X0))).
% 1.73/0.63 thf(func_def_264, type, sK197: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X1 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X3 @ X2 > $o) > X4))).
% 1.73/0.63 thf(func_def_265, type, sK198: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 1.73/0.63 thf(func_def_266, type, sK199: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 1.73/0.63 thf(func_def_267, type, sK200: (option @ trm > trm)).
% 1.73/0.63 thf(func_def_268, type, sK201: (option @ trm > option @ trm > option @ trm > trm)).
% 1.73/0.63 thf(func_def_269, type, sK202: (option @ trm > option @ trm > option @ trm > trm)).
% 1.73/0.63 thf(func_def_270, type, sK203: (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)).
% 1.73/0.63 thf(func_def_271, type, sK204: (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)).
% 1.73/0.63 thf(func_def_272, type, sK205: (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))).
% 1.73/0.63 thf(func_def_273, type, sK206: (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)).
% 1.73/0.63 thf(func_def_274, type, sK207: (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)).
% 1.73/0.63 thf(func_def_275, type, sK208: (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))).
% 1.73/0.63 thf(func_def_276, type, sK209: (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)).
% 1.73/0.63 thf(func_def_277, type, sK210: (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)).
% 1.73/0.63 thf(func_def_278, type, sK211: (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)).
% 1.73/0.63 thf(func_def_279, type, sK212: (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))).
% 1.73/0.63 thf(func_def_280, type, sK213: (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)).
% 1.73/0.63 thf(func_def_281, type, sK214: (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))).
% 1.73/0.63 thf(func_def_282, type, sK215: (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)).
% 1.73/0.63 thf(func_def_283, type, sK216: (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)).
% 1.73/0.63 thf(func_def_284, type, sK217: (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)).
% 1.73/0.63 thf(func_def_285, type, sK218: (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)).
% 1.73/0.63 thf(func_def_286, type, sK219: (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))).
% 1.73/0.63 thf(func_def_287, type, sK220: (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)).
% 1.73/0.63 thf(func_def_288, type, sK221: (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)).
% 1.73/0.63 thf(func_def_289, type, sK222: (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)).
% 1.73/0.63 thf(func_def_290, type, sK223: (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))).
% 1.73/0.63 thf(func_def_291, type, sK224: (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)).
% 1.73/0.63 thf(func_def_292, type, sK225: (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))).
% 1.73/0.63 thf(func_def_293, type, sK226: (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)).
% 1.73/0.63 thf(func_def_294, type, sK227: (trm > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > option @ trm > char)).
% 1.73/0.63 thf(func_def_295, type, sK228: (trm > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > option @ trm > trm)).
% 1.73/0.63 thf(func_def_296, type, sK229: (trm > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > option @ trm > trm)).
% 1.73/0.63 thf(func_def_297, type, sK230: (trm > option @ trm > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > variable)).
% 1.73/0.63 thf(func_def_298, type, sK231: (trm > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > option @ trm > char)).
% 1.73/0.63 thf(func_def_299, type, sK232: (trm > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > option @ trm > trm)).
% 1.73/0.63 thf(func_def_300, type, sK233: (trm > set @ variable > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > option @ trm > trm)).
% 1.73/0.63 thf(func_def_301, type, sK234: (trm > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > option @ trm > trm)).
% 1.73/0.63 thf(func_def_302, type, sK235: (trm > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > set @ variable > option @ trm > trm)).
% 1.73/0.63 thf(func_def_303, type, sK236: (trm > option @ trm > set @ variable > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > real)).
% 1.73/0.63 thf(func_def_304, type, sK237: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X4 @ product_prod @ X1 @ X2 > X3))).
% 1.73/0.63 thf(func_def_305, type, sK238: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X4 @ product_prod @ X1 @ X2 > X2))).
% 1.73/0.63 thf(func_def_306, type, sK239: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X4 @ product_prod @ X1 @ X2 > X0))).
% 1.73/0.63 thf(func_def_307, type, sK240: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X4 @ product_prod @ X1 @ X2 > X4))).
% 1.73/0.63 thf(func_def_308, type, sK241: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X4 @ product_prod @ X1 @ X2 > X5))).
% 1.73/0.63 thf(func_def_309, type, sK242: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X4 @ product_prod @ X1 @ X2 > X1))).
% 1.73/0.63 thf(func_def_310, type, sK243: (product_prod @ option @ trm @ option @ trm > option @ trm)).
% 1.73/0.63 thf(func_def_311, type, sK244: (product_prod @ option @ trm @ option @ trm > trm)).
% 1.73/0.63 thf(func_def_312, type, sK245: (product_prod @ option @ trm @ option @ trm > trm)).
% 1.73/0.63 thf(func_def_313, type, sK246: (product_prod @ option @ trm @ option @ trm > trm)).
% 1.73/0.63 thf(func_def_314, type, sK247: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ X1 > (X0 > X1 > X2) > (X0 > X1 > X2) > X0))).
% 1.73/0.63 thf(func_def_315, type, sK248: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ X1 > (X0 > X1 > X2) > (X0 > X1 > X2) > X1))).
% 1.73/0.63 thf(func_def_316, type, sK249: (product_prod @ option @ game @ option @ fml > game)).
% 1.73/0.63 thf(func_def_317, type, sK250: (product_prod @ option @ game @ option @ fml > option @ fml)).
% 1.73/0.63 thf(func_def_318, type, sK251: (product_prod @ option @ game @ option @ fml > game)).
% 1.73/0.63 thf(func_def_319, type, sK252: (product_prod @ option @ game @ option @ fml > fml)).
% 1.73/0.63 thf(func_def_320, type, sK253: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X1 @ product_prod @ X0 @ X2 > X1))).
% 1.73/0.63 thf(func_def_321, type, sK254: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X1 @ product_prod @ X0 @ X2 > X0))).
% 1.73/0.63 thf(func_def_322, type, sK255: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X1 @ product_prod @ X0 @ X2 > X2))).
% 1.73/0.63 thf(func_def_323, type, sK256: (set @ variable > product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) > char > trm)).
% 1.73/0.63 thf(func_def_324, type, sK257: (option @ trm > trm)).
% 1.73/0.63 thf(func_def_325, type, sK258: !>[X0: $tType, X1: $tType]:(((option @ X0 > option @ X1 > $o) > option @ X1 > option @ X0 > X0))).
% 1.73/0.63 thf(func_def_326, type, sK259: !>[X0: $tType, X1: $tType]:(((option @ X0 > option @ X1 > $o) > option @ X1 > option @ X0 > X1))).
% 1.73/0.63 thf(func_def_327, type, sK260: !>[X0: $tType]:((set @ X0 > X0))).
% 1.73/0.63 thf(func_def_328, type, sK261: (option @ trm > trm)).
% 1.73/0.63 thf(func_def_329, type, sK262: (option @ trm > option @ trm > option @ trm > trm)).
% 1.73/0.63 thf(func_def_330, type, sK263: (option @ trm > option @ trm > option @ trm > trm)).
% 1.73/0.63 thf(func_def_331, type, sK264: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > product_prod @ X0 @ X1 > (X0 > X1 > X2 > $o) > X1))).
% 1.73/0.63 thf(func_def_332, type, sK265: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > product_prod @ X0 @ X1 > (X0 > X1 > X2 > $o) > X0))).
% 1.73/0.63 thf(func_def_333, type, sK266: (product_prod @ option @ game @ option @ game > game)).
% 1.73/0.63 thf(func_def_334, type, sK267: (product_prod @ option @ game @ option @ game > game)).
% 1.73/0.63 thf(func_def_335, type, sK268: (product_prod @ option @ game @ option @ game > game)).
% 1.73/0.63 thf(func_def_336, type, sK269: (product_prod @ option @ game @ option @ game > option @ game)).
% 1.73/0.63 thf(func_def_337, type, sK270: !>[X0: $tType]:((option @ X0 > X0))).
% 1.73/0.63 thf(func_def_338, type, sK271: !>[X0: $tType]:(((X0 > $o) > X0))).
% 1.73/0.63 thf(func_def_339, type, sK272: !>[X0: $tType]:((option @ X0 > X0))).
% 1.73/0.63 thf(func_def_340, type, sK273: (option @ trm > trm)).
% 1.73/0.63 thf(func_def_341, type, sK274: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 1.73/0.63 thf(func_def_342, type, sK275: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 1.73/0.63 thf(func_def_343, type, sK276: !>[X0: $tType]:((set @ X0 > X0))).
% 1.73/0.63 thf(func_def_344, type, sK277: !>[X0: $tType]:(((X0 > $o) > X0))).
% 1.73/0.63 thf(func_def_345, type, sK278: !>[X0: $tType]:((set @ X0 > X0))).
% 1.73/0.63 thf(func_def_346, type, sK279: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 1.73/0.63 thf(f4,axiom,(
% 1.73/0.63 (none @ trm != ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X0 : (char > option @ trm)] : ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X1 : (char > option @ trm)] : ((product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X2 : (char > option @ fml), X3 : (char > option @ game)] : (X0)))))))) @ sigma @ f))) => (((inf_inf @ set @ variable @ (static_FVT @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X0 : (char > option @ trm)] : ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X1 : (char > option @ trm)] : ((product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X2 : (char > option @ fml), X3 : (char > option @ game)] : (X0)))))))) @ sigma @ f))) @ u)) = bot_bot @ set @ variable)),
% 1.73/0.63 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_f3)).
% 1.73/0.63 thf(f5,axiom,(
% 1.73/0.63 (none @ trm != ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X0 : (char > option @ trm)] : ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X1 : (char > option @ trm)] : ((product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X2 : (char > option @ fml), X3 : (char > option @ game)] : (X0)))))))) @ sigma @ f))) => (bot_bot @ set @ variable = ((inf_inf @ set @ variable @ (static_FVT @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X0 : (char > option @ trm)] : ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X1 : (char > option @ trm)] : ((product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X2 : (char > option @ fml), X3 : (char > option @ game)] : (X0)))))))) @ sigma @ f))) @ v)))),
% 1.73/0.63 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4__092_060open_062SConst_A_092_060sigma_062_Af_A_092_060noteq_062_Aundeft_A_092_060longrightarrow_062_AFVT_A_Ithe_A_ISConst_A_092_060sigma_062_Af_J_J_A_092_060inter_062_AV_A_061_A_123_125_092_060close_062)).
% 1.73/0.63 thf(f6,axiom,(
% 1.73/0.63 ((^[X0 : product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game), X1 : set @ variable, X2 : char] : ((case_option @ option @ trm @ trm @ (some @ trm @ (const @ X2)) @ (^[X3 : trm] : ((if @ option @ trm @ (((inf_inf @ set @ variable @ (static_FVT @ X3) @ X1)) = bot_bot @ set @ variable) @ (some @ trm @ X3) @ none @ trm))) @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X4 : (char > option @ trm)] : ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X5 : (char > option @ trm)] : ((product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X6 : (char > option @ fml), X7 : (char > option @ game)] : (X4)))))))) @ X0 @ X2)))) = uSubst1138577137pconst)),
% 1.73/0.63 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_usappconst__def)).
% 1.73/0.63 thf(f8,axiom,(
% 1.73/0.63 ! [X1 : set @ variable,X0 : product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game),X2 : char] : (((uSubst95898992stappt @ X0 @ X1 @ (const @ X2))) = ((uSubst1138577137pconst @ X0 @ X1 @ X2)))),
% 1.73/0.63 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_usubstappt_Osimps_I3_J)).
% 1.73/0.63 thf(f34,axiom,(
% 1.73/0.63 ! [X1 : $tType,X0 : $tType] : ((^[X2 : X1, X3 : (X0 > X1), X4 : option @ X0] : ((if @ X1 @ (X4 = none @ X0) @ X2 @ (X3 @ (the @ X0 @ X4))))) = case_option @ X1 @ X0)),
% 1.73/0.63 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_option_Ocase__eq__if)).
% 1.73/0.63 thf(f276,conjecture,(
% 1.73/0.63 (none @ trm = ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X0 : (char > option @ trm)] : ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X1 : (char > option @ trm)] : ((product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X2 : (char > option @ fml), X3 : (char > option @ game)] : (X0)))))))) @ sigma @ f))) | (((uSubst95898992stappt @ sigma @ u @ (const @ f))) = ((uSubst1138577137pconst @ sigma @ v @ f)))),
% 1.73/0.63 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 1.73/0.63 thf(f277,negated_conjecture,(
% 1.73/0.63 ~((none @ trm = ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X0 : (char > option @ trm)] : ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X1 : (char > option @ trm)] : ((product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X2 : (char > option @ fml), X3 : (char > option @ game)] : (X0)))))))) @ sigma @ f))) | (((uSubst95898992stappt @ sigma @ u @ (const @ f))) = ((uSubst1138577137pconst @ sigma @ v @ f))))),
% 1.73/0.63 inference(negated_conjecture,[status(cth)],[f276])).
% 1.73/0.63 thf(f356,plain,(
% 1.73/0.63 ~((none @ trm = ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X0 : (char > option @ trm)] : ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X1 : (char > option @ trm)] : ((product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X2 : (char > option @ fml), X3 : (char > option @ game)] : (X0)))))))) @ sigma @ f))) | (((uSubst95898992stappt @ sigma @ u @ (const @ f))) = ((uSubst1138577137pconst @ sigma @ v @ f))))),
% 1.73/0.63 inference(rectify,[],[f277])).
% 1.73/0.63 thf(f357,plain,(
% 1.73/0.63 ~((((uSubst95898992stappt @ sigma @ u @ (const @ f))) = ((uSubst1138577137pconst @ sigma @ v @ f))) | (none @ trm = ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f))))),
% 1.73/0.63 inference(fool_elimination,[],[f356])).
% 1.73/0.63 thf(f410,plain,(
% 1.73/0.63 (none @ trm != ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X0 : (char > option @ trm)] : ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X1 : (char > option @ trm)] : ((product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X2 : (char > option @ fml), X3 : (char > option @ game)] : (X0)))))))) @ sigma @ f))) => (((inf_inf @ set @ variable @ (static_FVT @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X4 : (char > option @ trm)] : ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X5 : (char > option @ trm)] : ((product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X6 : (char > option @ fml), X7 : (char > option @ game)] : (X4)))))))) @ sigma @ f))) @ u)) = bot_bot @ set @ variable)),
% 1.73/0.63 inference(rectify,[],[f4])).
% 1.73/0.63 thf(f411,plain,(
% 1.73/0.63 (none @ trm != ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f))) => (bot_bot @ set @ variable = ((inf_inf @ set @ variable @ (static_FVT @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f))) @ u)))),
% 1.73/0.63 inference(fool_elimination,[],[f410])).
% 1.73/0.63 thf(f532,plain,(
% 1.73/0.63 (none @ trm != ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X0 : (char > option @ trm)] : ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X1 : (char > option @ trm)] : ((product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X2 : (char > option @ fml), X3 : (char > option @ game)] : (X0)))))))) @ sigma @ f))) => (bot_bot @ set @ variable = ((inf_inf @ set @ variable @ (static_FVT @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X4 : (char > option @ trm)] : ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X5 : (char > option @ trm)] : ((product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X6 : (char > option @ fml), X7 : (char > option @ game)] : (X4)))))))) @ sigma @ f))) @ v)))),
% 1.73/0.63 inference(rectify,[],[f5])).
% 1.73/0.63 thf(f533,plain,(
% 1.73/0.63 (none @ trm != ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f))) => (bot_bot @ set @ variable = ((inf_inf @ set @ variable @ (static_FVT @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f))) @ v)))),
% 1.73/0.63 inference(fool_elimination,[],[f532])).
% 1.73/0.63 thf(f593,plain,(
% 1.73/0.63 ! [X0 : $tType,X1 : $tType] : ((^[X2 : X0, X3 : (X1 > X0), X4 : option @ X1] : ((if @ X0 @ (none @ X1 = X4) @ X2 @ (X3 @ (the @ X1 @ X4))))) = case_option @ X0 @ X1)),
% 1.73/0.63 inference(rectify,[],[f34])).
% 1.73/0.63 thf(f594,plain,(
% 1.73/0.63 ! [X1 : $tType,X0 : $tType] : (case_option @ X0 @ X1 = (^[Y0 : X0]: ((^[Y1 : X1 > X0]: ((^[Y2 : option @ X1]: (if @ X0 @ (none @ X1 = Y2) @ Y0 @ (Y1 @ (the @ X1 @ Y2)))))))))),
% 1.73/0.63 inference(fool_elimination,[],[f593])).
% 1.73/0.63 thf(f607,plain,(
% 1.73/0.63 ((^[X0 : product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game), X1 : set @ variable, X2 : char] : ((case_option @ option @ trm @ trm @ (some @ trm @ (const @ X2)) @ (^[X3 : trm] : ((if @ option @ trm @ (((inf_inf @ set @ variable @ (static_FVT @ X3) @ X1)) = bot_bot @ set @ variable) @ (some @ trm @ X3) @ none @ trm))) @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X4 : (char > option @ trm)] : ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X5 : (char > option @ trm)] : ((product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[X6 : (char > option @ fml), X7 : (char > option @ game)] : (X4)))))))) @ X0 @ X2)))) = uSubst1138577137pconst)),
% 1.73/0.63 inference(rectify,[],[f6])).
% 1.73/0.63 thf(f608,plain,(
% 1.73/0.63 (uSubst1138577137pconst = (^[Y0 : product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game)]: ((^[Y1 : set @ variable]: ((^[Y2 : char]: (case_option @ option @ trm @ trm @ (some @ trm @ (const @ Y2)) @ (^[Y3 : trm]: (if @ option @ trm @ (bot_bot @ set @ variable = (inf_inf @ set @ variable @ (static_FVT @ Y3) @ Y1)) @ (some @ trm @ Y3) @ none @ trm)) @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y3 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y4 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y5 : char > option @ fml]: ((^[Y6 : char > option @ game]: (Y3)))))))) @ Y0 @ Y2))))))))),
% 1.73/0.63 inference(fool_elimination,[],[f607])).
% 1.73/0.63 thf(f642,plain,(
% 1.73/0.63 ! [X2 : char,X0 : set @ variable,X1 : product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game)] : (((uSubst1138577137pconst @ X1 @ X0 @ X2)) = ((uSubst95898992stappt @ X1 @ X0 @ (const @ X2))))),
% 1.73/0.63 inference(rectify,[],[f8])).
% 1.73/0.63 thf(f705,plain,(
% 1.73/0.63 (none @ trm = ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f))) | (bot_bot @ set @ variable = ((inf_inf @ set @ variable @ (static_FVT @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f))) @ u)))),
% 1.73/0.63 inference(ennf_transformation,[],[f411])).
% 1.73/0.63 thf(f726,plain,(
% 1.73/0.63 (none @ trm != ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f))) & (((uSubst95898992stappt @ sigma @ u @ (const @ f))) != ((uSubst1138577137pconst @ sigma @ v @ f)))),
% 1.73/0.63 inference(ennf_transformation,[],[f357])).
% 1.73/0.63 thf(f805,plain,(
% 1.73/0.63 (none @ trm = ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f))) | (bot_bot @ set @ variable = ((inf_inf @ set @ variable @ (static_FVT @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f))) @ v)))),
% 1.73/0.63 inference(ennf_transformation,[],[f533])).
% 1.73/0.63 thf(f999,plain,(
% 1.73/0.63 ! [X0 : $tType,X1 : $tType] : (case_option @ X1 @ X0 = (^[Y0 : X1]: ((^[Y1 : X0 > X1]: ((^[Y2 : option @ X0]: (if @ X1 @ (none @ X0 = Y2) @ Y0 @ (Y1 @ (the @ X0 @ Y2)))))))))),
% 1.73/0.63 inference(rectify,[],[f594])).
% 1.73/0.63 thf(f1062,plain,(
% 1.73/0.63 ! [X0 : char,X1 : set @ variable,X2 : product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game)] : (((uSubst1138577137pconst @ X2 @ X1 @ X0)) = ((uSubst95898992stappt @ X2 @ X1 @ (const @ X0))))),
% 1.73/0.63 inference(rectify,[],[f642])).
% 1.73/0.63 thf(f1248,plain,(
% 1.73/0.63 (bot_bot @ set @ variable = ((inf_inf @ set @ variable @ (static_FVT @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f))) @ v))) | (none @ trm = ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f)))),
% 1.73/0.63 inference(cnf_transformation,[],[f805])).
% 1.73/0.63 thf(f1322,plain,(
% 1.73/0.63 ( ! [X1 : $tType,X0 : $tType] : ((case_option @ X1 @ X0 = (^[Y0 : X1]: ((^[Y1 : X0 > X1]: ((^[Y2 : option @ X0]: (if @ X1 @ (none @ X0 = Y2) @ Y0 @ (Y1 @ (the @ X0 @ Y2)))))))))) )),
% 1.73/0.63 inference(cnf_transformation,[],[f999])).
% 1.73/0.63 thf(f1399,plain,(
% 1.73/0.63 (bot_bot @ set @ variable = ((inf_inf @ set @ variable @ (static_FVT @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f))) @ u))) | (none @ trm = ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f)))),
% 1.73/0.63 inference(cnf_transformation,[],[f705])).
% 1.73/0.63 thf(f1416,plain,(
% 1.73/0.63 ( ! [X2 : product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game),X0 : char,X1 : set @ variable] : ((((uSubst1138577137pconst @ X2 @ X1 @ X0)) = ((uSubst95898992stappt @ X2 @ X1 @ (const @ X0))))) )),
% 1.73/0.63 inference(cnf_transformation,[],[f1062])).
% 1.73/0.63 thf(f1477,plain,(
% 1.73/0.63 (((uSubst95898992stappt @ sigma @ u @ (const @ f))) != ((uSubst1138577137pconst @ sigma @ v @ f)))),
% 1.73/0.63 inference(cnf_transformation,[],[f726])).
% 1.73/0.63 thf(f1478,plain,(
% 1.73/0.63 (none @ trm != ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f)))),
% 1.73/0.63 inference(cnf_transformation,[],[f726])).
% 1.73/0.63 thf(f1501,plain,(
% 1.73/0.63 (uSubst1138577137pconst = (^[Y0 : product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game)]: ((^[Y1 : set @ variable]: ((^[Y2 : char]: (case_option @ option @ trm @ trm @ (some @ trm @ (const @ Y2)) @ (^[Y3 : trm]: (if @ option @ trm @ (bot_bot @ set @ variable = (inf_inf @ set @ variable @ (static_FVT @ Y3) @ Y1)) @ (some @ trm @ Y3) @ none @ trm)) @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y3 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y4 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y5 : char > option @ fml]: ((^[Y6 : char > option @ game]: (Y3)))))))) @ Y0 @ Y2))))))))),
% 1.73/0.63 inference(cnf_transformation,[],[f608])).
% 1.73/0.63 thf(f1524,plain,(
% 1.73/0.63 (uSubst1138577137pconst = (^[Y0 : product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game)]: ((^[Y1 : set @ variable]: ((^[Y2 : char]: ((^[Y3 : option @ trm]: ((^[Y4 : trm > option @ trm]: ((^[Y5 : option @ trm]: (if @ option @ trm @ (none @ trm = Y5) @ Y3 @ (Y4 @ (the @ trm @ Y5)))))))) @ (some @ trm @ (const @ Y2)) @ (^[Y3 : trm]: (if @ option @ trm @ (bot_bot @ set @ variable = (inf_inf @ set @ variable @ (static_FVT @ Y3) @ Y1)) @ (some @ trm @ Y3) @ none @ trm)) @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y3 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y4 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y5 : char > option @ fml]: ((^[Y6 : char > option @ game]: (Y3)))))))) @ Y0 @ Y2))))))))),
% 1.73/0.63 inference(definition_unfolding,[],[f1501,f1322])).
% 1.73/0.63 thf(f1549,plain,(
% 1.73/0.63 ( ! [X2 : product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game),X0 : char,X1 : set @ variable] : (((((^[Y0 : product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game)]: ((^[Y1 : set @ variable]: ((^[Y2 : char]: ((^[Y3 : option @ trm]: ((^[Y4 : trm > option @ trm]: ((^[Y5 : option @ trm]: (if @ option @ trm @ (none @ trm = Y5) @ Y3 @ (Y4 @ (the @ trm @ Y5)))))))) @ (some @ trm @ (const @ Y2)) @ (^[Y3 : trm]: (if @ option @ trm @ (bot_bot @ set @ variable = (inf_inf @ set @ variable @ (static_FVT @ Y3) @ Y1)) @ (some @ trm @ Y3) @ none @ trm)) @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y3 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y4 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y5 : char > option @ fml]: ((^[Y6 : char > option @ game]: (Y3)))))))) @ Y0 @ Y2))))))) @ X2 @ X1 @ X0)) = ((uSubst95898992stappt @ X2 @ X1 @ (const @ X0))))) )),
% 1.73/0.63 inference(definition_unfolding,[],[f1416,f1524])).
% 1.73/0.63 thf(f1556,plain,(
% 1.73/0.63 (((uSubst95898992stappt @ sigma @ u @ (const @ f))) != (((^[Y0 : product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game)]: ((^[Y1 : set @ variable]: ((^[Y2 : char]: ((^[Y3 : option @ trm]: ((^[Y4 : trm > option @ trm]: ((^[Y5 : option @ trm]: (if @ option @ trm @ (none @ trm = Y5) @ Y3 @ (Y4 @ (the @ trm @ Y5)))))))) @ (some @ trm @ (const @ Y2)) @ (^[Y3 : trm]: (if @ option @ trm @ (bot_bot @ set @ variable = (inf_inf @ set @ variable @ (static_FVT @ Y3) @ Y1)) @ (some @ trm @ Y3) @ none @ trm)) @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y3 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y4 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y5 : char > option @ fml]: ((^[Y6 : char > option @ game]: (Y3)))))))) @ Y0 @ Y2))))))) @ sigma @ v @ f)))),
% 1.73/0.63 inference(definition_unfolding,[],[f1477,f1524])).
% 1.73/0.63 thf(f1670,plain,(
% 1.73/0.63 ( ! [X2 : product_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game),X0 : char,X1 : set @ variable] : ((((uSubst95898992stappt @ X2 @ X1 @ (const @ X0))) = ((if @ option @ trm @ (none @ trm = (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ X2 @ X0)) @ (some @ trm @ (const @ X0)) @ (if @ option @ trm @ (bot_bot @ set @ variable = (inf_inf @ set @ variable @ (static_FVT @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ X2 @ X0))) @ X1)) @ (some @ trm @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ X2 @ X0))) @ none @ trm))))) )),
% 1.73/0.63 inference(beta-eta_normalization,[],[f1549])).
% 1.73/0.63 thf(f1692,plain,(
% 1.73/0.63 (((uSubst95898992stappt @ sigma @ u @ (const @ f))) != ((if @ option @ trm @ (none @ trm = (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f)) @ (some @ trm @ (const @ f)) @ (if @ option @ trm @ (bot_bot @ set @ variable = (inf_inf @ set @ variable @ (static_FVT @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f))) @ v)) @ (some @ trm @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f))) @ none @ trm))))),
% 1.73/0.63 inference(beta-eta_normalization,[],[f1556])).
% 1.73/0.63 thf(f1983,definition,(
% 1.73/0.63 spl280_1 <=> (none @ trm = ((product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f)))),
% 1.73/0.63 introduced(definition,[new_symbols(definition,[spl280_1])],[avatar_definition])).
% 1.73/0.63 thf(f1987,definition,(
% 1.73/0.63 spl280_2 <=> (bot_bot @ set @ variable = ((inf_inf @ set @ variable @ (static_FVT @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f))) @ u)))),
% 1.73/0.63 introduced(definition,[new_symbols(definition,[spl280_2])],[avatar_definition])).
% 1.73/0.63 thf(f1988,plain,(
% 1.73/0.63 (bot_bot @ set @ variable = ((inf_inf @ set @ variable @ (static_FVT @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f))) @ u))) | ~spl280_2),
% 1.73/0.63 inference(avatar_component_clause,[],[f1987])).
% 1.73/0.63 thf(f1996,definition,(
% 1.73/0.63 spl280_4 <=> (bot_bot @ set @ variable = ((inf_inf @ set @ variable @ (static_FVT @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f))) @ v)))),
% 1.73/0.63 introduced(definition,[new_symbols(definition,[spl280_4])],[avatar_definition])).
% 1.73/0.63 thf(f1997,plain,(
% 1.73/0.63 (bot_bot @ set @ variable = ((inf_inf @ set @ variable @ (static_FVT @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f))) @ v))) | ~spl280_4),
% 1.73/0.63 inference(avatar_component_clause,[],[f1996])).
% 1.73/0.63 thf(f2009,plain,(
% 1.73/0.63 spl280_1 | spl280_2),
% 1.73/0.63 inference(avatar_split_clause,[],[f1399,f1987,f1983])).
% 1.73/0.63 thf(f2015,plain,(
% 1.73/0.63 spl280_4 | spl280_1),
% 1.73/0.63 inference(avatar_split_clause,[],[f1248,f1983,f1996])).
% 1.73/0.63 thf(f2016,plain,(
% 1.73/0.63 ~spl280_1),
% 1.73/0.63 inference(avatar_split_clause,[],[f1478,f1983])).
% 1.73/0.63 thf(f2033,definition,(
% 1.73/0.63 spl280_8 <=> (((uSubst95898992stappt @ sigma @ u @ (const @ f))) = ((if @ option @ trm @ (none @ trm = (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f)) @ (some @ trm @ (const @ f)) @ (if @ option @ trm @ $true @ (some @ trm @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f))) @ none @ trm))))),
% 1.73/0.63 introduced(definition,[new_symbols(definition,[spl280_8])],[avatar_definition])).
% 1.73/0.63 thf(f2285,plain,(
% 1.73/0.63 (((uSubst95898992stappt @ sigma @ u @ (const @ f))) != ((if @ option @ trm @ (none @ trm = (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f)) @ (some @ trm @ (const @ f)) @ (if @ option @ trm @ (bot_bot @ set @ variable = bot_bot @ set @ variable) @ (some @ trm @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f))) @ none @ trm)))) | ~spl280_4),
% 1.73/0.63 inference(superposition,[],[f1692,f1997])).
% 1.73/0.63 thf(f2286,plain,(
% 1.73/0.63 (((uSubst95898992stappt @ sigma @ u @ (const @ f))) != ((if @ option @ trm @ (none @ trm = (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f)) @ (some @ trm @ (const @ f)) @ (if @ option @ trm @ $true @ (some @ trm @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f))) @ none @ trm)))) | ~spl280_4),
% 1.73/0.63 inference(boolean_simplification,[],[f2285])).
% 1.73/0.63 thf(f2287,plain,(
% 1.73/0.63 ~spl280_8 | ~spl280_4),
% 1.73/0.63 inference(avatar_split_clause,[],[f2286,f1996,f2033])).
% 1.73/0.63 thf(f2328,plain,(
% 1.73/0.63 (((uSubst95898992stappt @ sigma @ u @ (const @ f))) = ((if @ option @ trm @ (none @ trm = (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f)) @ (some @ trm @ (const @ f)) @ (if @ option @ trm @ (bot_bot @ set @ variable = bot_bot @ set @ variable) @ (some @ trm @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f))) @ none @ trm)))) | ~spl280_2),
% 1.73/0.63 inference(superposition,[],[f1670,f1988])).
% 1.73/0.63 thf(f2338,plain,(
% 1.73/0.63 (((uSubst95898992stappt @ sigma @ u @ (const @ f))) = ((if @ option @ trm @ (none @ trm = (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f)) @ (some @ trm @ (const @ f)) @ (if @ option @ trm @ $true @ (some @ trm @ (the @ trm @ (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y0 : char > option @ trm]: (product_case_prod @ (char > option @ trm) @ product_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y1 : char > option @ trm]: (product_case_prod @ (char > option @ fml) @ (char > option @ game) @ (char > option @ trm) @ (^[Y2 : char > option @ fml]: ((^[Y3 : char > option @ game]: (Y0)))))))) @ sigma @ f))) @ none @ trm)))) | ~spl280_2),
% 1.73/0.63 inference(boolean_simplification,[],[f2328])).
% 1.73/0.63 thf(f2340,plain,(
% 1.73/0.63 spl280_8 | ~spl280_2),
% 1.73/0.63 inference(avatar_split_clause,[],[f2338,f1987,f2033])).
% 1.73/0.63 cnf(s4, plain, spl280_1 | spl280_2, inference(sat_conversion,[],[f2009])).
% 1.73/0.63 cnf(s6, plain, spl280_1 | spl280_4, inference(sat_conversion,[],[f2015])).
% 1.73/0.63 cnf(s7, plain, ~spl280_1, inference(sat_conversion,[],[f2016])).
% 1.73/0.63 cnf(s10, plain, ~spl280_4 | ~spl280_8, inference(sat_conversion,[],[f2287])).
% 1.73/0.63 cnf(s15, plain, ~spl280_2 | spl280_8, inference(sat_conversion,[],[f2340])).
% 1.73/0.63 cnf(s17, plain, spl280_4, inference(rat,[],[s6,s7])).
% 1.73/0.63 cnf(s18, plain, ~spl280_8, inference(rat,[],[s10,s17])).
% 1.73/0.63 cnf(s19, plain, ~spl280_2, inference(rat,[],[s15,s18])).
% 1.73/0.63 cnf(s20, plain, $false, inference(rat,[],[s4,s19,s7])).
% 1.73/0.63 thf(f2341,plain,(
% 1.73/0.63 $false),
% 1.73/0.63 inference(avatar_sat_refutation,[],[s20])).
% 1.73/0.63 % SZS output end Proof for theBenchmark
% 1.73/0.63 % (852809)------------------------------
% 1.73/0.63 % (852809)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.73/0.63 % (852809)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.73/0.63 % (852809)CaDiCaL version: 2.1.3
% 1.73/0.63 % (852809)Termination reason: Refutation
% 1.73/0.63 % (852809)Time elapsed: 0.145 s
% 1.73/0.63 % (852809)Peak memory usage: 15 MB
% 1.73/0.63 % (852809)Instructions burned: 300 (million)
% 1.73/0.63 % (852767)Success in time 0.311 s
% 1.73/0.63 % Vampire exiting
%------------------------------------------------------------------------------