%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP178^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 08:08:41 AM UTC 2026
% Result : Theorem 0.29s 0.47s
% Output : Refutation 0.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP178^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n014.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 20:06:30 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.21/0.30 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.29/0.47 % (3151502)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.29/0.47 % (3151510)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=3186532044: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)
% 0.29/0.47 % (3151508)lrs+10_16_si=on:nwc=1.5:random_seed=3262055062:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.29/0.47 % (3151507)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3605445872:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.29/0.47 % (3151509)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=785900409:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.29/0.47 % (3151511)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1382666984:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.29/0.47 % (3151509)Instruction limit reached!
% 0.29/0.47 % (3151509)------------------------------
% 0.29/0.47 % (3151509)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.29/0.47 % (3151509)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.29/0.47 % (3151509)CaDiCaL version: 2.1.3
% 0.29/0.47 % (3151509)Termination reason: Instruction limit
% 0.29/0.47 % (3151509)Termination phase: shuffling
% 0.29/0.47 % (3151509)Time elapsed: 0.003 s
% 0.29/0.47 % (3151509)Peak memory usage: 10 MB
% 0.29/0.47 % (3151509)Instructions burned: 5 (million)
% 0.29/0.47 % (3151508)Instruction limit reached!
% 0.29/0.47 % (3151508)------------------------------
% 0.29/0.47 % (3151508)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.29/0.47 % (3151508)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.29/0.47 % (3151508)CaDiCaL version: 2.1.3
% 0.29/0.47 % (3151508)Termination reason: Instruction limit
% 0.29/0.47 % (3151508)Termination phase: shuffling
% 0.29/0.47 % (3151508)Time elapsed: 0.009 s
% 0.29/0.47 % (3151508)Peak memory usage: 10 MB
% 0.29/0.47 % (3151508)Instructions burned: 19 (million)
% 0.29/0.47 % (3151513)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.29/0.47 % (3151513)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
% 0.29/0.47 % (3151511)Instruction limit reached!
% 0.29/0.47 % (3151511)------------------------------
% 0.29/0.47 % (3151511)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.29/0.47 % (3151511)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.29/0.47 % (3151511)CaDiCaL version: 2.1.3
% 0.29/0.47 % (3151511)Termination reason: Instruction limit
% 0.29/0.47 % (3151511)Termination phase: shuffling
% 0.29/0.47 % (3151511)Time elapsed: 0.012 s
% 0.29/0.47 % (3151511)Peak memory usage: 10 MB
% 0.29/0.47 % (3151511)Instructions burned: 26 (million)
% 0.29/0.47 % (3151512)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2558150501:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.29/0.47 % (3151513)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=2511231925:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.29/0.47 % (3151519)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1655371142:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.29/0.47 % (3151519)Instruction limit reached!
% 0.29/0.47 % (3151519)------------------------------
% 0.29/0.47 % (3151519)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.29/0.47 % (3151519)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.29/0.47 % (3151519)CaDiCaL version: 2.1.3
% 0.29/0.47 % (3151519)Termination reason: Instruction limit
% 0.29/0.47 % (3151519)Termination phase: shuffling
% 0.29/0.47 % (3151519)Time elapsed: 0.002 s
% 0.29/0.47 % (3151519)Peak memory usage: 10 MB
% 0.29/0.47 % (3151519)Instructions burned: 2 (million)
% 0.29/0.47 % (3151523)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.29/0.47 % (3151520)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=4020697010:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.29/0.47 % (3151523)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3644775447:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.29/0.47 % (3151520)Instruction limit reached!
% 0.29/0.47 % (3151520)------------------------------
% 0.29/0.47 % (3151520)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.29/0.47 % (3151520)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.29/0.47 % (3151520)CaDiCaL version: 2.1.3
% 0.29/0.47 % (3151520)Termination reason: Instruction limit
% 0.29/0.47 % (3151520)Termination phase: shuffling
% 0.29/0.47 % (3151520)Time elapsed: 0.004 s
% 0.29/0.47 % (3151520)Peak memory usage: 10 MB
% 0.29/0.47 % (3151520)Instructions burned: 6 (million)
% 0.29/0.47 % (3151523)Instruction limit reached!
% 0.29/0.47 % (3151523)------------------------------
% 0.29/0.47 % (3151523)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.29/0.47 % (3151523)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.29/0.47 % (3151523)CaDiCaL version: 2.1.3
% 0.29/0.47 % (3151523)Termination reason: Instruction limit
% 0.29/0.47 % (3151523)Termination phase: shuffling
% 0.29/0.47 % (3151523)Time elapsed: 0.005 s
% 0.29/0.47 % (3151523)Peak memory usage: 10 MB
% 0.29/0.47 % (3151523)Instructions burned: 9 (million)
% 0.29/0.47 % (3151507)Instruction limit reached!
% 0.29/0.47 % (3151507)------------------------------
% 0.29/0.47 % (3151507)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.29/0.47 % (3151507)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.29/0.47 % (3151507)CaDiCaL version: 2.1.3
% 0.29/0.47 % (3151507)Termination reason: Instruction limit
% 0.29/0.47 % (3151507)Termination phase: Preprocessing 3
% 0.29/0.47 % (3151507)Time elapsed: 0.043 s
% 0.29/0.47 % (3151507)Peak memory usage: 12 MB
% 0.29/0.47 % (3151507)Instructions burned: 88 (million)
% 0.29/0.47 % (3151512)Instruction limit reached!
% 0.29/0.47 % (3151512)------------------------------
% 0.29/0.47 % (3151512)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.29/0.47 % (3151512)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.29/0.47 % (3151512)CaDiCaL version: 2.1.3
% 0.29/0.47 % (3151512)Termination reason: Instruction limit
% 0.29/0.47 % (3151512)Termination phase: Preprocessing 3
% 0.29/0.47 % (3151512)Time elapsed: 0.037 s
% 0.29/0.47 % (3151512)Peak memory usage: 12 MB
% 0.29/0.47 % (3151512)Instructions burned: 77 (million)
% 0.29/0.47 % (3151528)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
% 0.29/0.47 % (3151528)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.29/0.47 % (3151525)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2158295108:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.29/0.47 % (3151528)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1706236265:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.29/0.47 % (3151525)Instruction limit reached!
% 0.29/0.47 % (3151525)------------------------------
% 0.29/0.47 % (3151525)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.29/0.47 % (3151525)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.29/0.47 % (3151525)CaDiCaL version: 2.1.3
% 0.29/0.47 % (3151525)Termination reason: Instruction limit
% 0.29/0.47 % (3151525)Termination phase: shuffling
% 0.29/0.47 % (3151525)Time elapsed: 0.007 s
% 0.29/0.47 % (3151525)Peak memory usage: 10 MB
% 0.29/0.47 % (3151525)Instructions burned: 12 (million)
% 0.29/0.47 % (3151530)lrs+10_1_si=on:cs=on:random_seed=1327855304:i=8:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/8Mi)
% 0.29/0.47 % (3151529)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=2076706337:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.29/0.47 % (3151531)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.29/0.47 % (3151530)Instruction limit reached!
% 0.29/0.47 % (3151530)------------------------------
% 0.29/0.47 % (3151530)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.29/0.47 % (3151530)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.29/0.47 % (3151530)CaDiCaL version: 2.1.3
% 0.29/0.47 % (3151530)Termination reason: Instruction limit
% 0.29/0.47 % (3151530)Termination phase: shuffling
% 0.29/0.47 % (3151530)Time elapsed: 0.005 s
% 0.29/0.47 % (3151530)Peak memory usage: 10 MB
% 0.29/0.47 % (3151530)Instructions burned: 9 (million)
% 0.29/0.47 % (3151528)Instruction limit reached!
% 0.29/0.47 % (3151528)------------------------------
% 0.29/0.47 % (3151528)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.29/0.47 % (3151528)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.29/0.47 % (3151528)CaDiCaL version: 2.1.3
% 0.29/0.47 % (3151528)Termination reason: Instruction limit
% 0.29/0.47 % (3151528)Termination phase: shuffling
% 0.29/0.47 % (3151528)Time elapsed: 0.014 s
% 0.29/0.47 % (3151528)Peak memory usage: 10 MB
% 0.29/0.47 % (3151528)Instructions burned: 29 (million)
% 0.29/0.47 % (3151531)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=3684549276:i=2:add=on:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 0.29/0.47 % (3151531)Instruction limit reached!
% 0.29/0.47 % (3151531)------------------------------
% 0.29/0.47 % (3151531)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.29/0.47 % (3151531)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.29/0.47 % (3151531)CaDiCaL version: 2.1.3
% 0.29/0.47 % (3151531)Termination reason: Instruction limit
% 0.29/0.47 % (3151531)Termination phase: shuffling
% 0.29/0.47 % (3151531)Time elapsed: 0.002 s
% 0.29/0.47 % (3151531)Peak memory usage: 10 MB
% 0.29/0.47 % (3151531)Instructions burned: 2 (million)
% 0.29/0.47 % (3151534)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1081756341:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 0.29/0.47 % (3151537)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=3181835977:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.29/0.47 % (3151513)Instruction limit reached!
% 0.29/0.47 % (3151513)------------------------------
% 0.29/0.47 % (3151513)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.29/0.47 % (3151513)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.29/0.47 % (3151513)CaDiCaL version: 2.1.3
% 0.29/0.47 % (3151513)Termination reason: Instruction limit
% 0.29/0.47 % (3151513)Termination phase: Property scanning
% 0.29/0.47 % (3151513)Time elapsed: 0.075 s
% 0.29/0.47 % (3151513)Peak memory usage: 13 MB
% 0.29/0.47 % (3151513)Instructions burned: 158 (million)
% 0.29/0.47 % (3151539)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=1246685127:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.29/0.47 % (3151540)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=419591972:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.29/0.47 % (3151510) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3151502-3151510"...
% 0.29/0.47 % (3151540)Instruction limit reached!
% 0.29/0.47 % (3151540)------------------------------
% 0.29/0.47 % (3151540)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.29/0.47 % (3151540)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.29/0.47 % (3151540)CaDiCaL version: 2.1.3
% 0.29/0.47 % (3151540)Termination reason: Instruction limit
% 0.29/0.47 % (3151540)Termination phase: shuffling
% 0.29/0.47 % (3151540)Time elapsed: 0.007 s
% 0.29/0.47 % (3151540)Peak memory usage: 10 MB
% 0.29/0.47 % (3151540)Instructions burned: 14 (million)
% 0.29/0.47 % (3151510)...printing done.
% 0.29/0.47 % (3151534)Instruction limit reached!
% 0.29/0.47 % (3151534)------------------------------
% 0.29/0.47 % (3151534)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.29/0.47 % (3151534)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.29/0.47 % (3151534)CaDiCaL version: 2.1.3
% 0.29/0.47 % (3151534)Termination reason: Instruction limit
% 0.29/0.47 % (3151534)Termination phase: Property scanning
% 0.29/0.47 % (3151534)Time elapsed: 0.019 s
% 0.29/0.47 % (3151534)Peak memory usage: 11 MB
% 0.29/0.47 % (3151534)Instructions burned: 39 (million)
% 0.29/0.47 % (3151510)Refutation found. Thanks to Tanya!
% 0.29/0.47 % SZS status Theorem for theBenchmark
% 0.29/0.47 % SZS output start Proof for theBenchmark
% 0.29/0.47 thf(type_def_5, type, standard_Constant: $tType > $tType).
% 0.29/0.47 thf(type_def_6, type, allegorical_term: $tType > $tType).
% 0.29/0.47 thf(type_def_7, type, labeled_graph: ($tType * $tType) > $tType).
% 0.29/0.47 thf(type_def_8, type, product_prod: ($tType * $tType) > $tType).
% 0.29/0.47 thf(type_def_9, type, set: $tType > $tType).
% 0.29/0.47 thf(type_def_10, type, nat: $tType).
% 0.29/0.47 thf(type_def_11, type, itself: $tType > $tType).
% 0.29/0.47 thf(type_def_12, type, b: $tType).
% 0.29/0.47 thf(type_def_13, type, a: $tType).
% 0.29/0.47 thf(type_def_14, type, sTfun: ($tType * $tType) > $tType).
% 0.29/0.47 thf(func_def_0, type, type: !>[X0: $tType]:($o)).
% 0.29/0.47 thf(func_def_1, type, ord: !>[X0: $tType]:($o)).
% 0.29/0.47 thf(func_def_2, type, order: !>[X0: $tType]:($o)).
% 0.29/0.47 thf(func_def_3, type, finite_finite: !>[X0: $tType]:($o)).
% 0.29/0.47 thf(func_def_4, type, linorder: !>[X0: $tType]:($o)).
% 0.29/0.47 thf(func_def_5, type, preorder: !>[X0: $tType]:($o)).
% 0.29/0.47 thf(func_def_6, type, order_bot: !>[X0: $tType]:($o)).
% 0.29/0.47 thf(func_def_7, type, finite_finite2: !>[X0: $tType]:((set @ X0 > $o))).
% 0.29/0.47 thf(func_def_8, type, allegorical_A_Int: !>[X0: $tType]:((allegorical_term @ X0 > allegorical_term @ X0 > allegorical_term @ X0))).
% 0.29/0.47 thf(func_def_9, type, semantics: !>[X0: $tType, X1: $tType]:((labeled_graph @ X0 @ X1 > allegorical_term @ X0 > set @ product_prod @ X1 @ X1))).
% 0.29/0.47 thf(func_def_10, type, graph_homomorphism: !>[X0: $tType, X1: $tType, X2: $tType]:((labeled_graph @ X0 @ X1 > labeled_graph @ X0 @ X2 > set @ product_prod @ X1 @ X2 > $o))).
% 0.29/0.47 thf(func_def_11, type, graph_union: !>[X0: $tType, X1: $tType]:((labeled_graph @ X0 @ X1 > labeled_graph @ X0 @ X1 > labeled_graph @ X0 @ X1))).
% 0.29/0.47 thf(func_def_12, type, labeled_LG: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ product_prod @ X1 @ X1 > set @ X1 > labeled_graph @ X0 @ X1))).
% 0.29/0.47 thf(func_def_13, type, labele1974067554_graph: !>[X0: $tType, X1: $tType, X2: $tType]:(((set @ product_prod @ X0 @ product_prod @ X1 @ X1 > set @ X1 > X2) > labeled_graph @ X0 @ X1 > X2))).
% 0.29/0.47 thf(func_def_14, type, labeled_edges: !>[X0: $tType, X1: $tType]:((labeled_graph @ X0 @ X1 > set @ product_prod @ X0 @ product_prod @ X1 @ X1))).
% 0.29/0.47 thf(func_def_15, type, labeled_vertices: !>[X0: $tType, X1: $tType]:((labeled_graph @ X0 @ X1 > set @ X1))).
% 0.29/0.47 thf(func_def_16, type, restrict: !>[X0: $tType, X1: $tType]:((labeled_graph @ X0 @ X1 > labeled_graph @ X0 @ X1))).
% 0.29/0.47 thf(func_def_17, type, univalent: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X1 > $o))).
% 0.29/0.47 thf(func_def_18, type, bot_bot: !>[X0: $tType]:(X0)).
% 0.29/0.47 thf(func_def_19, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.29/0.47 thf(func_def_20, type, product_Pair: !>[X0: $tType, X1: $tType]:((X0 > X1 > product_prod @ X0 @ X1))).
% 0.29/0.47 thf(func_def_21, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 0.29/0.47 thf(func_def_22, type, product_fst: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 0.29/0.47 thf(func_def_23, type, product_snd: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 0.29/0.47 thf(func_def_24, type, domain: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X1 > set @ X0))).
% 0.29/0.47 thf(func_def_25, type, id_on: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0))).
% 0.29/0.47 thf(func_def_26, type, image: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X1 > set @ X0 > set @ X1))).
% 0.29/0.47 thf(func_def_27, type, relcomp: !>[X0: $tType, X1: $tType, X2: $tType]:((set @ product_prod @ X0 @ X1 > set @ product_prod @ X1 @ X2 > set @ product_prod @ X0 @ X2))).
% 0.29/0.47 thf(func_def_28, type, inv_translation: (set @ nat > $o)).
% 0.29/0.47 thf(func_def_29, type, translation: !>[X0: $tType]:((allegorical_term @ X0 > labeled_graph @ X0 @ nat))).
% 0.29/0.47 thf(func_def_30, type, agree_on: !>[X0: $tType, X1: $tType, X2: $tType]:((labeled_graph @ X0 @ X1 > set @ product_prod @ X1 @ X2 > set @ product_prod @ X1 @ X2 > $o))).
% 0.29/0.47 thf(func_def_31, type, chain: !>[X0: $tType, X1: $tType]:(((nat > labeled_graph @ X0 @ X1) > $o))).
% 0.29/0.47 thf(func_def_32, type, chain_sup: !>[X0: $tType, X1: $tType]:(((nat > labeled_graph @ X0 @ X1) > labeled_graph @ X0 @ X1))).
% 0.29/0.47 thf(func_def_33, type, consequence_graph: !>[X0: $tType, X1: $tType, X2: $tType]:((set @ product_prod @ labeled_graph @ X0 @ X1 @ labeled_graph @ X0 @ X1 > labeled_graph @ X0 @ X2 > $o))).
% 0.29/0.47 thf(func_def_34, type, extensible: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ labeled_graph @ X0 @ X1 @ labeled_graph @ X0 @ X1 > labeled_graph @ X0 @ X2 > set @ product_prod @ X1 @ X2 > $o))).
% 0.29/0.47 thf(func_def_35, type, fair_chain: !>[X0: $tType, X1: $tType, X2: $tType]:((set @ product_prod @ labeled_graph @ X0 @ X1 @ labeled_graph @ X0 @ X1 > (nat > labeled_graph @ X0 @ X2) > $o))).
% 0.29/0.47 thf(func_def_36, type, fin_maintained: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ labeled_graph @ X0 @ X1 @ labeled_graph @ X0 @ X1 > labeled_graph @ X0 @ X2 > $o))).
% 0.29/0.47 thf(func_def_37, type, least: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((itself @ X0 > set @ product_prod @ labeled_graph @ X1 @ X2 @ labeled_graph @ X1 @ X2 > labeled_graph @ X1 @ X3 > labeled_graph @ X1 @ X3 > $o))).
% 0.29/0.47 thf(func_def_38, type, least_559130134_graph: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((itself @ X0 > set @ product_prod @ labeled_graph @ X1 @ X2 @ labeled_graph @ X1 @ X2 > labeled_graph @ X1 @ X3 > labeled_graph @ X1 @ X3 > $o))).
% 0.29/0.47 thf(func_def_39, type, maintained: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ labeled_graph @ X0 @ X1 @ labeled_graph @ X0 @ X1 > labeled_graph @ X0 @ X2 > $o))).
% 0.29/0.47 thf(func_def_40, type, pushout_step: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((itself @ X0 > product_prod @ labeled_graph @ X1 @ X2 @ labeled_graph @ X1 @ X2 > labeled_graph @ X1 @ X3 > labeled_graph @ X1 @ X3 > $o))).
% 0.29/0.47 thf(func_def_41, type, set_of_graph_rules: !>[X0: $tType, X1: $tType]:((set @ product_prod @ labeled_graph @ X0 @ X1 @ labeled_graph @ X0 @ X1 > $o))).
% 0.29/0.47 thf(func_def_42, type, weak_universal: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((itself @ X0 > product_prod @ labeled_graph @ X1 @ X2 @ labeled_graph @ X1 @ X2 > labeled_graph @ X1 @ X3 > labeled_graph @ X1 @ X3 > set @ product_prod @ X2 @ X3 > set @ product_prod @ X2 @ X3 > $o))).
% 0.29/0.47 thf(func_def_43, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.29/0.47 thf(func_def_44, type, standa1138209853_rules: !>[X0: $tType]:((set @ X0 > set @ product_prod @ labeled_graph @ standard_Constant @ X0 @ nat @ labeled_graph @ standard_Constant @ X0 @ nat))).
% 0.29/0.47 thf(func_def_45, type, standa2002409347_rules: !>[X0: $tType]:((set @ standard_Constant @ X0 > set @ product_prod @ labeled_graph @ standard_Constant @ X0 @ nat @ labeled_graph @ standard_Constant @ X0 @ nat))).
% 0.29/0.47 thf(func_def_46, type, standa244753842y_rule: !>[X0: $tType]:(product_prod @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat)).
% 0.29/0.47 thf(func_def_47, type, standa245363227y_rule: !>[X0: $tType]:((X0 > product_prod @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat))).
% 0.29/0.47 thf(func_def_48, type, standa400804411p_rule: !>[X0: $tType]:((X0 > product_prod @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat))).
% 0.29/0.47 thf(func_def_49, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.29/0.47 thf(func_def_50, type, c: set @ a).
% 0.29/0.47 thf(func_def_51, type, u: allegorical_term @ b).
% 0.29/0.47 thf(func_def_52, type, v: allegorical_term @ b).
% 0.29/0.47 thf(func_def_53, type, x: product_prod @ labeled_graph @ standard_Constant @ a @ nat @ labeled_graph @ standard_Constant @ a @ nat).
% 0.29/0.47 thf(func_def_57, type, db0: !>[X0: $tType]:(X0)).
% 0.29/0.47 thf(func_def_58, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.29/0.47 thf(func_def_59, type, vAND: ($o > $o > $o)).
% 0.29/0.47 thf(func_def_60, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.29/0.47 thf(func_def_61, type, db5: !>[X0: $tType]:(X0)).
% 0.29/0.47 thf(func_def_62, type, db4: !>[X0: $tType]:(X0)).
% 0.29/0.47 thf(func_def_63, type, db3: !>[X0: $tType]:(X0)).
% 0.29/0.47 thf(func_def_64, type, db2: !>[X0: $tType]:(X0)).
% 0.29/0.47 thf(func_def_65, type, db1: !>[X0: $tType]:(X0)).
% 0.29/0.47 thf(func_def_66, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.29/0.47 thf(func_def_67, type, vIMP: ($o > $o > $o)).
% 0.29/0.47 thf(func_def_68, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.29/0.47 thf(func_def_69, type, db6: !>[X0: $tType]:(X0)).
% 0.29/0.47 thf(func_def_70, type, db7: !>[X0: $tType]:(X0)).
% 0.29/0.47 thf(func_def_71, type, sP0: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.29/0.47 thf(func_def_72, type, sP1: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.29/0.47 thf(func_def_73, type, sK2: !>[X0: $tType, X1: $tType]:((X0 > set @ product_prod @ X0 @ X1 > X1))).
% 0.29/0.47 thf(func_def_74, type, sK3: !>[X0: $tType, X1: $tType, X2: $tType]:((set @ X0 > set @ product_prod @ X0 @ X2 > (nat > labeled_graph @ X1 @ X2) > nat))).
% 0.29/0.47 thf(func_def_75, type, sK4: !>[X0: $tType, X1: $tType, X2: $tType]:(((nat > labeled_graph @ X1 @ X0) > set @ product_prod @ X2 @ X0 > set @ product_prod @ X1 @ product_prod @ X2 @ X2 > set @ X2 > nat))).
% 0.29/0.47 thf(func_def_76, type, sK5: !>[X0: $tType, X1: $tType, X2: $tType]:((set @ product_prod @ X2 @ X0 > set @ product_prod @ X1 @ X2 > X0 > X1 > X2))).
% 0.29/0.47 thf(func_def_77, type, sK6: !>[X0: $tType]:((set @ X0 > X0))).
% 0.29/0.47 thf(func_def_78, type, sK7: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X2 > $o) > set @ product_prod @ X1 @ X2 > set @ product_prod @ X0 @ X1 > X1))).
% 0.29/0.47 thf(func_def_79, type, sK8: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X2 > $o) > set @ product_prod @ X1 @ X2 > set @ product_prod @ X0 @ X1 > X0))).
% 0.29/0.47 thf(func_def_80, type, sK9: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X2 > $o) > set @ product_prod @ X1 @ X2 > set @ product_prod @ X0 @ X1 > X2))).
% 0.29/0.47 thf(func_def_81, type, sK10: !>[X0: $tType, X1: $tType, X2: $tType]:((set @ product_prod @ X1 @ X0 > labeled_graph @ X2 @ X0 > labeled_graph @ X2 @ X1 > set @ product_prod @ X1 @ X0))).
% 0.29/0.47 thf(func_def_82, type, sK11: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > X0))).
% 0.29/0.47 thf(func_def_83, type, sK12: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.29/0.47 thf(func_def_84, type, sK13: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.29/0.47 thf(func_def_85, type, sK14: !>[X0: $tType, X1: $tType]:((X1 > product_prod @ X1 @ X0 > X0))).
% 0.29/0.47 thf(func_def_86, type, sK15: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.29/0.47 thf(func_def_87, type, sK16: !>[X0: $tType, X1: $tType]:(((product_prod @ X0 @ X1 > $o) > X1))).
% 0.29/0.47 thf(func_def_88, type, sK17: !>[X0: $tType, X1: $tType]:(((product_prod @ X0 @ X1 > $o) > X0))).
% 0.29/0.47 thf(func_def_89, type, sK18: !>[X0: $tType, X1: $tType, X2: $tType]:((labeled_graph @ X1 @ X2 > product_prod @ labeled_graph @ X1 @ X0 @ labeled_graph @ X1 @ X0 > set @ product_prod @ X0 @ X2))).
% 0.29/0.47 thf(func_def_90, type, sK19: !>[X0: $tType, X1: $tType, X2: $tType]:((labeled_graph @ X1 @ X2 > product_prod @ labeled_graph @ X1 @ X0 @ labeled_graph @ X1 @ X0 > labeled_graph @ X1 @ X0))).
% 0.29/0.47 thf(func_def_91, type, sK20: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.29/0.47 thf(func_def_92, type, sK21: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.29/0.47 thf(func_def_93, type, sK22: !>[X0: $tType, X1: $tType, X2: $tType]:((set @ product_prod @ labeled_graph @ X2 @ X1 @ labeled_graph @ X2 @ X1 > labeled_graph @ X2 @ X0 > product_prod @ labeled_graph @ X2 @ X1 @ labeled_graph @ X2 @ X1))).
% 0.29/0.47 thf(func_def_94, type, sK23: !>[X0: $tType, X1: $tType]:((set @ product_prod @ labeled_graph @ X1 @ X0 @ labeled_graph @ X1 @ X0 > product_prod @ labeled_graph @ X1 @ X0 @ labeled_graph @ X1 @ X0))).
% 0.29/0.47 thf(func_def_95, type, sK24: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X1 @ product_prod @ X4 @ product_prod @ X5 @ product_prod @ X0 @ product_prod @ X3 @ X2 > $o) > X4))).
% 0.29/0.47 thf(func_def_96, type, sK25: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X1 @ product_prod @ X4 @ product_prod @ X5 @ product_prod @ X0 @ product_prod @ X3 @ X2 > $o) > X3))).
% 0.29/0.47 thf(func_def_97, type, sK26: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X1 @ product_prod @ X4 @ product_prod @ X5 @ product_prod @ X0 @ product_prod @ X3 @ X2 > $o) > X2))).
% 0.29/0.47 thf(func_def_98, type, sK27: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X1 @ product_prod @ X4 @ product_prod @ X5 @ product_prod @ X0 @ product_prod @ X3 @ X2 > $o) > X1))).
% 0.29/0.47 thf(func_def_99, type, sK28: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X1 @ product_prod @ X4 @ product_prod @ X5 @ product_prod @ X0 @ product_prod @ X3 @ X2 > $o) > X5))).
% 0.29/0.47 thf(func_def_100, type, sK29: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X1 @ product_prod @ X4 @ product_prod @ X5 @ product_prod @ X0 @ product_prod @ X3 @ X2 > $o) > X0))).
% 0.29/0.47 thf(func_def_101, type, sK30: !>[X0: $tType, X1: $tType, X2: $tType]:((labeled_graph @ X1 @ X2 > set @ product_prod @ X0 @ X2 > labeled_graph @ X1 @ X0 > set @ product_prod @ X0 @ X2))).
% 0.29/0.47 thf(func_def_102, type, sK31: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X2 @ product_prod @ X0 @ product_prod @ X3 @ X1 > X2))).
% 0.29/0.47 thf(func_def_103, type, sK32: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X2 @ product_prod @ X0 @ product_prod @ X3 @ X1 > X1))).
% 0.29/0.47 thf(func_def_104, type, sK33: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X2 @ product_prod @ X0 @ product_prod @ X3 @ X1 > X0))).
% 0.29/0.47 thf(func_def_105, type, sK34: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X2 @ product_prod @ X0 @ product_prod @ X3 @ X1 > X3))).
% 0.29/0.47 thf(func_def_106, type, sK35: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((labeled_graph @ X0 @ X2 > labeled_graph @ X0 @ X2 > set @ product_prod @ labeled_graph @ X0 @ X1 @ labeled_graph @ X0 @ X1 > labeled_graph @ X0 @ X3))).
% 0.29/0.47 thf(func_def_107, type, sK36: !>[X0: $tType, X1: $tType, X2: $tType]:((set @ product_prod @ X2 @ X0 > set @ product_prod @ X0 @ X1 > product_prod @ X2 @ X1 > X2))).
% 0.29/0.47 thf(func_def_108, type, sK37: !>[X0: $tType, X1: $tType, X2: $tType]:((set @ product_prod @ X2 @ X0 > set @ product_prod @ X0 @ X1 > product_prod @ X2 @ X1 > X1))).
% 0.29/0.47 thf(func_def_109, type, sK38: !>[X0: $tType, X1: $tType, X2: $tType]:((set @ product_prod @ X2 @ X0 > set @ product_prod @ X0 @ X1 > product_prod @ X2 @ X1 > X0))).
% 0.29/0.47 thf(func_def_110, type, sK39: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.29/0.47 thf(func_def_111, type, sK40: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.29/0.47 thf(func_def_112, type, sK41: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > set @ product_prod @ X1 @ X0 > X1))).
% 0.29/0.47 thf(func_def_113, type, sK42: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > set @ product_prod @ X1 @ X0 > X0))).
% 0.29/0.47 thf(func_def_114, type, sK43: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((labeled_graph @ X1 @ X3 > set @ product_prod @ labeled_graph @ X1 @ X0 @ labeled_graph @ X1 @ X0 > labeled_graph @ X1 @ X3 > labeled_graph @ X1 @ X2))).
% 0.29/0.47 thf(func_def_115, type, sK44: !>[X0: $tType, X1: $tType]:(((X0 > $o) > set @ product_prod @ X0 @ X1 > X1))).
% 0.29/0.47 thf(func_def_116, type, sK45: !>[X0: $tType, X1: $tType]:(((X0 > $o) > set @ product_prod @ X0 @ X1 > X0))).
% 0.29/0.47 thf(func_def_117, type, sK46: !>[X0: $tType, X1: $tType, X2: $tType]:((set @ product_prod @ X0 @ X1 > set @ product_prod @ X2 @ X0 > X2 > X1 > X0))).
% 0.29/0.47 thf(func_def_118, type, sK47: !>[X0: $tType, X1: $tType, X2: $tType]:((set @ product_prod @ X0 @ X1 > set @ product_prod @ X2 @ X0 > X2 > X1 > X1))).
% 0.29/0.47 thf(func_def_119, type, sK48: !>[X0: $tType, X1: $tType, X2: $tType]:((set @ product_prod @ X0 @ X1 > set @ product_prod @ X2 @ X0 > X2 > X1 > X2))).
% 0.29/0.47 thf(func_def_120, type, sK49: !>[X0: $tType]:((X0 > set @ X0 > X0))).
% 0.29/0.47 thf(func_def_121, type, sK50: !>[X0: $tType]:((set @ X0 > X0))).
% 0.29/0.47 thf(func_def_122, type, sK51: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X1 @ product_prod @ X2 @ X0 > $o) > X2))).
% 0.29/0.47 thf(func_def_123, type, sK52: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X1 @ product_prod @ X2 @ X0 > $o) > X0))).
% 0.29/0.47 thf(func_def_124, type, sK53: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X1 @ product_prod @ X2 @ X0 > $o) > X1))).
% 0.29/0.47 thf(func_def_125, type, sK54: !>[X0: $tType, X1: $tType, X2: $tType]:((set @ product_prod @ X1 @ X0 > set @ product_prod @ X0 @ X2 > X1 > X2 > X0))).
% 0.29/0.47 thf(func_def_126, type, sK55: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.29/0.47 thf(func_def_127, type, sK56: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.29/0.47 thf(func_def_128, type, sK57: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > X1))).
% 0.29/0.47 thf(func_def_129, type, sK58: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > X2))).
% 0.29/0.47 thf(func_def_130, type, sK59: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > X0))).
% 0.29/0.47 thf(func_def_131, type, sK60: !>[X0: $tType, X1: $tType, X2: $tType]:(((nat > labeled_graph @ X0 @ X2) > product_prod @ labeled_graph @ X0 @ X1 @ labeled_graph @ X0 @ X1 > set @ product_prod @ X1 @ X2 > nat))).
% 0.29/0.47 thf(func_def_132, type, sK61: !>[X0: $tType, X1: $tType]:((set @ X0 > set @ product_prod @ X0 @ X1 > X1 > X0))).
% 0.29/0.47 thf(func_def_133, type, sK62: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X1))).
% 0.29/0.47 thf(func_def_134, type, sK63: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X0))).
% 0.29/0.47 thf(func_def_135, type, sK64: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X2 @ product_prod @ X1 @ product_prod @ X4 @ X3 > X0))).
% 0.29/0.47 thf(func_def_136, type, sK65: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X2 @ product_prod @ X1 @ product_prod @ X4 @ X3 > X2))).
% 0.29/0.47 thf(func_def_137, type, sK66: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X2 @ product_prod @ X1 @ product_prod @ X4 @ X3 > X3))).
% 0.29/0.47 thf(func_def_138, type, sK67: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X2 @ product_prod @ X1 @ product_prod @ X4 @ X3 > X1))).
% 0.29/0.47 thf(func_def_139, type, sK68: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X2 @ product_prod @ X1 @ product_prod @ X4 @ X3 > X4))).
% 0.29/0.47 thf(func_def_140, type, sK69: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.29/0.47 thf(func_def_141, type, sK70: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.29/0.47 thf(func_def_142, type, sK71: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.29/0.47 thf(func_def_143, type, sK72: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.29/0.47 thf(func_def_144, type, sK73: !>[X0: $tType, X1: $tType]:((labeled_graph @ X1 @ X0 > set @ X0))).
% 0.29/0.47 thf(func_def_145, type, sK74: !>[X0: $tType, X1: $tType]:((labeled_graph @ X1 @ X0 > set @ product_prod @ X1 @ product_prod @ X0 @ X0))).
% 0.29/0.47 thf(func_def_146, type, sK75: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > X1 > X0))).
% 0.29/0.47 thf(func_def_147, type, sK76: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > X1 > X1))).
% 0.29/0.47 thf(func_def_148, type, sK77: !>[X0: $tType, X1: $tType, X2: $tType]:((labeled_graph @ X2 @ X1 > labeled_graph @ X2 @ X0 > labeled_graph @ X2 @ X0 > set @ product_prod @ X0 @ X1))).
% 0.29/0.47 thf(func_def_149, type, sK78: !>[X0: $tType, X1: $tType]:((labeled_graph @ X0 @ X1 > (nat > labeled_graph @ X0 @ X1) > nat))).
% 0.29/0.47 thf(func_def_150, type, sK79: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X3 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X4 @ product_prod @ X2 @ X0 > X4))).
% 0.29/0.47 thf(func_def_151, type, sK80: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X3 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X4 @ product_prod @ X2 @ X0 > X0))).
% 0.29/0.47 thf(func_def_152, type, sK81: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X3 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X4 @ product_prod @ X2 @ X0 > X5))).
% 0.29/0.47 thf(func_def_153, type, sK82: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X3 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X4 @ product_prod @ X2 @ X0 > X1))).
% 0.29/0.47 thf(func_def_154, type, sK83: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X3 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X4 @ product_prod @ X2 @ X0 > X2))).
% 0.29/0.47 thf(func_def_155, type, sK84: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X3 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X4 @ product_prod @ X2 @ X0 > X3))).
% 0.29/0.47 thf(func_def_156, type, sK85: !>[X0: $tType, X1: $tType]:((set @ product_prod @ labeled_graph @ X0 @ X1 @ labeled_graph @ X0 @ X1 > product_prod @ labeled_graph @ X0 @ X1 @ labeled_graph @ X0 @ X1))).
% 0.29/0.47 thf(func_def_157, type, sK86: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > X1))).
% 0.29/0.47 thf(func_def_158, type, sK87: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > X0))).
% 0.29/0.47 thf(func_def_159, type, sK88: !>[X0: $tType]:((X0 > set @ X0 > X0))).
% 0.29/0.47 thf(func_def_160, type, sK89: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 0.29/0.47 thf(func_def_161, type, sK90: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 0.29/0.47 thf(func_def_162, type, sK91: !>[X0: $tType, X1: $tType]:(((labeled_graph @ X0 @ X1 > $o) > set @ product_prod @ X0 @ product_prod @ X1 @ X1))).
% 0.29/0.47 thf(func_def_163, type, sK92: !>[X0: $tType, X1: $tType]:(((labeled_graph @ X0 @ X1 > $o) > set @ X1))).
% 0.29/0.47 thf(func_def_164, type, sK93: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X6 @ product_prod @ X1 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X2 @ X4 > X1))).
% 0.29/0.47 thf(func_def_165, type, sK94: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X6 @ product_prod @ X1 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X2 @ X4 > X0))).
% 0.29/0.47 thf(func_def_166, type, sK95: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X6 @ product_prod @ X1 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X2 @ X4 > X5))).
% 0.29/0.47 thf(func_def_167, type, sK96: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X6 @ product_prod @ X1 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X2 @ X4 > X6))).
% 0.29/0.47 thf(func_def_168, type, sK97: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X6 @ product_prod @ X1 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X2 @ X4 > X3))).
% 0.29/0.47 thf(func_def_169, type, sK98: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X6 @ product_prod @ X1 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X2 @ X4 > X2))).
% 0.29/0.47 thf(func_def_170, type, sK99: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X6 @ product_prod @ X1 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X2 @ X4 > X4))).
% 0.29/0.47 thf(func_def_171, type, sK100: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X2 @ X4 > $o) > X3))).
% 0.29/0.47 thf(func_def_172, type, sK101: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X2 @ X4 > $o) > X4))).
% 0.29/0.47 thf(func_def_173, type, sK102: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X2 @ X4 > $o) > X2))).
% 0.29/0.47 thf(func_def_174, type, sK103: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X2 @ X4 > $o) > X0))).
% 0.29/0.47 thf(func_def_175, type, sK104: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X2 @ X4 > $o) > X1))).
% 0.29/0.47 thf(func_def_176, type, sK105: !>[X0: $tType, X1: $tType]:((X1 > set @ product_prod @ X1 @ X0 > X0))).
% 0.29/0.47 thf(func_def_177, type, sK106: (nat > (nat > $o) > nat)).
% 0.29/0.47 thf(func_def_178, type, sK107: ((nat > $o) > nat)).
% 0.29/0.47 thf(func_def_179, type, sK108: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X1 @ product_prod @ X0 @ product_prod @ X3 @ X2 > $o) > X0))).
% 0.29/0.47 thf(func_def_180, type, sK109: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X1 @ product_prod @ X0 @ product_prod @ X3 @ X2 > $o) > X2))).
% 0.29/0.47 thf(func_def_181, type, sK110: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X1 @ product_prod @ X0 @ product_prod @ X3 @ X2 > $o) > X3))).
% 0.29/0.47 thf(func_def_182, type, sK111: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X1 @ product_prod @ X0 @ product_prod @ X3 @ X2 > $o) > X1))).
% 0.29/0.47 thf(func_def_183, type, sK112: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 0.29/0.47 thf(func_def_184, type, sK113: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 0.29/0.47 thf(func_def_185, type, sK114: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.29/0.47 thf(func_def_186, type, sK115: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X4 @ product_prod @ X1 @ product_prod @ X6 @ product_prod @ X5 @ product_prod @ X2 @ product_prod @ X3 @ X0 > $o) > X0))).
% 0.29/0.47 thf(func_def_187, type, sK116: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X4 @ product_prod @ X1 @ product_prod @ X6 @ product_prod @ X5 @ product_prod @ X2 @ product_prod @ X3 @ X0 > $o) > X1))).
% 0.29/0.47 thf(func_def_188, type, sK117: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X4 @ product_prod @ X1 @ product_prod @ X6 @ product_prod @ X5 @ product_prod @ X2 @ product_prod @ X3 @ X0 > $o) > X6))).
% 0.29/0.47 thf(func_def_189, type, sK118: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X4 @ product_prod @ X1 @ product_prod @ X6 @ product_prod @ X5 @ product_prod @ X2 @ product_prod @ X3 @ X0 > $o) > X2))).
% 0.29/0.47 thf(func_def_190, type, sK119: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X4 @ product_prod @ X1 @ product_prod @ X6 @ product_prod @ X5 @ product_prod @ X2 @ product_prod @ X3 @ X0 > $o) > X4))).
% 0.29/0.47 thf(func_def_191, type, sK120: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X4 @ product_prod @ X1 @ product_prod @ X6 @ product_prod @ X5 @ product_prod @ X2 @ product_prod @ X3 @ X0 > $o) > X5))).
% 0.29/0.47 thf(func_def_192, type, sK121: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X4 @ product_prod @ X1 @ product_prod @ X6 @ product_prod @ X5 @ product_prod @ X2 @ product_prod @ X3 @ X0 > $o) > X3))).
% 0.29/0.47 thf(func_def_193, type, sK122: !>[X0: $tType]:((set @ X0 > X0))).
% 0.29/0.47 thf(func_def_194, type, sK123: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > X1 > $o) > X0))).
% 0.29/0.47 thf(func_def_195, type, sK124: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > X1 > $o) > X0 > X1))).
% 0.29/0.47 thf(func_def_196, type, sK125: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1 > X0))).
% 0.29/0.47 thf(func_def_197, type, sK126: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.29/0.47 thf(func_def_198, type, sK127: !>[X0: $tType, X1: $tType]:((X1 > set @ product_prod @ X1 @ X0 > X0))).
% 0.29/0.47 thf(func_def_199, type, sK128: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ labeled_graph @ X1 @ X3 @ labeled_graph @ X1 @ X3 > set @ product_prod @ X3 @ X0 > labeled_graph @ X1 @ X0 > labeled_graph @ X1 @ X0 > labeled_graph @ X1 @ X2))).
% 0.29/0.47 thf(func_def_200, type, sK129: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ labeled_graph @ X1 @ X3 @ labeled_graph @ X1 @ X3 > set @ product_prod @ X3 @ X0 > labeled_graph @ X1 @ X0 > labeled_graph @ X1 @ X0 > set @ product_prod @ X0 @ X2))).
% 0.29/0.47 thf(func_def_201, type, sK130: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ labeled_graph @ X1 @ X3 @ labeled_graph @ X1 @ X3 > set @ product_prod @ X3 @ X0 > labeled_graph @ X1 @ X0 > labeled_graph @ X1 @ X0 > set @ product_prod @ X3 @ X2))).
% 0.29/0.47 thf(func_def_202, type, sK131: !>[X0: $tType, X1: $tType, X2: $tType]:(((nat > labeled_graph @ X2 @ X0) > set @ product_prod @ labeled_graph @ X2 @ X1 @ labeled_graph @ X2 @ X1 > set @ product_prod @ X1 @ X0))).
% 0.29/0.47 thf(func_def_203, type, sK132: !>[X0: $tType, X1: $tType, X2: $tType]:(((nat > labeled_graph @ X2 @ X0) > set @ product_prod @ labeled_graph @ X2 @ X1 @ labeled_graph @ X2 @ X1 > product_prod @ labeled_graph @ X2 @ X1 @ labeled_graph @ X2 @ X1))).
% 0.29/0.47 thf(func_def_204, type, sK133: !>[X0: $tType, X1: $tType, X2: $tType]:(((nat > labeled_graph @ X2 @ X0) > set @ product_prod @ labeled_graph @ X2 @ X1 @ labeled_graph @ X2 @ X1 > nat))).
% 0.29/0.47 thf(func_def_205, type, sK134: !>[X0: $tType]:((product_prod @ X0 @ X0 > set @ X0 > X0))).
% 0.29/0.47 thf(func_def_206, type, sK135: !>[X0: $tType, X1: $tType, X2: $tType]:((labeled_graph @ X0 @ X1 > product_prod @ labeled_graph @ X0 @ X2 @ labeled_graph @ X0 @ X2 > set @ product_prod @ X2 @ X1 > set @ product_prod @ X2 @ X1))).
% 0.29/0.47 thf(func_def_207, type, sK136: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.29/0.47 thf(func_def_208, type, vNOT: ($o > $o)).
% 0.29/0.47 thf(f2,axiom,(
% 0.29/0.47 ! [X0 : $tType,X1 : allegorical_term @ X0,X2 : allegorical_term @ X0] : ((graph_homomorphism @ X0 @ nat @ nat @ (product_fst @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat @ (product_Pair @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat @ (translation @ X0 @ X1) @ (translation @ X0 @ (allegorical_A_Int @ X0 @ X1 @ X2)))) @ (product_snd @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat @ (product_Pair @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat @ (translation @ X0 @ X1) @ (translation @ X0 @ (allegorical_A_Int @ X0 @ X1 @ X2)))) @ (id_on @ nat @ (labeled_vertices @ X0 @ nat @ (product_fst @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat @ (product_Pair @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat @ (translation @ X0 @ X1) @ (translation @ X0 @ (allegorical_A_Int @ X0 @ X1 @ X2))))))) & (finite_finite2 @ nat @ (labeled_vertices @ X0 @ nat @ (product_snd @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat @ (product_Pair @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat @ (translation @ X0 @ X1) @ (translation @ X0 @ (allegorical_A_Int @ X0 @ X1 @ X2)))))) & (((product_snd @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat @ (product_Pair @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat @ (translation @ X0 @ X1) @ (translation @ X0 @ (allegorical_A_Int @ X0 @ X1 @ X2))))) = ((restrict @ X0 @ nat @ (product_snd @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat @ (product_Pair @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat @ (translation @ X0 @ X1) @ (translation @ X0 @ (allegorical_A_Int @ X0 @ X1 @ X2))))))) & (finite_finite2 @ product_prod @ X0 @ product_prod @ nat @ nat @ (labeled_edges @ X0 @ nat @ (product_snd @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat @ (product_Pair @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat @ (translation @ X0 @ X1) @ (translation @ X0 @ (allegorical_A_Int @ X0 @ X1 @ X2)))))))),
% 0.29/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_graph__rule__translation)).
% 0.29/0.47 thf(f6,axiom,(
% 0.29/0.47 ! [X0 : $tType,X1 : allegorical_term @ X0] : (finite_finite2 @ product_prod @ X0 @ product_prod @ nat @ nat @ (labeled_edges @ X0 @ nat @ (translation @ X0 @ X1)))),
% 0.29/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_verts__in__translation__finite_I2_J)).
% 0.29/0.47 thf(f9,axiom,(
% 0.29/0.47 ! [X0 : $tType,X1 : allegorical_term @ X0] : (finite_finite2 @ nat @ (labeled_vertices @ X0 @ nat @ (translation @ X0 @ X1)))),
% 0.29/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_verts__in__translation__finite_I1_J)).
% 0.29/0.47 thf(f12,axiom,(
% 0.29/0.47 ! [X0 : $tType] : ((^[X1 : allegorical_term @ X0] : ((restrict @ X0 @ nat @ (translation @ X0 @ X1)))) = translation @ X0)),
% 0.29/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_translation__graph)).
% 0.29/0.47 thf(f32,axiom,(
% 0.29/0.47 ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : X0] : (((product_fst @ X1 @ X0 @ (product_Pair @ X1 @ X0 @ X2 @ X3))) = X2)),
% 0.29/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_fst__conv)).
% 0.29/0.47 thf(f34,axiom,(
% 0.29/0.47 ! [X0 : $tType,X1 : $tType,X2 : X0,X3 : X1] : (((product_snd @ X0 @ X1 @ (product_Pair @ X0 @ X1 @ X2 @ X3))) = X3)),
% 0.29/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_snd__conv)).
% 0.29/0.47 thf(f279,conjecture,(
% 0.29/0.47 (graph_homomorphism @ b @ nat @ nat @ (product_fst @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (product_Pair @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (translation @ b @ (product_fst @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))) @ (translation @ b @ (product_snd @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))))) @ (product_snd @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (product_Pair @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (translation @ b @ (product_fst @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))) @ (translation @ b @ (product_snd @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))))) @ (id_on @ nat @ (labeled_vertices @ b @ nat @ (product_fst @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (product_Pair @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (translation @ b @ (product_fst @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))) @ (translation @ b @ (product_snd @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v))))))))) & (finite_finite2 @ nat @ (labeled_vertices @ b @ nat @ (product_snd @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (product_Pair @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (translation @ b @ (product_fst @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))) @ (translation @ b @ (product_snd @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))))))) & (((product_snd @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (product_Pair @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (translation @ b @ (product_fst @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))) @ (translation @ b @ (product_snd @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v))))))) = ((restrict @ b @ nat @ (product_snd @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (product_Pair @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (translation @ b @ (product_fst @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))) @ (translation @ b @ (product_snd @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v))))))))) & (finite_finite2 @ product_prod @ b @ product_prod @ nat @ nat @ (labeled_edges @ b @ nat @ (product_snd @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (product_Pair @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (translation @ b @ (product_fst @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))) @ (translation @ b @ (product_snd @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v))))))))),
% 0.29/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 0.29/0.47 thf(f280,negated_conjecture,(
% 0.29/0.47 ~((graph_homomorphism @ b @ nat @ nat @ (product_fst @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (product_Pair @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (translation @ b @ (product_fst @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))) @ (translation @ b @ (product_snd @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))))) @ (product_snd @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (product_Pair @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (translation @ b @ (product_fst @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))) @ (translation @ b @ (product_snd @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))))) @ (id_on @ nat @ (labeled_vertices @ b @ nat @ (product_fst @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (product_Pair @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (translation @ b @ (product_fst @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))) @ (translation @ b @ (product_snd @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v))))))))) & (finite_finite2 @ nat @ (labeled_vertices @ b @ nat @ (product_snd @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (product_Pair @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (translation @ b @ (product_fst @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))) @ (translation @ b @ (product_snd @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))))))) & (((product_snd @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (product_Pair @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (translation @ b @ (product_fst @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))) @ (translation @ b @ (product_snd @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v))))))) = ((restrict @ b @ nat @ (product_snd @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (product_Pair @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (translation @ b @ (product_fst @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))) @ (translation @ b @ (product_snd @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v))))))))) & (finite_finite2 @ product_prod @ b @ product_prod @ nat @ nat @ (labeled_edges @ b @ nat @ (product_snd @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (product_Pair @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (translation @ b @ (product_fst @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))) @ (translation @ b @ (product_snd @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))))))))),
% 0.29/0.47 inference(negated_conjecture,[status(cth)],[f279])).
% 0.29/0.47 thf(f334,plain,(
% 0.29/0.47 ~((graph_homomorphism @ b @ nat @ nat @ (product_fst @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (product_Pair @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (translation @ b @ (product_fst @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))) @ (translation @ b @ (product_snd @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))))) @ (product_snd @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (product_Pair @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (translation @ b @ (product_fst @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))) @ (translation @ b @ (product_snd @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))))) @ (id_on @ nat @ (labeled_vertices @ b @ nat @ (product_fst @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (product_Pair @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (translation @ b @ (product_fst @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))) @ (translation @ b @ (product_snd @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v))))))))) & (finite_finite2 @ nat @ (labeled_vertices @ b @ nat @ (product_snd @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (product_Pair @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (translation @ b @ (product_fst @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))) @ (translation @ b @ (product_snd @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))))))) & (((product_snd @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (product_Pair @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (translation @ b @ (product_fst @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))) @ (translation @ b @ (product_snd @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v))))))) = ((restrict @ b @ nat @ (product_snd @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (product_Pair @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (translation @ b @ (product_fst @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))) @ (translation @ b @ (product_snd @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v))))))))) & (finite_finite2 @ product_prod @ b @ product_prod @ nat @ nat @ (labeled_edges @ b @ nat @ (product_snd @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (product_Pair @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (translation @ b @ (product_fst @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))) @ (translation @ b @ (product_snd @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))))))))),
% 0.29/0.47 inference(rectify,[],[f280])).
% 0.29/0.47 thf(f335,plain,(
% 0.29/0.47 ~((((product_snd @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (product_Pair @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (translation @ b @ (product_fst @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))) @ (translation @ b @ (product_snd @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v))))))) = ((restrict @ b @ nat @ (product_snd @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (product_Pair @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (translation @ b @ (product_fst @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))) @ (translation @ b @ (product_snd @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v))))))))) & (((finite_finite2 @ nat @ (labeled_vertices @ b @ nat @ (product_snd @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (product_Pair @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (translation @ b @ (product_fst @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))) @ (translation @ b @ (product_snd @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v))))))))) = $true) & (((graph_homomorphism @ b @ nat @ nat @ (product_fst @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (product_Pair @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (translation @ b @ (product_fst @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))) @ (translation @ b @ (product_snd @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))))) @ (product_snd @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (product_Pair @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (translation @ b @ (product_fst @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))) @ (translation @ b @ (product_snd @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))))) @ (id_on @ nat @ (labeled_vertices @ b @ nat @ (product_fst @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (product_Pair @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (translation @ b @ (product_fst @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))) @ (translation @ b @ (product_snd @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))))))))) = $true) & (((finite_finite2 @ product_prod @ b @ product_prod @ nat @ nat @ (labeled_edges @ b @ nat @ (product_snd @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (product_Pair @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (translation @ b @ (product_fst @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))) @ (translation @ b @ (product_snd @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v))))))))) = $true))),
% 0.29/0.47 inference(fool_elimination,[],[f334])).
% 0.29/0.47 thf(f456,plain,(
% 0.29/0.47 ! [X0 : $tType,X1 : allegorical_term @ X0] : (finite_finite2 @ product_prod @ X0 @ product_prod @ nat @ nat @ (labeled_edges @ X0 @ nat @ (translation @ X0 @ X1)))),
% 0.29/0.47 inference(rectify,[],[f6])).
% 0.29/0.47 thf(f457,plain,(
% 0.29/0.47 ! [X0 : $tType,X1 : allegorical_term @ X0] : (((finite_finite2 @ product_prod @ X0 @ product_prod @ nat @ nat @ (labeled_edges @ X0 @ nat @ (translation @ X0 @ X1)))) = $true)),
% 0.29/0.47 inference(fool_elimination,[],[f456])).
% 0.29/0.47 thf(f462,plain,(
% 0.29/0.47 ! [X0 : $tType,X1 : allegorical_term @ X0] : (finite_finite2 @ nat @ (labeled_vertices @ X0 @ nat @ (translation @ X0 @ X1)))),
% 0.29/0.47 inference(rectify,[],[f9])).
% 0.29/0.47 thf(f463,plain,(
% 0.29/0.47 ! [X0 : $tType,X1 : allegorical_term @ X0] : (((finite_finite2 @ nat @ (labeled_vertices @ X0 @ nat @ (translation @ X0 @ X1)))) = $true)),
% 0.29/0.47 inference(fool_elimination,[],[f462])).
% 0.29/0.47 thf(f632,plain,(
% 0.29/0.47 ! [X0 : $tType,X1 : allegorical_term @ X0,X2 : allegorical_term @ X0] : ((graph_homomorphism @ X0 @ nat @ nat @ (product_fst @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat @ (product_Pair @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat @ (translation @ X0 @ X1) @ (translation @ X0 @ (allegorical_A_Int @ X0 @ X1 @ X2)))) @ (product_snd @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat @ (product_Pair @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat @ (translation @ X0 @ X1) @ (translation @ X0 @ (allegorical_A_Int @ X0 @ X1 @ X2)))) @ (id_on @ nat @ (labeled_vertices @ X0 @ nat @ (product_fst @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat @ (product_Pair @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat @ (translation @ X0 @ X1) @ (translation @ X0 @ (allegorical_A_Int @ X0 @ X1 @ X2))))))) & (finite_finite2 @ nat @ (labeled_vertices @ X0 @ nat @ (product_snd @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat @ (product_Pair @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat @ (translation @ X0 @ X1) @ (translation @ X0 @ (allegorical_A_Int @ X0 @ X1 @ X2)))))) & (((product_snd @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat @ (product_Pair @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat @ (translation @ X0 @ X1) @ (translation @ X0 @ (allegorical_A_Int @ X0 @ X1 @ X2))))) = ((restrict @ X0 @ nat @ (product_snd @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat @ (product_Pair @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat @ (translation @ X0 @ X1) @ (translation @ X0 @ (allegorical_A_Int @ X0 @ X1 @ X2))))))) & (finite_finite2 @ product_prod @ X0 @ product_prod @ nat @ nat @ (labeled_edges @ X0 @ nat @ (product_snd @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat @ (product_Pair @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat @ (translation @ X0 @ X1) @ (translation @ X0 @ (allegorical_A_Int @ X0 @ X1 @ X2)))))))),
% 0.29/0.47 inference(rectify,[],[f2])).
% 0.29/0.47 thf(f633,plain,(
% 0.29/0.47 ! [X0 : $tType,X1 : allegorical_term @ X0,X2 : allegorical_term @ X0] : ((((finite_finite2 @ product_prod @ X0 @ product_prod @ nat @ nat @ (labeled_edges @ X0 @ nat @ (product_snd @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat @ (product_Pair @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat @ (translation @ X0 @ X1) @ (translation @ X0 @ (allegorical_A_Int @ X0 @ X1 @ X2))))))) = $true) & (((product_snd @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat @ (product_Pair @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat @ (translation @ X0 @ X1) @ (translation @ X0 @ (allegorical_A_Int @ X0 @ X1 @ X2))))) = ((restrict @ X0 @ nat @ (product_snd @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat @ (product_Pair @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat @ (translation @ X0 @ X1) @ (translation @ X0 @ (allegorical_A_Int @ X0 @ X1 @ X2))))))) & (((finite_finite2 @ nat @ (labeled_vertices @ X0 @ nat @ (product_snd @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat @ (product_Pair @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat @ (translation @ X0 @ X1) @ (translation @ X0 @ (allegorical_A_Int @ X0 @ X1 @ X2))))))) = $true) & (((graph_homomorphism @ X0 @ nat @ nat @ (product_fst @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat @ (product_Pair @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat @ (translation @ X0 @ X1) @ (translation @ X0 @ (allegorical_A_Int @ X0 @ X1 @ X2)))) @ (product_snd @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat @ (product_Pair @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat @ (translation @ X0 @ X1) @ (translation @ X0 @ (allegorical_A_Int @ X0 @ X1 @ X2)))) @ (id_on @ nat @ (labeled_vertices @ X0 @ nat @ (product_fst @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat @ (product_Pair @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat @ (translation @ X0 @ X1) @ (translation @ X0 @ (allegorical_A_Int @ X0 @ X1 @ X2)))))))) = $true))),
% 0.29/0.47 inference(fool_elimination,[],[f632])).
% 0.29/0.47 thf(f738,plain,(
% 0.29/0.47 ! [X0 : $tType] : (translation @ X0 = (^[Y0 : allegorical_term @ X0]: (restrict @ X0 @ nat @ (translation @ X0 @ Y0))))),
% 0.29/0.47 inference(fool_elimination,[],[f12])).
% 0.29/0.47 thf(f768,plain,(
% 0.29/0.47 ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X1] : (((product_fst @ X0 @ X1 @ (product_Pair @ X0 @ X1 @ X2 @ X3))) = X2)),
% 0.29/0.47 inference(rectify,[],[f32])).
% 0.29/0.47 thf(f992,plain,(
% 0.29/0.47 (((product_snd @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (product_Pair @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (translation @ b @ (product_fst @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))) @ (translation @ b @ (product_snd @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v))))))) != ((restrict @ b @ nat @ (product_snd @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (product_Pair @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (translation @ b @ (product_fst @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))) @ (translation @ b @ (product_snd @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v))))))))) | (((finite_finite2 @ nat @ (labeled_vertices @ b @ nat @ (product_snd @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (product_Pair @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (translation @ b @ (product_fst @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))) @ (translation @ b @ (product_snd @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v))))))))) != $true) | (((graph_homomorphism @ b @ nat @ nat @ (product_fst @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (product_Pair @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (translation @ b @ (product_fst @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))) @ (translation @ b @ (product_snd @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))))) @ (product_snd @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (product_Pair @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (translation @ b @ (product_fst @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))) @ (translation @ b @ (product_snd @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))))) @ (id_on @ nat @ (labeled_vertices @ b @ nat @ (product_fst @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (product_Pair @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (translation @ b @ (product_fst @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))) @ (translation @ b @ (product_snd @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))))))))) != $true) | (((finite_finite2 @ product_prod @ b @ product_prod @ nat @ nat @ (labeled_edges @ b @ nat @ (product_snd @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (product_Pair @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (translation @ b @ (product_fst @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))) @ (translation @ b @ (product_snd @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v))))))))) != $true)),
% 0.29/0.47 inference(ennf_transformation,[],[f335])).
% 0.29/0.47 thf(f1177,plain,(
% 0.29/0.47 ! [X0 : $tType,X1 : $tType,X2 : X1,X3 : X0] : (((product_fst @ X1 @ X0 @ (product_Pair @ X1 @ X0 @ X2 @ X3))) = X2)),
% 0.29/0.47 inference(rectify,[],[f768])).
% 0.29/0.47 thf(f1359,plain,(
% 0.29/0.47 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X1] : ((((product_snd @ X0 @ X1 @ (product_Pair @ X0 @ X1 @ X2 @ X3))) = X3)) )),
% 0.29/0.47 inference(cnf_transformation,[],[f34])).
% 0.29/0.47 thf(f1401,plain,(
% 0.29/0.47 ( ! [X0 : $tType] : ((translation @ X0 = (^[Y0 : allegorical_term @ X0]: (restrict @ X0 @ nat @ (translation @ X0 @ Y0))))) )),
% 0.29/0.47 inference(cnf_transformation,[],[f738])).
% 0.29/0.47 thf(f1444,plain,(
% 0.29/0.47 ( ! [X0 : $tType,X1 : allegorical_term @ X0] : ((((finite_finite2 @ product_prod @ X0 @ product_prod @ nat @ nat @ (labeled_edges @ X0 @ nat @ (translation @ X0 @ X1)))) = $true)) )),
% 0.29/0.47 inference(cnf_transformation,[],[f457])).
% 0.29/0.47 thf(f1534,plain,(
% 0.29/0.47 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : X0] : ((((product_fst @ X1 @ X0 @ (product_Pair @ X1 @ X0 @ X2 @ X3))) = X2)) )),
% 0.29/0.47 inference(cnf_transformation,[],[f1177])).
% 0.29/0.47 thf(f1553,plain,(
% 0.29/0.47 ( ! [X0 : $tType,X1 : allegorical_term @ X0] : ((((finite_finite2 @ nat @ (labeled_vertices @ X0 @ nat @ (translation @ X0 @ X1)))) = $true)) )),
% 0.29/0.47 inference(cnf_transformation,[],[f463])).
% 0.29/0.47 thf(f1711,plain,(
% 0.29/0.47 ( ! [X0 : $tType,X2 : allegorical_term @ X0,X1 : allegorical_term @ X0] : ((((graph_homomorphism @ X0 @ nat @ nat @ (product_fst @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat @ (product_Pair @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat @ (translation @ X0 @ X1) @ (translation @ X0 @ (allegorical_A_Int @ X0 @ X1 @ X2)))) @ (product_snd @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat @ (product_Pair @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat @ (translation @ X0 @ X1) @ (translation @ X0 @ (allegorical_A_Int @ X0 @ X1 @ X2)))) @ (id_on @ nat @ (labeled_vertices @ X0 @ nat @ (product_fst @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat @ (product_Pair @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat @ (translation @ X0 @ X1) @ (translation @ X0 @ (allegorical_A_Int @ X0 @ X1 @ X2)))))))) = $true)) )),
% 0.29/0.47 inference(cnf_transformation,[],[f633])).
% 0.29/0.47 thf(f1718,plain,(
% 0.29/0.47 (((finite_finite2 @ nat @ (labeled_vertices @ b @ nat @ (product_snd @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (product_Pair @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (translation @ b @ (product_fst @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))) @ (translation @ b @ (product_snd @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v))))))))) != $true) | (((graph_homomorphism @ b @ nat @ nat @ (product_fst @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (product_Pair @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (translation @ b @ (product_fst @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))) @ (translation @ b @ (product_snd @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))))) @ (product_snd @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (product_Pair @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (translation @ b @ (product_fst @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))) @ (translation @ b @ (product_snd @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))))) @ (id_on @ nat @ (labeled_vertices @ b @ nat @ (product_fst @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (product_Pair @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (translation @ b @ (product_fst @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))) @ (translation @ b @ (product_snd @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))))))))) != $true) | (((finite_finite2 @ product_prod @ b @ product_prod @ nat @ nat @ (labeled_edges @ b @ nat @ (product_snd @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (product_Pair @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (translation @ b @ (product_fst @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))) @ (translation @ b @ (product_snd @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v))))))))) != $true) | (((product_snd @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (product_Pair @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (translation @ b @ (product_fst @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))) @ (translation @ b @ (product_snd @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v))))))) != ((restrict @ b @ nat @ (product_snd @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (product_Pair @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (translation @ b @ (product_fst @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))) @ (translation @ b @ (product_snd @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))))))))),
% 0.29/0.47 inference(cnf_transformation,[],[f992])).
% 0.29/0.47 thf(f1895,definition,(
% 0.29/0.47 spl137_12 <=> (((product_snd @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (product_Pair @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (translation @ b @ (product_fst @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))) @ (translation @ b @ (product_snd @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v))))))) = ((restrict @ b @ nat @ (product_snd @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (product_Pair @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (translation @ b @ (product_fst @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))) @ (translation @ b @ (product_snd @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))))))))),
% 0.29/0.47 introduced(definition,[new_symbols(definition,[spl137_12])],[avatar_definition])).
% 0.29/0.47 thf(f1897,plain,(
% 0.29/0.47 (((product_snd @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (product_Pair @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (translation @ b @ (product_fst @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))) @ (translation @ b @ (product_snd @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v))))))) != ((restrict @ b @ nat @ (product_snd @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (product_Pair @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (translation @ b @ (product_fst @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))) @ (translation @ b @ (product_snd @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v))))))))) | spl137_12),
% 0.29/0.47 inference(avatar_component_clause,[],[f1895])).
% 0.29/0.47 thf(f1899,definition,(
% 0.29/0.47 spl137_13 <=> (((finite_finite2 @ nat @ (labeled_vertices @ b @ nat @ (product_snd @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (product_Pair @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (translation @ b @ (product_fst @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))) @ (translation @ b @ (product_snd @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v))))))))) = $true)),
% 0.29/0.47 introduced(definition,[new_symbols(definition,[spl137_13])],[avatar_definition])).
% 0.29/0.47 thf(f1901,plain,(
% 0.29/0.47 (((finite_finite2 @ nat @ (labeled_vertices @ b @ nat @ (product_snd @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (product_Pair @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (translation @ b @ (product_fst @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))) @ (translation @ b @ (product_snd @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v))))))))) != $true) | spl137_13),
% 0.29/0.47 inference(avatar_component_clause,[],[f1899])).
% 0.29/0.47 thf(f1903,definition,(
% 0.29/0.47 spl137_14 <=> (((finite_finite2 @ product_prod @ b @ product_prod @ nat @ nat @ (labeled_edges @ b @ nat @ (product_snd @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (product_Pair @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (translation @ b @ (product_fst @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))) @ (translation @ b @ (product_snd @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v))))))))) = $true)),
% 0.29/0.47 introduced(definition,[new_symbols(definition,[spl137_14])],[avatar_definition])).
% 0.29/0.47 thf(f1905,plain,(
% 0.29/0.47 (((finite_finite2 @ product_prod @ b @ product_prod @ nat @ nat @ (labeled_edges @ b @ nat @ (product_snd @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (product_Pair @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (translation @ b @ (product_fst @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))) @ (translation @ b @ (product_snd @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v))))))))) != $true) | spl137_14),
% 0.29/0.47 inference(avatar_component_clause,[],[f1903])).
% 0.29/0.47 thf(f1907,definition,(
% 0.29/0.47 spl137_15 <=> (((graph_homomorphism @ b @ nat @ nat @ (product_fst @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (product_Pair @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (translation @ b @ (product_fst @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))) @ (translation @ b @ (product_snd @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))))) @ (product_snd @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (product_Pair @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (translation @ b @ (product_fst @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))) @ (translation @ b @ (product_snd @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))))) @ (id_on @ nat @ (labeled_vertices @ b @ nat @ (product_fst @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (product_Pair @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (translation @ b @ (product_fst @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))) @ (translation @ b @ (product_snd @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))))))))) = $true)),
% 0.29/0.47 introduced(definition,[new_symbols(definition,[spl137_15])],[avatar_definition])).
% 0.29/0.47 thf(f1909,plain,(
% 0.29/0.47 (((graph_homomorphism @ b @ nat @ nat @ (product_fst @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (product_Pair @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (translation @ b @ (product_fst @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))) @ (translation @ b @ (product_snd @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))))) @ (product_snd @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (product_Pair @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (translation @ b @ (product_fst @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))) @ (translation @ b @ (product_snd @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))))) @ (id_on @ nat @ (labeled_vertices @ b @ nat @ (product_fst @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (product_Pair @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (translation @ b @ (product_fst @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))) @ (translation @ b @ (product_snd @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))))))))) != $true) | spl137_15),
% 0.29/0.47 inference(avatar_component_clause,[],[f1907])).
% 0.29/0.47 thf(f1910,plain,(
% 0.29/0.47 ~spl137_12 | ~spl137_13 | ~spl137_14 | ~spl137_15),
% 0.29/0.47 inference(avatar_split_clause,[],[f1718,f1907,f1903,f1899,f1895])).
% 0.29/0.47 thf(f1924,plain,(
% 0.29/0.47 (((product_snd @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (product_Pair @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (translation @ b @ (product_fst @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))) @ (translation @ b @ (allegorical_A_Int @ b @ u @ v))))) != ((restrict @ b @ nat @ (product_snd @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (product_Pair @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (translation @ b @ (product_fst @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))) @ (translation @ b @ (allegorical_A_Int @ b @ u @ v))))))) | spl137_12),
% 0.29/0.47 inference(superposition,[],[f1897,f1359])).
% 0.29/0.47 thf(f1926,plain,(
% 0.29/0.47 (((restrict @ b @ nat @ (translation @ b @ (allegorical_A_Int @ b @ u @ v)))) != ((translation @ b @ (allegorical_A_Int @ b @ u @ v)))) | spl137_12),
% 0.29/0.47 inference(forward_demodulation,[],[f1924,f1359])).
% 0.29/0.47 thf(f1929,definition,(
% 0.29/0.47 spl137_18 <=> (((restrict @ b @ nat @ (translation @ b @ (allegorical_A_Int @ b @ u @ v)))) = ((translation @ b @ (allegorical_A_Int @ b @ u @ v))))),
% 0.29/0.47 introduced(definition,[new_symbols(definition,[spl137_18])],[avatar_definition])).
% 0.29/0.47 thf(f1931,plain,(
% 0.29/0.47 (((restrict @ b @ nat @ (translation @ b @ (allegorical_A_Int @ b @ u @ v)))) != ((translation @ b @ (allegorical_A_Int @ b @ u @ v)))) | spl137_18),
% 0.29/0.47 inference(avatar_component_clause,[],[f1929])).
% 0.29/0.47 thf(f1932,plain,(
% 0.29/0.47 ~spl137_18 | spl137_12),
% 0.29/0.47 inference(avatar_split_clause,[],[f1926,f1895,f1929])).
% 0.29/0.47 thf(f1940,plain,(
% 0.29/0.47 ( ! [X0 : $tType,X1 : allegorical_term @ X0] : ((((translation @ X0 @ X1)) = (((^[Y0 : allegorical_term @ X0]: (restrict @ X0 @ nat @ (translation @ X0 @ Y0))) @ X1)))) )),
% 0.29/0.47 inference(argument_congruence,[],[f1401])).
% 0.29/0.47 thf(f1941,plain,(
% 0.29/0.47 ( ! [X0 : $tType,X1 : allegorical_term @ X0] : ((((translation @ X0 @ X1)) = ((restrict @ X0 @ nat @ (translation @ X0 @ X1))))) )),
% 0.29/0.47 inference(beta-eta_normalization,[],[f1940])).
% 0.29/0.47 thf(f1945,plain,(
% 0.29/0.47 (((translation @ b @ (allegorical_A_Int @ b @ u @ v))) != ((translation @ b @ (allegorical_A_Int @ b @ u @ v)))) | spl137_18),
% 0.29/0.47 inference(superposition,[],[f1931,f1941])).
% 0.29/0.47 thf(f1947,plain,(
% 0.29/0.47 $false | spl137_18),
% 0.29/0.47 inference(trivial_inequality_removal,[],[f1945])).
% 0.29/0.47 thf(f1948,plain,(
% 0.29/0.47 spl137_18),
% 0.29/0.47 inference(avatar_contradiction_clause,[],[f1947])).
% 0.29/0.47 thf(f1950,plain,(
% 0.29/0.47 (((finite_finite2 @ nat @ (labeled_vertices @ b @ nat @ (translation @ b @ (product_snd @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v))))))) != $true) | spl137_13),
% 0.29/0.47 inference(forward_demodulation,[],[f1901,f1359])).
% 0.29/0.47 thf(f1951,plain,(
% 0.29/0.47 $false | spl137_13),
% 0.29/0.47 inference(forward_subsumption_resolution,[],[f1950,f1553])).
% 0.29/0.47 thf(f1952,plain,(
% 0.29/0.47 spl137_13),
% 0.29/0.47 inference(avatar_contradiction_clause,[],[f1951])).
% 0.29/0.47 thf(f1953,plain,(
% 0.29/0.47 (((finite_finite2 @ product_prod @ b @ product_prod @ nat @ nat @ (labeled_edges @ b @ nat @ (translation @ b @ (product_snd @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v))))))) != $true) | spl137_14),
% 0.29/0.47 inference(forward_demodulation,[],[f1905,f1359])).
% 0.29/0.47 thf(f1955,plain,(
% 0.29/0.47 (((finite_finite2 @ product_prod @ b @ product_prod @ nat @ nat @ (labeled_edges @ b @ nat @ (translation @ b @ (allegorical_A_Int @ b @ u @ v))))) != $true) | spl137_14),
% 0.29/0.47 inference(forward_demodulation,[],[f1953,f1359])).
% 0.29/0.47 thf(f1957,definition,(
% 0.29/0.47 spl137_19 <=> (((finite_finite2 @ product_prod @ b @ product_prod @ nat @ nat @ (labeled_edges @ b @ nat @ (translation @ b @ (allegorical_A_Int @ b @ u @ v))))) = $true)),
% 0.29/0.47 introduced(definition,[new_symbols(definition,[spl137_19])],[avatar_definition])).
% 0.29/0.47 thf(f1959,plain,(
% 0.29/0.47 (((finite_finite2 @ product_prod @ b @ product_prod @ nat @ nat @ (labeled_edges @ b @ nat @ (translation @ b @ (allegorical_A_Int @ b @ u @ v))))) != $true) | spl137_19),
% 0.29/0.47 inference(avatar_component_clause,[],[f1957])).
% 0.29/0.47 thf(f1960,plain,(
% 0.29/0.47 ~spl137_19 | spl137_14),
% 0.29/0.47 inference(avatar_split_clause,[],[f1955,f1903,f1957])).
% 0.29/0.47 thf(f1965,plain,(
% 0.29/0.47 ($true != $true) | spl137_19),
% 0.29/0.47 inference(superposition,[],[f1959,f1444])).
% 0.29/0.47 thf(f1966,plain,(
% 0.29/0.47 $false | spl137_19),
% 0.29/0.47 inference(trivial_inequality_removal,[],[f1965])).
% 0.29/0.47 thf(f1967,plain,(
% 0.29/0.47 spl137_19),
% 0.29/0.47 inference(avatar_contradiction_clause,[],[f1966])).
% 0.29/0.47 thf(f1968,plain,(
% 0.29/0.47 (((graph_homomorphism @ b @ nat @ nat @ (translation @ b @ (product_fst @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))) @ (product_snd @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (product_Pair @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (translation @ b @ (product_fst @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))) @ (translation @ b @ (product_snd @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))))) @ (id_on @ nat @ (labeled_vertices @ b @ nat @ (translation @ b @ (product_fst @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))))))) != $true) | spl137_15),
% 0.29/0.47 inference(forward_demodulation,[],[f1909,f1534])).
% 0.29/0.47 thf(f1970,plain,(
% 0.29/0.47 (((graph_homomorphism @ b @ nat @ nat @ (translation @ b @ u) @ (product_snd @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (product_Pair @ labeled_graph @ b @ nat @ labeled_graph @ b @ nat @ (translation @ b @ u) @ (translation @ b @ (product_snd @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))))) @ (id_on @ nat @ (labeled_vertices @ b @ nat @ (translation @ b @ u))))) != $true) | spl137_15),
% 0.29/0.47 inference(forward_demodulation,[],[f1968,f1534])).
% 0.29/0.47 thf(f1971,plain,(
% 0.29/0.47 (((graph_homomorphism @ b @ nat @ nat @ (translation @ b @ u) @ (translation @ b @ (product_snd @ allegorical_term @ b @ allegorical_term @ b @ (product_Pair @ allegorical_term @ b @ allegorical_term @ b @ u @ (allegorical_A_Int @ b @ u @ v)))) @ (id_on @ nat @ (labeled_vertices @ b @ nat @ (translation @ b @ u))))) != $true) | spl137_15),
% 0.29/0.47 inference(forward_demodulation,[],[f1970,f1359])).
% 0.29/0.47 thf(f1972,plain,(
% 0.29/0.47 (((graph_homomorphism @ b @ nat @ nat @ (translation @ b @ u) @ (translation @ b @ (allegorical_A_Int @ b @ u @ v)) @ (id_on @ nat @ (labeled_vertices @ b @ nat @ (translation @ b @ u))))) != $true) | spl137_15),
% 0.29/0.47 inference(forward_demodulation,[],[f1971,f1359])).
% 0.29/0.47 thf(f1974,definition,(
% 0.29/0.47 spl137_20 <=> (((graph_homomorphism @ b @ nat @ nat @ (translation @ b @ u) @ (translation @ b @ (allegorical_A_Int @ b @ u @ v)) @ (id_on @ nat @ (labeled_vertices @ b @ nat @ (translation @ b @ u))))) = $true)),
% 0.29/0.47 introduced(definition,[new_symbols(definition,[spl137_20])],[avatar_definition])).
% 0.29/0.47 thf(f1976,plain,(
% 0.29/0.47 (((graph_homomorphism @ b @ nat @ nat @ (translation @ b @ u) @ (translation @ b @ (allegorical_A_Int @ b @ u @ v)) @ (id_on @ nat @ (labeled_vertices @ b @ nat @ (translation @ b @ u))))) != $true) | spl137_20),
% 0.29/0.47 inference(avatar_component_clause,[],[f1974])).
% 0.29/0.47 thf(f1977,plain,(
% 0.29/0.47 ~spl137_20 | spl137_15),
% 0.29/0.47 inference(avatar_split_clause,[],[f1972,f1907,f1974])).
% 0.29/0.47 thf(f2586,plain,(
% 0.29/0.47 ( ! [X0 : $tType,X2 : allegorical_term @ X0,X1 : allegorical_term @ X0] : ((((graph_homomorphism @ X0 @ nat @ nat @ (translation @ X0 @ X1) @ (product_snd @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat @ (product_Pair @ labeled_graph @ X0 @ nat @ labeled_graph @ X0 @ nat @ (translation @ X0 @ X1) @ (translation @ X0 @ (allegorical_A_Int @ X0 @ X1 @ X2)))) @ (id_on @ nat @ (labeled_vertices @ X0 @ nat @ (translation @ X0 @ X1))))) = $true)) )),
% 0.29/0.47 inference(forward_demodulation,[],[f1711,f1534])).
% 0.29/0.47 thf(f2587,plain,(
% 0.29/0.47 ( ! [X0 : $tType,X2 : allegorical_term @ X0,X1 : allegorical_term @ X0] : ((((graph_homomorphism @ X0 @ nat @ nat @ (translation @ X0 @ X1) @ (translation @ X0 @ (allegorical_A_Int @ X0 @ X1 @ X2)) @ (id_on @ nat @ (labeled_vertices @ X0 @ nat @ (translation @ X0 @ X1))))) = $true)) )),
% 0.29/0.47 inference(forward_demodulation,[],[f2586,f1359])).
% 0.29/0.47 thf(f2588,plain,(
% 0.29/0.47 ($true != $true) | spl137_20),
% 0.29/0.47 inference(superposition,[],[f1976,f2587])).
% 0.29/0.47 thf(f2594,plain,(
% 0.29/0.47 $false | spl137_20),
% 0.29/0.47 inference(trivial_inequality_removal,[],[f2588])).
% 0.29/0.47 thf(f2595,plain,(
% 0.29/0.47 spl137_20),
% 0.29/0.47 inference(avatar_contradiction_clause,[],[f2594])).
% 0.29/0.47 cnf(s12, plain, ~spl137_12 | ~spl137_13 | ~spl137_14 | ~spl137_15, inference(sat_conversion,[],[f1910])).
% 0.29/0.47 cnf(s15, plain, spl137_12 | ~spl137_18, inference(sat_conversion,[],[f1932])).
% 0.29/0.47 cnf(s17, plain, spl137_18, inference(sat_conversion,[],[f1948])).
% 0.29/0.47 cnf(s18, plain, spl137_13, inference(sat_conversion,[],[f1952])).
% 0.29/0.47 cnf(s19, plain, spl137_14 | ~spl137_19, inference(sat_conversion,[],[f1960])).
% 0.29/0.47 cnf(s20, plain, spl137_19, inference(sat_conversion,[],[f1967])).
% 0.29/0.47 cnf(s21, plain, spl137_15 | ~spl137_20, inference(sat_conversion,[],[f1977])).
% 0.29/0.47 cnf(s23, plain, spl137_20, inference(sat_conversion,[],[f2595])).
% 0.29/0.47 cnf(s24, plain, spl137_15, inference(rat,[],[s21,s23])).
% 0.29/0.47 cnf(s25, plain, spl137_14, inference(rat,[],[s19,s20])).
% 0.29/0.47 cnf(s26, plain, spl137_12, inference(rat,[],[s15,s17])).
% 0.29/0.47 cnf(s27, plain, $false, inference(rat,[],[s12,s24,s25,s18,s26])).
% 0.29/0.47 thf(f2599,plain,(
% 0.29/0.47 $false),
% 0.29/0.47 inference(avatar_sat_refutation,[],[s27])).
% 0.29/0.47 % SZS output end Proof for theBenchmark
% 0.29/0.47 % (3151510)------------------------------
% 0.29/0.47 % (3151510)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.29/0.47 % (3151510)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.29/0.47 % (3151510)CaDiCaL version: 2.1.3
% 0.29/0.47 % (3151510)Termination reason: Refutation
% 0.29/0.47 % (3151510)Time elapsed: 0.107 s
% 0.29/0.47 % (3151510)Peak memory usage: 16 MB
% 0.29/0.47 % (3151510)Instructions burned: 364 (million)
% 0.29/0.47 % (3151502)Success in time 0.164 s
% 0.29/0.47 % Vampire exiting
%------------------------------------------------------------------------------