%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COM165^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 07:46:22 AM UTC 2026
% Result : Theorem 0.48s 0.43s
% Output : Refutation 0.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COM165^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n018.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 17:49:56 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.20/0.27 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.48/0.41 % (413707)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.48/0.41 % (413712)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2084555172:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.48/0.41 % (413718)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.48/0.41 % (413718)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
% 0.48/0.41 % (413714)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2495900487:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.48/0.41 % (413715)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=1055466298: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)
% 0.48/0.41 % (413716)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2299397741:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.48/0.41 % (413717)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2394653460:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.48/0.41 % (413718)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=222273996:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.48/0.41 % (413713)lrs+10_16_si=on:nwc=1.5:random_seed=2440150505:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.48/0.41 % (413714)Instruction limit reached!
% 0.48/0.41 % (413714)------------------------------
% 0.48/0.41 % (413714)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.41 % (413714)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.41 % (413714)CaDiCaL version: 2.1.3
% 0.48/0.41 % (413714)Termination reason: Instruction limit
% 0.48/0.41 % (413714)Termination phase: shuffling
% 0.48/0.41 % (413714)Time elapsed: 0.004 s
% 0.48/0.41 % (413714)Peak memory usage: 10 MB
% 0.48/0.41 % (413714)Instructions burned: 7 (million)
% 0.48/0.41 % (413713)Instruction limit reached!
% 0.48/0.41 % (413713)------------------------------
% 0.48/0.41 % (413713)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.41 % (413713)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.41 % (413713)CaDiCaL version: 2.1.3
% 0.48/0.41 % (413713)Termination reason: Instruction limit
% 0.48/0.41 % (413713)Termination phase: Property scanning
% 0.48/0.41 % (413713)Time elapsed: 0.009 s
% 0.48/0.41 % (413713)Peak memory usage: 10 MB
% 0.48/0.41 % (413713)Instructions burned: 18 (million)
% 0.48/0.41 % (413716)Instruction limit reached!
% 0.48/0.41 % (413716)------------------------------
% 0.48/0.41 % (413716)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.41 % (413716)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.41 % (413716)CaDiCaL version: 2.1.3
% 0.48/0.41 % (413716)Termination reason: Instruction limit
% 0.48/0.41 % (413716)Termination phase: Property scanning
% 0.48/0.41 % (413716)Time elapsed: 0.012 s
% 0.48/0.41 % (413716)Peak memory usage: 10 MB
% 0.48/0.41 % (413716)Instructions burned: 25 (million)
% 0.48/0.41 % (413712)Instruction limit reached!
% 0.48/0.41 % (413712)------------------------------
% 0.48/0.41 % (413712)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.41 % (413712)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.41 % (413712)CaDiCaL version: 2.1.3
% 0.48/0.41 % (413712)Termination reason: Instruction limit
% 0.48/0.41 % (413712)Termination phase: Property scanning
% 0.48/0.41 % (413712)Time elapsed: 0.022 s
% 0.48/0.41 % (413712)Peak memory usage: 12 MB
% 0.48/0.41 % (413712)Instructions burned: 89 (million)
% 0.48/0.41 % (413726)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=122589021:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.48/0.41 % (413729)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3845063834:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.48/0.43 % (413726)Instruction limit reached!
% 0.48/0.43 % (413726)------------------------------
% 0.48/0.43 % (413726)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.43 % (413726)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.43 % (413726)CaDiCaL version: 2.1.3
% 0.48/0.43 % (413726)Termination reason: Instruction limit
% 0.48/0.43 % (413726)Termination phase: shuffling
% 0.48/0.43 % (413726)Time elapsed: 0.002 s
% 0.48/0.43 % (413726)Peak memory usage: 10 MB
% 0.48/0.43 % (413726)Instructions burned: 3 (million)
% 0.48/0.43 % (413729)Instruction limit reached!
% 0.48/0.43 % (413729)------------------------------
% 0.48/0.43 % (413729)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.43 % (413729)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.43 % (413729)CaDiCaL version: 2.1.3
% 0.48/0.43 % (413729)Termination reason: Instruction limit
% 0.48/0.43 % (413729)Termination phase: shuffling
% 0.48/0.43 % (413729)Time elapsed: 0.003 s
% 0.48/0.43 % (413729)Peak memory usage: 10 MB
% 0.48/0.43 % (413729)Instructions burned: 14 (million)
% 0.48/0.43 % (413728)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.48/0.43 % (413727)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=634458518:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.48/0.43 % (413728)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=472139179:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.48/0.43 % (413727)Instruction limit reached!
% 0.48/0.43 % (413727)------------------------------
% 0.48/0.43 % (413727)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.43 % (413727)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.43 % (413727)CaDiCaL version: 2.1.3
% 0.48/0.43 % (413727)Termination reason: Instruction limit
% 0.48/0.43 % (413727)Termination phase: shuffling
% 0.48/0.43 % (413727)Time elapsed: 0.004 s
% 0.48/0.43 % (413727)Peak memory usage: 10 MB
% 0.48/0.43 % (413727)Instructions burned: 7 (million)
% 0.48/0.43 % (413728)Instruction limit reached!
% 0.48/0.43 % (413728)------------------------------
% 0.48/0.43 % (413728)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.43 % (413728)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.43 % (413728)CaDiCaL version: 2.1.3
% 0.48/0.43 % (413728)Termination reason: Instruction limit
% 0.48/0.43 % (413728)Termination phase: shuffling
% 0.48/0.43 % (413728)Time elapsed: 0.004 s
% 0.48/0.43 % (413728)Peak memory usage: 10 MB
% 0.48/0.43 % (413728)Instructions burned: 8 (million)
% 0.48/0.43 % (413717)Instruction limit reached!
% 0.48/0.43 % (413717)------------------------------
% 0.48/0.43 % (413717)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.43 % (413717)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.43 % (413717)CaDiCaL version: 2.1.3
% 0.48/0.43 % (413717)Termination reason: Instruction limit
% 0.48/0.43 % (413717)Termination phase: Property scanning
% 0.48/0.43 % (413717)Time elapsed: 0.036 s
% 0.48/0.43 % (413717)Peak memory usage: 12 MB
% 0.48/0.43 % (413717)Instructions burned: 77 (million)
% 0.48/0.43 % (413733)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=715346491:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.48/0.43 % (413732)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
% 0.48/0.43 % (413732)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.48/0.43 % (413732)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1296106808:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.48/0.43 % (413737)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.48/0.43 % (413736)lrs+10_1_si=on:cs=on:random_seed=2584264092:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.48/0.43 % (413737)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=3666341859:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.48/0.43 % (413738)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2336062692:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.48/0.43 % (413737)Instruction limit reached!
% 0.48/0.43 % (413737)------------------------------
% 0.48/0.43 % (413737)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.43 % (413737)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.43 % (413737)CaDiCaL version: 2.1.3
% 0.48/0.43 % (413737)Termination reason: Instruction limit
% 0.48/0.43 % (413737)Termination phase: shuffling
% 0.48/0.43 % (413737)Time elapsed: 0.002 s
% 0.48/0.43 % (413737)Peak memory usage: 10 MB
% 0.48/0.43 % (413737)Instructions burned: 3 (million)
% 0.48/0.43 % (413736)Instruction limit reached!
% 0.48/0.43 % (413736)------------------------------
% 0.48/0.43 % (413736)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.43 % (413736)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.43 % (413736)CaDiCaL version: 2.1.3
% 0.48/0.43 % (413736)Termination reason: Instruction limit
% 0.48/0.43 % (413736)Termination phase: shuffling
% 0.48/0.43 % (413736)Time elapsed: 0.004 s
% 0.48/0.43 % (413736)Peak memory usage: 10 MB
% 0.48/0.43 % (413736)Instructions burned: 8 (million)
% 0.48/0.43 % (413732)Instruction limit reached!
% 0.48/0.43 % (413732)------------------------------
% 0.48/0.43 % (413732)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.43 % (413732)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.43 % (413732)CaDiCaL version: 2.1.3
% 0.48/0.43 % (413732)Termination reason: Instruction limit
% 0.48/0.43 % (413732)Termination phase: shuffling
% 0.48/0.43 % (413732)Time elapsed: 0.013 s
% 0.48/0.43 % (413732)Peak memory usage: 10 MB
% 0.48/0.43 % (413732)Instructions burned: 28 (million)
% 0.48/0.43 % (413733)Instruction limit reached!
% 0.48/0.43 % (413733)------------------------------
% 0.48/0.43 % (413733)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.43 % (413733)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.43 % (413733)CaDiCaL version: 2.1.3
% 0.48/0.43 % (413733)Termination reason: Instruction limit
% 0.48/0.43 % (413733)Termination phase: Property scanning
% 0.48/0.43 % (413733)Time elapsed: 0.019 s
% 0.48/0.43 % (413733)Peak memory usage: 11 MB
% 0.48/0.43 % (413733)Instructions burned: 86 (million)
% 0.48/0.43 % (413747)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=280638390:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.48/0.43 % (413718)Instruction limit reached!
% 0.48/0.43 % (413718)------------------------------
% 0.48/0.43 % (413718)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.43 % (413718)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.43 % (413718)CaDiCaL version: 2.1.3
% 0.48/0.43 % (413718)Termination reason: Instruction limit
% 0.48/0.43 % (413718)Termination phase: Saturation
% 0.48/0.43 % (413718)Time elapsed: 0.072 s
% 0.48/0.43 % (413718)Peak memory usage: 13 MB
% 0.48/0.43 % (413718)Instructions burned: 158 (million)
% 0.48/0.43 % (413744)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=2398870359:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.48/0.43 % (413738)Instruction limit reached!
% 0.48/0.43 % (413738)------------------------------
% 0.48/0.43 % (413738)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.43 % (413738)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.43 % (413738)CaDiCaL version: 2.1.3
% 0.48/0.43 % (413738)Termination reason: Instruction limit
% 0.48/0.43 % (413738)Termination phase: Equality resolution with deletion
% 0.48/0.43 % (413738)Time elapsed: 0.019 s
% 0.48/0.43 % (413738)Peak memory usage: 12 MB
% 0.48/0.43 % (413738)Instructions burned: 39 (million)
% 0.48/0.43 % (413745)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=1239299992:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.48/0.43 % (413746)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=3029744189:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.48/0.43 % (413749)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=1665739277:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 0.48/0.43 % (413715) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-413707-413715"...
% 0.48/0.43 % (413753)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=3886143185:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 0.48/0.43 % (413715)...printing done.
% 0.48/0.43 % (413753)Instruction limit reached!
% 0.48/0.43 % (413753)------------------------------
% 0.48/0.43 % (413753)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.43 % (413753)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.43 % (413753)CaDiCaL version: 2.1.3
% 0.48/0.43 % (413753)Termination reason: Instruction limit
% 0.48/0.43 % (413753)Termination phase: shuffling
% 0.48/0.43 % (413753)Time elapsed: 0.002 s
% 0.48/0.43 % (413753)Peak memory usage: 10 MB
% 0.48/0.43 % (413753)Instructions burned: 3 (million)
% 0.48/0.43 % (413715)Refutation found. Thanks to Tanya!
% 0.48/0.43 % SZS status Theorem for theBenchmark
% 0.48/0.43 % SZS output start Proof for theBenchmark
% 0.48/0.43 thf(type_def_5, type, binDag_Mirabelle_dag: $tType).
% 0.48/0.43 thf(type_def_6, type, simpl_ref: $tType).
% 0.48/0.43 thf(type_def_7, type, set: $tType > $tType).
% 0.48/0.43 thf(type_def_8, type, nat: $tType).
% 0.48/0.43 thf(type_def_9, type, itself: $tType > $tType).
% 0.48/0.43 thf(type_def_10, type, sTfun: ($tType * $tType) > $tType).
% 0.48/0.43 thf(func_def_0, type, type: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.48/0.43 thf(func_def_1, type, bot: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.48/0.43 thf(func_def_2, type, ord: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.48/0.43 thf(func_def_3, type, order: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.48/0.43 thf(func_def_4, type, no_bot: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.48/0.43 thf(func_def_5, type, no_top: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.48/0.43 thf(func_def_6, type, linorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.48/0.43 thf(func_def_7, type, preorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.48/0.43 thf(func_def_8, type, zero_neq_one: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.48/0.43 thf(func_def_9, type, order_bot: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.48/0.43 thf(func_def_10, type, wellorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.48/0.43 thf(func_def_11, type, zero_less_one: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.48/0.43 thf(func_def_12, type, dense_order: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.48/0.43 thf(func_def_13, type, linordered_idom: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.48/0.43 thf(func_def_14, type, linordered_field: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.48/0.43 thf(func_def_15, type, dense_linorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.48/0.43 thf(func_def_16, type, linordered_semidom: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.48/0.43 thf(func_def_17, type, linord1659791738miring: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.48/0.43 thf(func_def_18, type, canoni770627133id_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.48/0.43 thf(func_def_19, type, condit1656338222tinuum: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.48/0.43 thf(func_def_20, type, condit1037483654norder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.48/0.43 thf(func_def_21, type, binDag_Mirabelle_DAG: (binDag_Mirabelle_dag > $o)).
% 0.48/0.43 thf(func_def_22, type, binDag476092410e_Node: (binDag_Mirabelle_dag > simpl_ref > binDag_Mirabelle_dag > binDag_Mirabelle_dag)).
% 0.48/0.43 thf(func_def_23, type, binDag_Mirabelle_Tip: binDag_Mirabelle_dag).
% 0.48/0.43 thf(func_def_24, type, binDag1297733282se_dag: !>[X0: $tType]:((X0 > (binDag_Mirabelle_dag > simpl_ref > binDag_Mirabelle_dag > X0) > binDag_Mirabelle_dag > X0))).
% 0.48/0.43 thf(func_def_25, type, binDag1442713106ec_dag: !>[X0: $tType]:((X0 > (binDag_Mirabelle_dag > simpl_ref > binDag_Mirabelle_dag > X0 > X0 > X0) > binDag_Mirabelle_dag > X0))).
% 0.48/0.43 thf(func_def_26, type, binDag1924123185ze_dag: (binDag_Mirabelle_dag > nat)).
% 0.48/0.43 thf(func_def_27, type, binDag1380252983set_of: (binDag_Mirabelle_dag > set @ simpl_ref)).
% 0.48/0.43 thf(func_def_28, type, binDag786255756subdag: (binDag_Mirabelle_dag > binDag_Mirabelle_dag > $o)).
% 0.48/0.43 thf(func_def_29, type, one_one: !>[X0: $tType]:(X0)).
% 0.48/0.43 thf(func_def_30, type, sgn_sgn: !>[X0: $tType]:((X0 > X0))).
% 0.48/0.43 thf(func_def_31, type, zero_zero: !>[X0: $tType]:(X0)).
% 0.48/0.43 thf(func_def_32, type, if: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 0.48/0.43 thf(func_def_33, type, size_size: !>[X0: $tType]:((X0 > nat))).
% 0.48/0.43 thf(func_def_34, type, bot_bot: !>[X0: $tType]:(X0)).
% 0.48/0.43 thf(func_def_35, type, ord_less: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.48/0.43 thf(func_def_36, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.48/0.43 thf(func_def_37, type, ordering: !>[X0: $tType]:(((X0 > X0 > $o) > (X0 > X0 > $o) > $o))).
% 0.48/0.43 thf(func_def_38, type, type2: !>[X0: $tType]:(itself @ X0)).
% 0.48/0.43 thf(func_def_39, type, inv_imagep: !>[X0: $tType, X1: $tType]:(((X0 > X0 > $o) > (X1 > X0) > X1 > X1 > $o))).
% 0.48/0.43 thf(func_def_40, type, zero_neq_one_of_bool: !>[X0: $tType]:(($o > X0))).
% 0.48/0.43 thf(func_def_41, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.48/0.43 thf(func_def_42, type, is_empty: !>[X0: $tType]:((set @ X0 > $o))).
% 0.48/0.43 thf(func_def_43, type, chain_subset: !>[X0: $tType]:((set @ set @ X0 > $o))).
% 0.48/0.43 thf(func_def_44, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.48/0.43 thf(func_def_45, type, a: simpl_ref).
% 0.48/0.43 thf(func_def_46, type, l: binDag_Mirabelle_dag).
% 0.48/0.43 thf(func_def_47, type, r: binDag_Mirabelle_dag).
% 0.48/0.43 thf(func_def_48, type, thesis: $o).
% 0.48/0.43 thf(func_def_49, type, x: binDag_Mirabelle_dag).
% 0.48/0.43 thf(func_def_50, type, y: binDag_Mirabelle_dag).
% 0.48/0.43 thf(func_def_54, type, db0: !>[X0: $tType]:(X0)).
% 0.48/0.43 thf(func_def_55, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.48/0.43 thf(func_def_56, type, vOR: ($o > $o > $o)).
% 0.48/0.43 thf(func_def_57, type, db1: !>[X0: $tType]:(X0)).
% 0.48/0.43 thf(func_def_58, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.48/0.43 thf(func_def_59, type, vAND: ($o > $o > $o)).
% 0.48/0.43 thf(func_def_60, type, vNOT: ($o > $o)).
% 0.48/0.43 thf(func_def_61, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.48/0.43 thf(func_def_62, type, db2: !>[X0: $tType]:(X0)).
% 0.48/0.43 thf(func_def_63, type, vIMP: ($o > $o > $o)).
% 0.48/0.43 thf(func_def_64, type, db4: !>[X0: $tType]:(X0)).
% 0.48/0.43 thf(func_def_65, type, db3: !>[X0: $tType]:(X0)).
% 0.48/0.43 thf(func_def_66, type, sP0: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.48/0.43 thf(func_def_67, type, sP1: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.48/0.43 thf(func_def_68, type, sP2: !>[X0: $tType]:(((X0 > X0 > $o) > (X0 > X0 > $o) > $o))).
% 0.48/0.43 thf(func_def_69, type, sK3: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.48/0.43 thf(func_def_70, type, sK4: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.48/0.43 thf(func_def_71, type, sK5: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.48/0.43 thf(func_def_72, type, sK6: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.48/0.43 thf(func_def_73, type, sK7: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.48/0.43 thf(func_def_74, type, sK8: !>[X0: $tType, X1: $tType]:((X0 > X1))).
% 0.48/0.43 thf(func_def_75, type, sK9: !>[X0: $tType]:((X0 > X0))).
% 0.48/0.43 thf(func_def_76, type, sK10: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.48/0.43 thf(func_def_77, type, sK11: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.48/0.43 thf(func_def_78, type, sK12: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.48/0.43 thf(func_def_79, type, sK13: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 0.48/0.43 thf(func_def_80, type, sK14: !>[X0: $tType]:((X0 > X0 > X0 > X0))).
% 0.48/0.43 thf(func_def_81, type, sK15: !>[X0: $tType, X1: $tType]:((X0 > X1))).
% 0.48/0.43 thf(func_def_82, type, sK16: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.48/0.43 thf(func_def_83, type, sK17: !>[X0: $tType]:((X0 > X0))).
% 0.48/0.43 thf(func_def_84, type, sK18: !>[X0: $tType]:((X0 > X0))).
% 0.48/0.43 thf(func_def_85, type, sK19: !>[X0: $tType, X1: $tType]:((((X1 > X0) > X1 > X0 > $o) > X1 > X0))).
% 0.48/0.43 thf(func_def_86, type, sK20: !>[X0: $tType, X1: $tType]:((((X1 > X0) > X1 > X0 > $o) > X1 > X0))).
% 0.48/0.43 thf(func_def_87, type, sK21: !>[X0: $tType, X1: $tType]:((((X1 > X0) > X1 > X0 > $o) > X1))).
% 0.48/0.43 thf(func_def_88, type, sK22: !>[X0: $tType, X1: $tType]:((((X1 > X0) > X1 > X0 > $o) > X1 > X0))).
% 0.48/0.43 thf(func_def_89, type, sK23: !>[X0: $tType, X1: $tType]:((((X1 > X0) > X1 > X0 > $o) > X1 > X0))).
% 0.48/0.43 thf(func_def_90, type, sK24: !>[X0: $tType, X1: $tType]:((((X1 > X0) > X1 > X0 > $o) > X0))).
% 0.48/0.43 thf(func_def_91, type, sK25: !>[X0: $tType, X1: $tType]:((((X1 > X0) > X1 > X0 > $o) > X1))).
% 0.48/0.43 thf(func_def_92, type, sK26: !>[X0: $tType]:((X0 > X0))).
% 0.48/0.43 thf(func_def_93, type, sK27: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.48/0.43 thf(func_def_94, type, sK28: (binDag_Mirabelle_dag > simpl_ref)).
% 0.48/0.43 thf(func_def_95, type, sK29: (binDag_Mirabelle_dag > binDag_Mirabelle_dag)).
% 0.48/0.43 thf(func_def_96, type, sK30: (binDag_Mirabelle_dag > binDag_Mirabelle_dag)).
% 0.48/0.43 thf(func_def_97, type, sK31: !>[X0: $tType]:((X0 > X0))).
% 0.48/0.43 thf(func_def_98, type, sK32: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.48/0.43 thf(func_def_99, type, sK33: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 0.48/0.43 thf(func_def_100, type, sK34: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.48/0.43 thf(func_def_101, type, sK35: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.48/0.43 thf(func_def_102, type, sK36: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.48/0.43 thf(func_def_103, type, sK37: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.48/0.43 thf(func_def_104, type, sK38: !>[X0: $tType]:((X0 > X0))).
% 0.48/0.43 thf(func_def_105, type, sK39: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.48/0.43 thf(func_def_106, type, sK40: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.48/0.43 thf(func_def_107, type, sK41: !>[X0: $tType]:((X0 > X0))).
% 0.48/0.43 thf(func_def_108, type, sK42: !>[X0: $tType]:((X0 > X0))).
% 0.48/0.43 thf(func_def_109, type, sK43: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.48/0.43 thf(func_def_110, type, sK44: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.48/0.43 thf(func_def_111, type, sK45: !>[X0: $tType]:((X0 > X0))).
% 0.48/0.43 thf(func_def_112, type, sK46: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.48/0.43 thf(func_def_113, type, sK47: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.48/0.43 thf(func_def_114, type, sK48: !>[X0: $tType]:((X0 > X0 > X0 > X0))).
% 0.48/0.43 thf(func_def_115, type, sK49: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.48/0.43 thf(func_def_116, type, sK50: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.48/0.43 thf(func_def_117, type, sK51: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.48/0.43 thf(func_def_118, type, sK52: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.48/0.43 thf(func_def_119, type, sK53: !>[X0: $tType]:((X0 > X0 > (X0 > $o) > X0))).
% 0.48/0.43 thf(func_def_120, type, sK54: !>[X0: $tType]:((X0 > X0 > (X0 > $o) > X0))).
% 0.48/0.43 thf(func_def_121, type, sK55: !>[X0: $tType]:((X0 > X0))).
% 0.48/0.43 thf(func_def_122, type, sK56: !>[X0: $tType]:((X0 > X0))).
% 0.48/0.43 thf(func_def_123, type, sK57: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.48/0.43 thf(func_def_124, type, sK58: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.48/0.43 thf(func_def_125, type, sK59: !>[X0: $tType]:((set @ X0 > X0))).
% 0.48/0.43 thf(func_def_126, type, sK60: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.48/0.43 thf(func_def_127, type, sK61: !>[X0: $tType]:((X0 > X0))).
% 0.48/0.43 thf(func_def_128, type, sK62: !>[X0: $tType]:((X0 > X0))).
% 0.48/0.43 thf(func_def_129, type, sK63: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > X0))).
% 0.48/0.43 thf(func_def_130, type, sK64: !>[X0: $tType]:((set @ X0 > X0))).
% 0.48/0.43 thf(func_def_131, type, sK65: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.48/0.43 thf(func_def_132, type, sK66: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 0.48/0.43 thf(func_def_133, type, sK67: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.48/0.43 thf(func_def_134, type, sK68: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.48/0.43 thf(func_def_135, type, sK69: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.48/0.43 thf(func_def_136, type, sK70: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.48/0.43 thf(func_def_137, type, sK71: !>[X0: $tType]:((X0 > X0))).
% 0.48/0.43 thf(func_def_138, type, sK72: ((binDag_Mirabelle_dag > $o) > simpl_ref)).
% 0.48/0.43 thf(func_def_139, type, sK73: ((binDag_Mirabelle_dag > $o) > binDag_Mirabelle_dag)).
% 0.48/0.43 thf(func_def_140, type, sK74: ((binDag_Mirabelle_dag > $o) > binDag_Mirabelle_dag)).
% 0.48/0.43 thf(func_def_141, type, sK75: !>[X0: $tType]:((set @ X0 > X0))).
% 0.48/0.43 thf(func_def_142, type, sK76: !>[X0: $tType]:((X0 > X0))).
% 0.48/0.43 thf(func_def_143, type, sK77: !>[X0: $tType]:(((X0 > X0 > $o) > (X0 > X0 > $o) > X0))).
% 0.48/0.43 thf(func_def_144, type, sK78: !>[X0: $tType]:(((X0 > X0 > $o) > (X0 > X0 > $o) > X0))).
% 0.48/0.43 thf(func_def_145, type, sK79: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.48/0.43 thf(func_def_146, type, sK80: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.48/0.43 thf(func_def_147, type, sK81: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.48/0.43 thf(func_def_148, type, sK82: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.48/0.43 thf(func_def_149, type, sK83: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.48/0.43 thf(func_def_150, type, sK84: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.48/0.43 thf(func_def_151, type, sK85: !>[X0: $tType]:((set @ X0 > X0))).
% 0.48/0.43 thf(func_def_152, type, sK86: !>[X0: $tType]:((X0 > X0))).
% 0.48/0.43 thf(func_def_153, type, sK87: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 0.48/0.43 thf(func_def_154, type, sK88: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.48/0.43 thf(func_def_155, type, sK89: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.48/0.43 thf(func_def_156, type, sK90: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.48/0.43 thf(func_def_157, type, sK91: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.48/0.43 thf(func_def_158, type, sK92: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.48/0.43 thf(func_def_159, type, sK93: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.48/0.43 thf(func_def_160, type, sK94: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > X0))).
% 0.48/0.43 thf(func_def_161, type, sK95: !>[X0: $tType]:((X0 > X0))).
% 0.48/0.43 thf(func_def_162, type, sK96: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.48/0.43 thf(func_def_163, type, sK97: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.48/0.43 thf(func_def_164, type, sK98: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.48/0.43 thf(func_def_165, type, sK99: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.48/0.43 thf(func_def_166, type, sK100: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.48/0.43 thf(func_def_167, type, sK101: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.48/0.43 thf(func_def_168, type, sK102: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.48/0.43 thf(f1,axiom,(
% 0.48/0.43 (y = ((binDag476092410e_Node @ l @ a @ r)))),
% 0.48/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_Node)).
% 0.48/0.43 thf(f3,axiom,(
% 0.48/0.43 ! [X2 : binDag_Mirabelle_dag,X1 : simpl_ref,X0 : binDag_Mirabelle_dag] : (~(member @ simpl_ref @ X1 @ (binDag1380252983set_of @ X2)) & (binDag_Mirabelle_DAG @ X2) & ~(member @ simpl_ref @ X1 @ (binDag1380252983set_of @ X0)) & (binDag_Mirabelle_DAG @ X0) = ((binDag_Mirabelle_DAG @ (binDag476092410e_Node @ X0 @ X1 @ X2))))),
% 0.48/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_DAG_Osimps_I2_J)).
% 0.48/0.43 thf(f13,axiom,(
% 0.48/0.43 (binDag_Mirabelle_DAG @ y)),
% 0.48/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_DAG__y)).
% 0.48/0.43 thf(f293,axiom,(
% 0.48/0.43 ~(member @ simpl_ref @ a @ (binDag1380252983set_of @ l)) => (~(member @ simpl_ref @ a @ (binDag1380252983set_of @ r)) => thesis)),
% 0.48/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 0.48/0.43 thf(f294,conjecture,(
% 0.48/0.43 thesis),
% 0.48/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1)).
% 0.48/0.43 thf(f295,negated_conjecture,(
% 0.48/0.43 ~thesis),
% 0.48/0.43 inference(negated_conjecture,[status(cth)],[f294])).
% 0.48/0.43 thf(f520,plain,(
% 0.48/0.43 ! [X0 : binDag_Mirabelle_dag,X1 : simpl_ref,X2 : binDag_Mirabelle_dag] : (~(member @ simpl_ref @ X1 @ (binDag1380252983set_of @ X0)) & (binDag_Mirabelle_DAG @ X0) & ~(member @ simpl_ref @ X1 @ (binDag1380252983set_of @ X2)) & (binDag_Mirabelle_DAG @ X2) = ((binDag_Mirabelle_DAG @ (binDag476092410e_Node @ X2 @ X1 @ X0))))),
% 0.48/0.43 inference(rectify,[],[f3])).
% 0.48/0.43 thf(f521,plain,(
% 0.48/0.43 ! [X0 : binDag_Mirabelle_dag,X1 : simpl_ref,X2 : binDag_Mirabelle_dag] : ((~ (((member @ simpl_ref @ X1 @ (binDag1380252983set_of @ X0))) = $true) & (((binDag_Mirabelle_DAG @ X0)) = $true) & ~ (((member @ simpl_ref @ X1 @ (binDag1380252983set_of @ X2))) = $true) & (((binDag_Mirabelle_DAG @ X2)) = $true)) <=> ($true = ((binDag_Mirabelle_DAG @ (binDag476092410e_Node @ X2 @ X1 @ X0)))))),
% 0.48/0.43 inference(fool_elimination,[],[f520])).
% 0.48/0.43 thf(f721,plain,(
% 0.48/0.43 ~thesis),
% 0.48/0.43 inference(rectify,[],[f295])).
% 0.48/0.43 thf(f722,plain,(
% 0.48/0.43 ~ (thesis = $true)),
% 0.48/0.43 inference(fool_elimination,[],[f721])).
% 0.48/0.43 thf(f786,plain,(
% 0.48/0.43 ~(member @ simpl_ref @ a @ (binDag1380252983set_of @ l)) => (~(member @ simpl_ref @ a @ (binDag1380252983set_of @ r)) => thesis)),
% 0.48/0.43 inference(rectify,[],[f293])).
% 0.48/0.43 thf(f787,plain,(
% 0.48/0.43 ~ (((member @ simpl_ref @ a @ (binDag1380252983set_of @ l))) = $true) => (~ (((member @ simpl_ref @ a @ (binDag1380252983set_of @ r))) = $true) => (thesis = $true))),
% 0.48/0.43 inference(fool_elimination,[],[f786])).
% 0.48/0.43 thf(f801,plain,(
% 0.48/0.43 (binDag_Mirabelle_DAG @ y)),
% 0.48/0.43 inference(rectify,[],[f13])).
% 0.48/0.43 thf(f802,plain,(
% 0.48/0.43 (((binDag_Mirabelle_DAG @ y)) = $true)),
% 0.48/0.43 inference(fool_elimination,[],[f801])).
% 0.48/0.43 thf(f876,plain,(
% 0.48/0.43 ! [X1 : simpl_ref,X2 : binDag_Mirabelle_dag,X0 : binDag_Mirabelle_dag] : (((((member @ simpl_ref @ X1 @ (binDag1380252983set_of @ X0))) != $true) & (((binDag_Mirabelle_DAG @ X2)) = $true) & (((member @ simpl_ref @ X1 @ (binDag1380252983set_of @ X2))) != $true) & (((binDag_Mirabelle_DAG @ X0)) = $true)) <=> ($true = ((binDag_Mirabelle_DAG @ (binDag476092410e_Node @ X2 @ X1 @ X0)))))),
% 0.48/0.43 inference(flattening,[],[f521])).
% 0.48/0.43 thf(f897,plain,(
% 0.48/0.43 (thesis != $true)),
% 0.48/0.43 inference(flattening,[],[f722])).
% 0.48/0.43 thf(f903,plain,(
% 0.48/0.43 (((member @ simpl_ref @ a @ (binDag1380252983set_of @ l))) != $true) => ((((member @ simpl_ref @ a @ (binDag1380252983set_of @ r))) != $true) => (thesis = $true))),
% 0.48/0.43 inference(flattening,[],[f787])).
% 0.48/0.43 thf(f1044,plain,(
% 0.48/0.43 ((thesis = $true) | (((member @ simpl_ref @ a @ (binDag1380252983set_of @ r))) = $true)) | (((member @ simpl_ref @ a @ (binDag1380252983set_of @ l))) = $true)),
% 0.48/0.43 inference(ennf_transformation,[],[f903])).
% 0.48/0.43 thf(f1045,plain,(
% 0.48/0.43 (((member @ simpl_ref @ a @ (binDag1380252983set_of @ r))) = $true) | (((member @ simpl_ref @ a @ (binDag1380252983set_of @ l))) = $true) | (thesis = $true)),
% 0.48/0.43 inference(flattening,[],[f1044])).
% 0.48/0.43 thf(f1264,plain,(
% 0.48/0.43 ! [X1 : simpl_ref,X2 : binDag_Mirabelle_dag,X0 : binDag_Mirabelle_dag] : ((((((member @ simpl_ref @ X1 @ (binDag1380252983set_of @ X0))) != $true) & (((binDag_Mirabelle_DAG @ X2)) = $true) & (((member @ simpl_ref @ X1 @ (binDag1380252983set_of @ X2))) != $true) & (((binDag_Mirabelle_DAG @ X0)) = $true)) | ($true != ((binDag_Mirabelle_DAG @ (binDag476092410e_Node @ X2 @ X1 @ X0))))) & (($true = ((binDag_Mirabelle_DAG @ (binDag476092410e_Node @ X2 @ X1 @ X0)))) | ((((member @ simpl_ref @ X1 @ (binDag1380252983set_of @ X0))) = $true) | (((binDag_Mirabelle_DAG @ X2)) != $true) | (((member @ simpl_ref @ X1 @ (binDag1380252983set_of @ X2))) = $true) | (((binDag_Mirabelle_DAG @ X0)) != $true))))),
% 0.48/0.43 inference(nnf_transformation,[],[f876])).
% 0.48/0.43 thf(f1265,plain,(
% 0.48/0.43 ! [X1 : simpl_ref,X2 : binDag_Mirabelle_dag,X0 : binDag_Mirabelle_dag] : ((((((member @ simpl_ref @ X1 @ (binDag1380252983set_of @ X0))) != $true) & (((binDag_Mirabelle_DAG @ X2)) = $true) & (((member @ simpl_ref @ X1 @ (binDag1380252983set_of @ X2))) != $true) & (((binDag_Mirabelle_DAG @ X0)) = $true)) | ($true != ((binDag_Mirabelle_DAG @ (binDag476092410e_Node @ X2 @ X1 @ X0))))) & (($true = ((binDag_Mirabelle_DAG @ (binDag476092410e_Node @ X2 @ X1 @ X0)))) | (((member @ simpl_ref @ X1 @ (binDag1380252983set_of @ X0))) = $true) | (((binDag_Mirabelle_DAG @ X2)) != $true) | (((member @ simpl_ref @ X1 @ (binDag1380252983set_of @ X2))) = $true) | (((binDag_Mirabelle_DAG @ X0)) != $true)))),
% 0.48/0.43 inference(flattening,[],[f1264])).
% 0.48/0.43 thf(f1266,plain,(
% 0.48/0.43 ! [X0 : simpl_ref,X1 : binDag_Mirabelle_dag,X2 : binDag_Mirabelle_dag] : (((($true != ((member @ simpl_ref @ X0 @ (binDag1380252983set_of @ X2)))) & (((binDag_Mirabelle_DAG @ X1)) = $true) & ($true != ((member @ simpl_ref @ X0 @ (binDag1380252983set_of @ X1)))) & (((binDag_Mirabelle_DAG @ X2)) = $true)) | ($true != ((binDag_Mirabelle_DAG @ (binDag476092410e_Node @ X1 @ X0 @ X2))))) & (($true = ((binDag_Mirabelle_DAG @ (binDag476092410e_Node @ X1 @ X0 @ X2)))) | ($true = ((member @ simpl_ref @ X0 @ (binDag1380252983set_of @ X2)))) | (((binDag_Mirabelle_DAG @ X1)) != $true) | ($true = ((member @ simpl_ref @ X0 @ (binDag1380252983set_of @ X1)))) | (((binDag_Mirabelle_DAG @ X2)) != $true)))),
% 0.48/0.43 inference(rectify,[],[f1265])).
% 0.48/0.43 thf(f1476,plain,(
% 0.48/0.43 (y = ((binDag476092410e_Node @ l @ a @ r)))),
% 0.48/0.43 inference(cnf_transformation,[],[f1])).
% 0.48/0.43 thf(f1549,plain,(
% 0.48/0.43 ( ! [X2 : binDag_Mirabelle_dag,X0 : simpl_ref,X1 : binDag_Mirabelle_dag] : (($true != ((binDag_Mirabelle_DAG @ (binDag476092410e_Node @ X1 @ X0 @ X2)))) | ($true != ((member @ simpl_ref @ X0 @ (binDag1380252983set_of @ X1))))) )),
% 0.48/0.43 inference(cnf_transformation,[],[f1266])).
% 0.48/0.43 thf(f1551,plain,(
% 0.48/0.43 ( ! [X2 : binDag_Mirabelle_dag,X0 : simpl_ref,X1 : binDag_Mirabelle_dag] : (($true != ((binDag_Mirabelle_DAG @ (binDag476092410e_Node @ X1 @ X0 @ X2)))) | ($true != ((member @ simpl_ref @ X0 @ (binDag1380252983set_of @ X2))))) )),
% 0.48/0.43 inference(cnf_transformation,[],[f1266])).
% 0.48/0.43 thf(f1635,plain,(
% 0.48/0.43 (thesis != $true)),
% 0.48/0.43 inference(cnf_transformation,[],[f897])).
% 0.48/0.43 thf(f1818,plain,(
% 0.48/0.43 (((binDag_Mirabelle_DAG @ y)) = $true)),
% 0.48/0.43 inference(cnf_transformation,[],[f802])).
% 0.48/0.43 thf(f1892,plain,(
% 0.48/0.43 (thesis = $true) | (((member @ simpl_ref @ a @ (binDag1380252983set_of @ r))) = $true) | (((member @ simpl_ref @ a @ (binDag1380252983set_of @ l))) = $true)),
% 0.48/0.43 inference(cnf_transformation,[],[f1045])).
% 0.48/0.43 thf(f2234,definition,(
% 0.48/0.43 spl103_12 <=> (((member @ simpl_ref @ a @ (binDag1380252983set_of @ r))) = $true)),
% 0.48/0.43 introduced(definition,[new_symbols(definition,[spl103_12])],[avatar_definition])).
% 0.48/0.43 thf(f2236,plain,(
% 0.48/0.43 (((member @ simpl_ref @ a @ (binDag1380252983set_of @ r))) = $true) | ~spl103_12),
% 0.48/0.43 inference(avatar_component_clause,[],[f2234])).
% 0.48/0.43 thf(f2238,definition,(
% 0.48/0.43 spl103_13 <=> (thesis = $true)),
% 0.48/0.43 introduced(definition,[new_symbols(definition,[spl103_13])],[avatar_definition])).
% 0.48/0.43 thf(f2242,definition,(
% 0.48/0.43 spl103_14 <=> (((member @ simpl_ref @ a @ (binDag1380252983set_of @ l))) = $true)),
% 0.48/0.43 introduced(definition,[new_symbols(definition,[spl103_14])],[avatar_definition])).
% 0.48/0.43 thf(f2245,plain,(
% 0.48/0.43 spl103_12 | spl103_13 | spl103_14),
% 0.48/0.43 inference(avatar_split_clause,[],[f1892,f2242,f2238,f2234])).
% 0.48/0.43 thf(f2246,plain,(
% 0.48/0.43 ~spl103_13),
% 0.48/0.43 inference(avatar_split_clause,[],[f1635,f2238])).
% 0.48/0.43 thf(f2298,definition,(
% 0.48/0.43 spl103_25 <=> (((binDag_Mirabelle_DAG @ y)) = $true)),
% 0.48/0.43 introduced(definition,[new_symbols(definition,[spl103_25])],[avatar_definition])).
% 0.48/0.43 thf(f2300,plain,(
% 0.48/0.43 (((binDag_Mirabelle_DAG @ y)) = $true) | ~spl103_25),
% 0.48/0.43 inference(avatar_component_clause,[],[f2298])).
% 0.48/0.43 thf(f2301,plain,(
% 0.48/0.43 spl103_25),
% 0.48/0.43 inference(avatar_split_clause,[],[f1818,f2298])).
% 0.48/0.43 thf(f2353,definition,(
% 0.48/0.43 spl103_36 <=> (y = ((binDag476092410e_Node @ l @ a @ r)))),
% 0.48/0.43 introduced(definition,[new_symbols(definition,[spl103_36])],[avatar_definition])).
% 0.48/0.43 thf(f2355,plain,(
% 0.48/0.43 (y = ((binDag476092410e_Node @ l @ a @ r))) | ~spl103_36),
% 0.48/0.43 inference(avatar_component_clause,[],[f2353])).
% 0.48/0.43 thf(f2356,plain,(
% 0.48/0.43 spl103_36),
% 0.48/0.43 inference(avatar_split_clause,[],[f1476,f2353])).
% 0.48/0.43 thf(f2589,plain,(
% 0.48/0.43 (((binDag_Mirabelle_DAG @ y)) != $true) | (((member @ simpl_ref @ a @ (binDag1380252983set_of @ l))) != $true) | ~spl103_36),
% 0.48/0.43 inference(superposition,[],[f1549,f2355])).
% 0.48/0.43 thf(f2591,plain,(
% 0.48/0.43 (((member @ simpl_ref @ a @ (binDag1380252983set_of @ l))) != $true) | (~spl103_25 | ~spl103_36)),
% 0.48/0.43 inference(forward_subsumption_resolution,[],[f2589,f2300])).
% 0.48/0.43 thf(f2592,plain,(
% 0.48/0.43 ~spl103_14 | ~spl103_25 | ~spl103_36),
% 0.48/0.43 inference(avatar_split_clause,[],[f2591,f2353,f2298,f2242])).
% 0.48/0.43 thf(f2667,plain,(
% 0.48/0.43 (((member @ simpl_ref @ a @ (binDag1380252983set_of @ r))) != $true) | (((binDag_Mirabelle_DAG @ y)) != $true) | ~spl103_36),
% 0.48/0.43 inference(superposition,[],[f1551,f2355])).
% 0.48/0.43 thf(f2669,plain,(
% 0.48/0.43 (((binDag_Mirabelle_DAG @ y)) != $true) | (~spl103_12 | ~spl103_36)),
% 0.48/0.43 inference(forward_subsumption_resolution,[],[f2667,f2236])).
% 0.48/0.43 thf(f2670,plain,(
% 0.48/0.43 $false | (~spl103_12 | ~spl103_25 | ~spl103_36)),
% 0.48/0.43 inference(forward_subsumption_resolution,[],[f2669,f2300])).
% 0.48/0.43 thf(f2671,plain,(
% 0.48/0.43 ~spl103_12 | ~spl103_25 | ~spl103_36),
% 0.48/0.43 inference(avatar_contradiction_clause,[],[f2670])).
% 0.48/0.43 cnf(s12, plain, spl103_12 | spl103_13 | spl103_14, inference(sat_conversion,[],[f2245])).
% 0.48/0.43 cnf(s13, plain, ~spl103_13, inference(sat_conversion,[],[f2246])).
% 0.48/0.43 cnf(s25, plain, spl103_25, inference(sat_conversion,[],[f2301])).
% 0.48/0.43 cnf(s37, plain, spl103_36, inference(sat_conversion,[],[f2356])).
% 0.48/0.43 cnf(s51, plain, ~spl103_14 | ~spl103_25 | ~spl103_36, inference(sat_conversion,[],[f2592])).
% 0.48/0.43 cnf(s52, plain, ~spl103_12 | ~spl103_25 | ~spl103_36, inference(sat_conversion,[],[f2671])).
% 0.48/0.43 cnf(s60, plain, ~spl103_12, inference(rat,[],[s52,s37,s25])).
% 0.48/0.43 cnf(s61, plain, ~spl103_14, inference(rat,[],[s51,s37,s25])).
% 0.48/0.43 cnf(s65, plain, $false, inference(rat,[],[s12,s61,s13,s60])).
% 0.48/0.43 thf(f2672,plain,(
% 0.48/0.43 $false),
% 0.48/0.43 inference(avatar_sat_refutation,[],[s65])).
% 0.48/0.43 % SZS output end Proof for theBenchmark
% 0.48/0.43 % (413715)------------------------------
% 0.48/0.43 % (413715)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.43 % (413715)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.43 % (413715)CaDiCaL version: 2.1.3
% 0.48/0.43 % (413715)Termination reason: Refutation
% 0.48/0.43 % (413715)Time elapsed: 0.096 s
% 0.48/0.43 % (413715)Peak memory usage: 15 MB
% 0.48/0.43 % (413715)Instructions burned: 188 (million)
% 0.48/0.43 % (413707)Success in time 0.152 s
% 0.48/0.43 % Vampire exiting
%------------------------------------------------------------------------------