%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP051^1 : 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 : 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 08:08:07 AM UTC 2026
% Result : ContradictoryAxioms 0.78s 0.42s
% Output : Refutation 0.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP051^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/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
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 19:45:56 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running higher-order theorem proving
% 0.08/0.26 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
% 0.78/0.42 % (554925)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.78/0.42 % (554935)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3284456971:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.78/0.42 % (554936)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.78/0.42 % (554936)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
% 0.78/0.42 % (554931)lrs+10_16_si=on:nwc=1.5:random_seed=2008955612:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.78/0.42 % (554933)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=3401556477: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)
% 0.78/0.42 % (554930)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3571735441:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.78/0.42 % (554936)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=2302758348:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.78/0.42 % (554934)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1749418496:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.78/0.42 % (554932)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2930194936:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.78/0.42 % (554932)Instruction limit reached!
% 0.78/0.42 % (554932)------------------------------
% 0.78/0.42 % (554932)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.42 % (554932)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.42 % (554932)CaDiCaL version: 2.1.3
% 0.78/0.42 % (554932)Termination reason: Instruction limit
% 0.78/0.42 % (554932)Termination phase: shuffling
% 0.78/0.42 % (554932)Time elapsed: 0.002 s
% 0.78/0.42 % (554932)Peak memory usage: 10 MB
% 0.78/0.42 % (554932)Instructions burned: 3 (million)
% 0.78/0.42 % (554931)Instruction limit reached!
% 0.78/0.42 % (554931)------------------------------
% 0.78/0.42 % (554931)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.42 % (554931)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.42 % (554931)CaDiCaL version: 2.1.3
% 0.78/0.42 % (554931)Termination reason: Instruction limit
% 0.78/0.42 % (554931)Termination phase: shuffling
% 0.78/0.42 % (554931)Time elapsed: 0.009 s
% 0.78/0.42 % (554931)Peak memory usage: 10 MB
% 0.78/0.42 % (554931)Instructions burned: 19 (million)
% 0.78/0.42 % (554934)Instruction limit reached!
% 0.78/0.42 % (554934)------------------------------
% 0.78/0.42 % (554934)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.42 % (554934)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.42 % (554934)CaDiCaL version: 2.1.3
% 0.78/0.42 % (554934)Termination reason: Instruction limit
% 0.78/0.42 % (554934)Termination phase: Property scanning
% 0.78/0.42 % (554934)Time elapsed: 0.013 s
% 0.78/0.42 % (554934)Peak memory usage: 10 MB
% 0.78/0.42 % (554934)Instructions burned: 29 (million)
% 0.78/0.42 % (554935)Instruction limit reached!
% 0.78/0.42 % (554935)------------------------------
% 0.78/0.42 % (554935)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.42 % (554935)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.42 % (554935)CaDiCaL version: 2.1.3
% 0.78/0.42 % (554935)Termination reason: Instruction limit
% 0.78/0.42 % (554935)Termination phase: Equality resolution with deletion
% 0.78/0.42 % (554935)Time elapsed: 0.021 s
% 0.78/0.42 % (554935)Peak memory usage: 12 MB
% 0.78/0.42 % (554935)Instructions burned: 78 (million)
% 0.78/0.42 % (554944)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1512109491:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.78/0.42 % (554944)Instruction limit reached!
% 0.78/0.42 % (554944)------------------------------
% 0.78/0.42 % (554944)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.42 % (554944)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.42 % (554944)CaDiCaL version: 2.1.3
% 0.78/0.42 % (554944)Termination reason: Instruction limit
% 0.78/0.42 % (554944)Termination phase: shuffling
% 0.78/0.42 % (554944)Time elapsed: 0.001 s
% 0.78/0.42 % (554944)Peak memory usage: 10 MB
% 0.78/0.42 % (554944)Instructions burned: 2 (million)
% 0.78/0.42 % (554947)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1796707464:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.78/0.42 % (554945)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1772207278:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.78/0.42 % (554946)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.78/0.42 % (554945)Instruction limit reached!
% 0.78/0.42 % (554945)------------------------------
% 0.78/0.42 % (554945)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.42 % (554945)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.42 % (554945)CaDiCaL version: 2.1.3
% 0.78/0.42 % (554945)Termination reason: Instruction limit
% 0.78/0.42 % (554945)Termination phase: shuffling
% 0.78/0.42 % (554945)Time elapsed: 0.002 s
% 0.78/0.42 % (554945)Peak memory usage: 10 MB
% 0.78/0.42 % (554945)Instructions burned: 5 (million)
% 0.78/0.42 % (554947)Instruction limit reached!
% 0.78/0.42 % (554947)------------------------------
% 0.78/0.42 % (554947)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.42 % (554947)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.42 % (554947)CaDiCaL version: 2.1.3
% 0.78/0.42 % (554947)Termination reason: Instruction limit
% 0.78/0.42 % (554947)Termination phase: shuffling
% 0.78/0.42 % (554947)Time elapsed: 0.004 s
% 0.78/0.42 % (554947)Peak memory usage: 10 MB
% 0.78/0.42 % (554947)Instructions burned: 13 (million)
% 0.78/0.42 % (554946)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3378025015:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.78/0.42 % (554949)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
% 0.78/0.42 % (554949)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.78/0.42 % (554930)Instruction limit reached!
% 0.78/0.42 % (554930)------------------------------
% 0.78/0.42 % (554930)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.42 % (554930)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.42 % (554930)CaDiCaL version: 2.1.3
% 0.78/0.42 % (554930)Termination reason: Instruction limit
% 0.78/0.42 % (554930)Termination phase: Property scanning
% 0.78/0.42 % (554930)Time elapsed: 0.040 s
% 0.78/0.42 % (554930)Peak memory usage: 12 MB
% 0.78/0.42 % (554930)Instructions burned: 87 (million)
% 0.78/0.42 % (554946)Instruction limit reached!
% 0.78/0.42 % (554946)------------------------------
% 0.78/0.42 % (554946)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.42 % (554946)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.42 % (554946)CaDiCaL version: 2.1.3
% 0.78/0.42 % (554946)Termination reason: Instruction limit
% 0.78/0.42 % (554946)Termination phase: shuffling
% 0.78/0.42 % (554946)Time elapsed: 0.007 s
% 0.78/0.42 % (554946)Peak memory usage: 10 MB
% 0.78/0.42 % (554946)Instructions burned: 7 (million)
% 0.78/0.42 % (554949)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2085197358:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.78/0.42 % (554952)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=2387362377:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.78/0.42 % (554955)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.78/0.42 % (554955)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=366300047:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.78/0.42 % (554956)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=3070641064:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.78/0.42 % (554949)Instruction limit reached!
% 0.78/0.42 % (554949)------------------------------
% 0.78/0.42 % (554949)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.42 % (554949)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.42 % (554949)CaDiCaL version: 2.1.3
% 0.78/0.42 % (554949)Termination reason: Instruction limit
% 0.78/0.42 % (554949)Termination phase: shuffling
% 0.78/0.42 % (554949)Time elapsed: 0.017 s
% 0.78/0.42 % (554949)Peak memory usage: 10 MB
% 0.78/0.42 % (554949)Instructions burned: 28 (million)
% 0.78/0.42 % (554955)Instruction limit reached!
% 0.78/0.42 % (554955)------------------------------
% 0.78/0.42 % (554955)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.42 % (554955)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.42 % (554955)CaDiCaL version: 2.1.3
% 0.78/0.42 % (554955)Termination reason: Instruction limit
% 0.78/0.42 % (554955)Termination phase: shuffling
% 0.78/0.42 % (554955)Time elapsed: 0.002 s
% 0.78/0.42 % (554955)Peak memory usage: 10 MB
% 0.78/0.42 % (554955)Instructions burned: 3 (million)
% 0.78/0.42 % (554954)lrs+10_1_si=on:cs=on:random_seed=2153090335:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.78/0.42 % (554936)Instruction limit reached!
% 0.78/0.42 % (554936)------------------------------
% 0.78/0.42 % (554936)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.42 % (554936)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.42 % (554936)CaDiCaL version: 2.1.3
% 0.78/0.42 % (554936)Termination reason: Instruction limit
% 0.78/0.42 % (554936)Termination phase: Saturation
% 0.78/0.42 % (554936)Time elapsed: 0.072 s
% 0.78/0.42 % (554954)Instruction limit reached!
% 0.78/0.42 % (554954)------------------------------
% 0.78/0.42 % (554954)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.42 % (554936)Peak memory usage: 14 MB
% 0.78/0.42 % (554954)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.42 % (554936)Instructions burned: 157 (million)
% 0.78/0.42 % (554954)CaDiCaL version: 2.1.3
% 0.78/0.42 % (554954)Termination reason: Instruction limit
% 0.78/0.42 % (554954)Termination phase: shuffling
% 0.78/0.42 % (554954)Time elapsed: 0.007 s
% 0.78/0.42 % (554954)Peak memory usage: 10 MB
% 0.78/0.42 % (554954)Instructions burned: 8 (million)
% 0.78/0.42 % (554961)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=766241214:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.78/0.42 % (554962)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=896333960:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.78/0.42 % (554956)Refutation not found, incomplete strategy
% 0.78/0.42 % (554956)------------------------------
% 0.78/0.42 % (554956)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.42 % (554956)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.42 % (554956)CaDiCaL version: 2.1.3
% 0.78/0.42 % (554956)Termination reason: Refutation not found, incomplete strategy
% 0.78/0.42 % (554956)Time elapsed: 0.026 s
% 0.78/0.42 % (554956)Peak memory usage: 12 MB
% 0.78/0.42 % (554956)Instructions burned: 38 (million)
% 0.78/0.42 % (554952)Instruction limit reached!
% 0.78/0.42 % (554952)------------------------------
% 0.78/0.42 % (554952)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.42 % (554952)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.42 % (554952)CaDiCaL version: 2.1.3
% 0.78/0.42 % (554952)Termination reason: Instruction limit
% 0.78/0.42 % (554952)Termination phase: Function definition elimination
% 0.78/0.42 % (554952)Time elapsed: 0.037 s
% 0.78/0.42 % (554952)Peak memory usage: 11 MB
% 0.78/0.42 % (554952)Instructions burned: 86 (million)
% 0.78/0.42 % (554956)------------------------------
% 0.78/0.42 % (554956)------------------------------
% 0.78/0.42 % (554933) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-554925-554933"...
% 0.78/0.42 % (554964)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=2629699051:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.78/0.42 % (554933)...printing done.
% 0.78/0.42 % (554962)Instruction limit reached!
% 0.78/0.42 % (554962)------------------------------
% 0.78/0.42 % (554962)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.42 % (554962)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.42 % (554962)CaDiCaL version: 2.1.3
% 0.78/0.42 % (554962)Termination reason: Instruction limit
% 0.78/0.42 % (554962)Termination phase: Property scanning
% 0.78/0.42 % (554962)Time elapsed: 0.011 s
% 0.78/0.42 % (554962)Peak memory usage: 10 MB
% 0.78/0.42 % (554962)Instructions burned: 26 (million)
% 0.78/0.42 % (554933)Refutation found. Thanks to Tanya!
% 0.78/0.42 % SZS status ContradictoryAxioms for theBenchmark
% 0.78/0.42 % SZS output start Proof for theBenchmark
% 0.78/0.42 thf(type_def_5, type, set_li664300135at_nat: $tType).
% 0.78/0.42 thf(type_def_6, type, set_se1612935105at_nat: $tType).
% 0.78/0.42 thf(type_def_7, type, list_P559422087at_nat: $tType).
% 0.78/0.42 thf(type_def_8, type, set_Pr1986765409at_nat: $tType).
% 0.78/0.42 thf(type_def_9, type, product_prod_nat_nat: $tType).
% 0.78/0.42 thf(type_def_10, type, set_set_nat: $tType).
% 0.78/0.42 thf(type_def_11, type, set_nat: $tType).
% 0.78/0.42 thf(type_def_12, type, nat: $tType).
% 0.78/0.42 thf(type_def_13, type, b: $tType).
% 0.78/0.42 thf(type_def_14, type, a: $tType).
% 0.78/0.42 thf(type_def_15, type, sTfun: ($tType * $tType) > $tType).
% 0.78/0.42 thf(func_def_0, type, edmond1517640972ysis_a: ((product_prod_nat_nat > a) > $o)).
% 0.78/0.42 thf(func_def_1, type, edmond1517640973ysis_b: ((product_prod_nat_nat > b) > $o)).
% 0.78/0.42 thf(func_def_2, type, edmond1022345716sure_a: ((product_prod_nat_nat > a) > nat > nat > nat)).
% 0.78/0.42 thf(func_def_3, type, edmond1022345717sure_b: ((product_prod_nat_nat > b) > nat > nat > nat)).
% 0.78/0.42 thf(func_def_4, type, edmond475474835dges_a: ((product_prod_nat_nat > a) > nat > nat > set_Pr1986765409at_nat)).
% 0.78/0.42 thf(func_def_5, type, edmond475474836dges_b: ((product_prod_nat_nat > b) > nat > nat > set_Pr1986765409at_nat)).
% 0.78/0.42 thf(func_def_6, type, edmond771116670s_uE_a: ((product_prod_nat_nat > a) > set_Pr1986765409at_nat)).
% 0.78/0.42 thf(func_def_7, type, edmond771116671s_uE_b: ((product_prod_nat_nat > b) > set_Pr1986765409at_nat)).
% 0.78/0.42 thf(func_def_8, type, finite83082927at_nat: (set_li664300135at_nat > nat)).
% 0.78/0.42 thf(func_def_9, type, finite_card_nat: (set_nat > nat)).
% 0.78/0.42 thf(func_def_10, type, finite447719721at_nat: (set_Pr1986765409at_nat > nat)).
% 0.78/0.42 thf(func_def_11, type, finite_card_set_nat: (set_set_nat > nat)).
% 0.78/0.42 thf(func_def_12, type, finite1701894793at_nat: (set_se1612935105at_nat > nat)).
% 0.78/0.42 thf(func_def_13, type, finite1299096496at_nat: (set_li664300135at_nat > $o)).
% 0.78/0.42 thf(func_def_14, type, finite_finite_nat: (set_nat > $o)).
% 0.78/0.42 thf(func_def_15, type, finite772653738at_nat: (set_Pr1986765409at_nat > $o)).
% 0.78/0.42 thf(func_def_16, type, finite2012248349et_nat: (set_set_nat > $o)).
% 0.78/0.42 thf(func_def_17, type, finite1457549322at_nat: (set_se1612935105at_nat > $o)).
% 0.78/0.42 thf(func_def_18, type, finite_Graph_a: ((product_prod_nat_nat > a) > $o)).
% 0.78/0.42 thf(func_def_19, type, finite_Graph_b: ((product_prod_nat_nat > b) > $o)).
% 0.78/0.42 thf(func_def_20, type, e_a: ((product_prod_nat_nat > a) > set_Pr1986765409at_nat)).
% 0.78/0.42 thf(func_def_21, type, e_b: ((product_prod_nat_nat > b) > set_Pr1986765409at_nat)).
% 0.78/0.42 thf(func_def_22, type, v_a: ((product_prod_nat_nat > a) > set_nat)).
% 0.78/0.42 thf(func_def_23, type, v_b: ((product_prod_nat_nat > b) > set_nat)).
% 0.78/0.42 thf(func_def_24, type, adjacent_nodes_a: ((product_prod_nat_nat > a) > nat > set_nat)).
% 0.78/0.42 thf(func_def_25, type, adjacent_nodes_b: ((product_prod_nat_nat > b) > nat > set_nat)).
% 0.78/0.42 thf(func_def_26, type, connected_a: ((product_prod_nat_nat > a) > nat > nat > $o)).
% 0.78/0.42 thf(func_def_27, type, connected_b: ((product_prod_nat_nat > b) > nat > nat > $o)).
% 0.78/0.42 thf(func_def_28, type, dist_a: ((product_prod_nat_nat > a) > nat > nat > nat > $o)).
% 0.78/0.42 thf(func_def_29, type, dist_b: ((product_prod_nat_nat > b) > nat > nat > nat > $o)).
% 0.78/0.42 thf(func_def_30, type, incoming_a: ((product_prod_nat_nat > a) > set_nat > set_Pr1986765409at_nat)).
% 0.78/0.42 thf(func_def_31, type, incoming_b: ((product_prod_nat_nat > b) > set_nat > set_Pr1986765409at_nat)).
% 0.78/0.42 thf(func_def_32, type, isPath_a: ((product_prod_nat_nat > a) > nat > list_P559422087at_nat > nat > $o)).
% 0.78/0.42 thf(func_def_33, type, isPath_b: ((product_prod_nat_nat > b) > nat > list_P559422087at_nat > nat > $o)).
% 0.78/0.42 thf(func_def_34, type, isShortestPath_a: ((product_prod_nat_nat > a) > nat > list_P559422087at_nat > nat > $o)).
% 0.78/0.42 thf(func_def_35, type, isShortestPath_b: ((product_prod_nat_nat > b) > nat > list_P559422087at_nat > nat > $o)).
% 0.78/0.42 thf(func_def_36, type, isSimplePath_a: ((product_prod_nat_nat > a) > nat > list_P559422087at_nat > nat > $o)).
% 0.78/0.42 thf(func_def_37, type, isSimplePath_b: ((product_prod_nat_nat > b) > nat > list_P559422087at_nat > nat > $o)).
% 0.78/0.42 thf(func_def_38, type, min_dist_a: ((product_prod_nat_nat > a) > nat > nat > nat)).
% 0.78/0.42 thf(func_def_39, type, min_dist_b: ((product_prod_nat_nat > b) > nat > nat > nat)).
% 0.78/0.42 thf(func_def_40, type, outgoing_a: ((product_prod_nat_nat > a) > set_nat > set_Pr1986765409at_nat)).
% 0.78/0.42 thf(func_def_41, type, outgoing_b: ((product_prod_nat_nat > b) > set_nat > set_Pr1986765409at_nat)).
% 0.78/0.42 thf(func_def_42, type, reachableNodes_a: ((product_prod_nat_nat > a) > nat > set_nat)).
% 0.78/0.42 thf(func_def_43, type, reachableNodes_b: ((product_prod_nat_nat > b) > nat > set_nat)).
% 0.78/0.42 thf(func_def_44, type, zero_zero_nat: nat).
% 0.78/0.42 thf(func_def_45, type, set_Pr2131844118at_nat: (list_P559422087at_nat > set_Pr1986765409at_nat)).
% 0.78/0.42 thf(func_def_46, type, size_s1990949619at_nat: (list_P559422087at_nat > nat)).
% 0.78/0.42 thf(func_def_47, type, ord_less_nat: (nat > nat > $o)).
% 0.78/0.42 thf(func_def_48, type, ord_less_set_nat: (set_nat > set_nat > $o)).
% 0.78/0.42 thf(func_def_49, type, ord_le116442893at_nat: (set_Pr1986765409at_nat > set_Pr1986765409at_nat > $o)).
% 0.78/0.42 thf(func_def_50, type, ord_less_eq_nat: (nat > nat > $o)).
% 0.78/0.42 thf(func_def_51, type, ord_less_eq_set_nat: (set_nat > set_nat > $o)).
% 0.78/0.42 thf(func_def_52, type, ord_le841296385at_nat: (set_Pr1986765409at_nat > set_Pr1986765409at_nat > $o)).
% 0.78/0.42 thf(func_def_53, type, ord_le1613022364et_nat: (set_set_nat > set_set_nat > $o)).
% 0.78/0.42 thf(func_def_54, type, ord_le2096002913at_nat: (set_se1612935105at_nat > set_se1612935105at_nat > $o)).
% 0.78/0.42 thf(func_def_55, type, collect_nat: ((nat > $o) > set_nat)).
% 0.78/0.42 thf(func_def_56, type, collec7649004at_nat: ((product_prod_nat_nat > $o) > set_Pr1986765409at_nat)).
% 0.78/0.42 thf(func_def_57, type, collect_set_nat: ((set_nat > $o) > set_set_nat)).
% 0.78/0.42 thf(func_def_58, type, collec1606769740at_nat: ((set_Pr1986765409at_nat > $o) > set_se1612935105at_nat)).
% 0.78/0.42 thf(func_def_59, type, member1608759472at_nat: (list_P559422087at_nat > set_li664300135at_nat > $o)).
% 0.78/0.42 thf(func_def_60, type, member_nat: (nat > set_nat > $o)).
% 0.78/0.42 thf(func_def_61, type, member701585322at_nat: (product_prod_nat_nat > set_Pr1986765409at_nat > $o)).
% 0.78/0.42 thf(func_def_62, type, member_set_nat: (set_nat > set_set_nat > $o)).
% 0.78/0.42 thf(func_def_63, type, member298845450at_nat: (set_Pr1986765409at_nat > set_se1612935105at_nat > $o)).
% 0.78/0.42 thf(func_def_64, type, c: (product_prod_nat_nat > a)).
% 0.78/0.42 thf(func_def_65, type, c2: (product_prod_nat_nat > b)).
% 0.78/0.42 thf(func_def_66, type, edges: set_Pr1986765409at_nat).
% 0.78/0.42 thf(func_def_67, type, p: list_P559422087at_nat).
% 0.78/0.42 thf(func_def_68, type, p2: list_P559422087at_nat).
% 0.78/0.42 thf(func_def_69, type, s: nat).
% 0.78/0.42 thf(func_def_70, type, t: nat).
% 0.78/0.42 thf(func_def_74, type, vAND: ($o > $o > $o)).
% 0.78/0.42 thf(func_def_75, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.78/0.42 thf(func_def_76, type, vIMP: ($o > $o > $o)).
% 0.78/0.42 thf(func_def_77, type, db4: !>[X0: $tType]:(X0)).
% 0.78/0.42 thf(func_def_78, type, db3: !>[X0: $tType]:(X0)).
% 0.78/0.42 thf(func_def_79, type, db0: !>[X0: $tType]:(X0)).
% 0.78/0.42 thf(func_def_80, type, db1: !>[X0: $tType]:(X0)).
% 0.78/0.42 thf(func_def_81, type, db2: !>[X0: $tType]:(X0)).
% 0.78/0.42 thf(func_def_82, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.78/0.42 thf(func_def_83, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.78/0.42 thf(func_def_84, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.78/0.42 thf(func_def_85, type, vOR: ($o > $o > $o)).
% 0.78/0.42 thf(func_def_86, type, vNOT: ($o > $o)).
% 0.78/0.42 thf(func_def_87, type, sK0: ((product_prod_nat_nat > b) > nat > nat > list_P559422087at_nat)).
% 0.78/0.42 thf(func_def_88, type, sK1: (nat > nat > nat > list_P559422087at_nat)).
% 0.78/0.42 thf(func_def_89, type, sK2: (nat > (nat > $o) > nat > nat)).
% 0.78/0.42 thf(func_def_90, type, sK3: (nat > nat > nat)).
% 0.78/0.42 thf(func_def_91, type, sK4: (nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat)).
% 0.78/0.42 thf(func_def_92, type, sK5: (nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat)).
% 0.78/0.42 thf(func_def_93, type, sK6: (set_Pr1986765409at_nat > set_se1612935105at_nat > set_Pr1986765409at_nat)).
% 0.78/0.42 thf(func_def_94, type, sK7: (nat > nat > list_P559422087at_nat)).
% 0.78/0.42 thf(func_def_95, type, sK8: (nat > nat > (product_prod_nat_nat > a) > list_P559422087at_nat)).
% 0.78/0.42 thf(func_def_96, type, sK9: (nat > nat > nat > list_P559422087at_nat)).
% 0.78/0.42 thf(func_def_97, type, sK10: (nat > (nat > $o) > nat)).
% 0.78/0.42 thf(func_def_98, type, sK11: ((nat > $o) > nat)).
% 0.78/0.42 thf(func_def_99, type, sK12: (nat > nat > list_P559422087at_nat)).
% 0.78/0.42 thf(func_def_100, type, sK13: (nat > nat > nat)).
% 0.78/0.42 thf(func_def_101, type, sK14: (set_li664300135at_nat > nat)).
% 0.78/0.42 thf(func_def_102, type, sK15: (nat > nat > nat > nat)).
% 0.78/0.42 thf(func_def_103, type, sK16: (nat > list_P559422087at_nat)).
% 0.78/0.42 thf(func_def_104, type, sK17: (set_nat > nat > nat)).
% 0.78/0.42 thf(func_def_105, type, sK18: (set_nat > set_nat > nat)).
% 0.78/0.42 thf(func_def_106, type, sK19: ((product_prod_nat_nat > $o) > (product_prod_nat_nat > $o) > product_prod_nat_nat)).
% 0.78/0.42 thf(func_def_107, type, sK20: (nat > nat > (product_prod_nat_nat > b) > list_P559422087at_nat)).
% 0.78/0.42 thf(func_def_108, type, sK21: (nat > list_P559422087at_nat > nat > list_P559422087at_nat)).
% 0.78/0.42 thf(func_def_109, type, sK22: ((nat > $o) > nat > nat > (product_prod_nat_nat > a) > nat)).
% 0.78/0.42 thf(func_def_110, type, sK23: ((product_prod_nat_nat > $o) > (product_prod_nat_nat > $o) > product_prod_nat_nat)).
% 0.78/0.42 thf(func_def_111, type, sK24: ((nat > $o) > nat)).
% 0.78/0.42 thf(func_def_112, type, sK25: (set_nat > nat > nat)).
% 0.78/0.42 thf(func_def_113, type, sK26: ((nat > $o) > nat)).
% 0.78/0.42 thf(func_def_114, type, sK27: (nat > nat > nat)).
% 0.78/0.42 thf(func_def_115, type, sK28: (nat > (product_prod_nat_nat > a) > nat > list_P559422087at_nat)).
% 0.78/0.42 thf(func_def_116, type, sK29: ((set_nat > $o) > set_nat)).
% 0.78/0.42 thf(func_def_117, type, sK30: (nat > nat > list_P559422087at_nat)).
% 0.78/0.42 thf(func_def_118, type, sK31: (set_set_nat > set_nat > set_nat)).
% 0.78/0.42 thf(func_def_119, type, sK32: (nat > nat > nat > (product_prod_nat_nat > a) > nat)).
% 0.78/0.42 thf(func_def_120, type, sK33: (set_se1612935105at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat)).
% 0.78/0.42 thf(func_def_121, type, sK34: (nat > (product_prod_nat_nat > a) > nat > nat)).
% 0.78/0.42 thf(func_def_122, type, sK35: ((nat > nat) > nat)).
% 0.78/0.42 thf(func_def_123, type, sK36: ((nat > nat) > nat)).
% 0.78/0.42 thf(func_def_124, type, sK37: ((list_P559422087at_nat > $o) > list_P559422087at_nat)).
% 0.78/0.42 thf(func_def_125, type, sK38: (set_nat > set_set_nat > set_nat)).
% 0.78/0.42 thf(func_def_126, type, sK39: ((product_prod_nat_nat > b) > nat > nat > nat)).
% 0.78/0.42 thf(func_def_127, type, sK40: (nat > nat > list_P559422087at_nat)).
% 0.78/0.42 thf(func_def_128, type, sK41: (set_nat > nat > set_nat)).
% 0.78/0.42 thf(func_def_129, type, sK42: (nat > (nat > $o) > nat > (product_prod_nat_nat > b) > nat)).
% 0.78/0.42 thf(func_def_130, type, sK43: (nat > nat > list_P559422087at_nat)).
% 0.78/0.42 thf(func_def_131, type, sK44: (nat > nat > nat > nat)).
% 0.78/0.42 thf(func_def_132, type, sK45: ((nat > $o) > nat)).
% 0.78/0.42 thf(func_def_133, type, sK46: (nat > set_nat > set_nat)).
% 0.78/0.42 thf(func_def_134, type, sK47: ((nat > $o) > (nat > $o) > nat)).
% 0.78/0.42 thf(func_def_135, type, sK48: (nat > nat > list_P559422087at_nat)).
% 0.78/0.42 thf(func_def_136, type, sK49: (nat > nat > (product_prod_nat_nat > a) > nat)).
% 0.78/0.42 thf(func_def_137, type, sK50: ((nat > $o) > (nat > $o) > nat)).
% 0.78/0.42 thf(func_def_138, type, sK51: ((nat > $o) > nat > nat > nat)).
% 0.78/0.42 thf(func_def_139, type, sK52: (nat > nat > nat)).
% 0.78/0.42 thf(func_def_140, type, sK53: (set_Pr1986765409at_nat > set_Pr1986765409at_nat > product_prod_nat_nat)).
% 0.78/0.42 thf(func_def_141, type, sK54: (nat > list_P559422087at_nat > nat > list_P559422087at_nat)).
% 0.78/0.42 thf(func_def_142, type, sK55: ((set_Pr1986765409at_nat > $o) > set_Pr1986765409at_nat)).
% 0.78/0.42 thf(func_def_143, type, sK56: list_P559422087at_nat).
% 0.78/0.42 thf(func_def_144, type, sK57: ((nat > $o) > nat > nat)).
% 0.78/0.42 thf(func_def_145, type, sK58: ((product_prod_nat_nat > b) > nat > nat > nat)).
% 0.78/0.42 thf(func_def_146, type, sK59: (nat > nat > nat)).
% 0.78/0.42 thf(func_def_147, type, sK60: (nat > nat > nat)).
% 0.78/0.42 thf(func_def_148, type, sK61: (nat > nat > nat > (product_prod_nat_nat > b) > nat)).
% 0.78/0.42 thf(f2,axiom,(
% 0.78/0.42 (((size_s1990949619at_nat @ p)) = ((min_dist_a @ c @ s @ t)))),
% 0.78/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_LENP)).
% 0.78/0.42 thf(f3,axiom,(
% 0.78/0.42 (((size_s1990949619at_nat @ p2)) = ((min_dist_b @ c2 @ s @ t)))),
% 0.78/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_LENP_H)).
% 0.78/0.42 thf(f7,axiom,(
% 0.78/0.42 (ord_less_nat @ (min_dist_b @ c2 @ s @ t) @ (min_dist_a @ c @ s @ t))),
% 0.78/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_SHORTER)).
% 0.78/0.42 thf(f14,axiom,(
% 0.78/0.42 (ord_less_nat @ (size_s1990949619at_nat @ p) @ (size_s1990949619at_nat @ p2))),
% 0.78/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13__092_060open_062length_Ap_A_060_Alength_Ap_H_092_060close_062)).
% 0.78/0.42 thf(f28,axiom,(
% 0.78/0.42 ~ ! [X0 : list_P559422087at_nat] : ((isPath_b @ c2 @ s @ X0 @ t) => (((size_s1990949619at_nat @ X0)) != ((min_dist_b @ c2 @ s @ t))))),
% 0.78/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062p_H_O_A_092_060lbrakk_062g_H_OisPath_As_Ap_H_At_059_Alength_Ap_H_A_061_Ag_H_Omin__dist_As_At_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062)).
% 0.78/0.42 thf(f97,axiom,(
% 0.78/0.42 ! [X1 : nat,X0 : nat] : ((ord_less_eq_nat @ X0 @ X1) => ((ord_less_eq_nat @ X1 @ X0) => (X0 = X1)))),
% 0.78/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_le__antisym)).
% 0.78/0.42 thf(f107,axiom,(
% 0.78/0.42 ! [X0 : nat,X1 : nat] : (((ord_less_nat @ X0 @ X1) | (X0 = X1)) => (ord_less_eq_nat @ X0 @ X1))),
% 0.78/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_less__or__eq__imp__le)).
% 0.78/0.42 thf(f126,axiom,(
% 0.78/0.42 ! [X0 : nat] : ~(ord_less_nat @ X0 @ X0)),
% 0.78/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_less__irrefl__nat)).
% 0.78/0.42 thf(f371,plain,(
% 0.78/0.42 ! [X0 : nat] : ~(ord_less_nat @ X0 @ X0)),
% 0.78/0.42 inference(rectify,[],[f126])).
% 0.78/0.42 thf(f372,plain,(
% 0.78/0.42 ! [X0 : nat] : ~ (((ord_less_nat @ X0 @ X0)) = $true)),
% 0.78/0.42 inference(fool_elimination,[],[f371])).
% 0.78/0.42 thf(f465,plain,(
% 0.78/0.42 (ord_less_nat @ (min_dist_b @ c2 @ s @ t) @ (min_dist_a @ c @ s @ t))),
% 0.78/0.42 inference(rectify,[],[f7])).
% 0.78/0.42 thf(f466,plain,(
% 0.78/0.42 (((ord_less_nat @ (min_dist_b @ c2 @ s @ t) @ (min_dist_a @ c @ s @ t))) = $true)),
% 0.78/0.42 inference(fool_elimination,[],[f465])).
% 0.78/0.42 thf(f490,plain,(
% 0.78/0.42 ! [X0 : nat,X1 : nat] : (((ord_less_nat @ X0 @ X1) | (X0 = X1)) => (ord_less_eq_nat @ X0 @ X1))),
% 0.78/0.42 inference(rectify,[],[f107])).
% 0.78/0.42 thf(f491,plain,(
% 0.78/0.42 ! [X1 : nat,X0 : nat] : (((X0 = X1) | (((ord_less_nat @ X0 @ X1)) = $true)) => (((ord_less_eq_nat @ X0 @ X1)) = $true))),
% 0.78/0.42 inference(fool_elimination,[],[f490])).
% 0.78/0.42 thf(f605,plain,(
% 0.78/0.42 (ord_less_nat @ (size_s1990949619at_nat @ p) @ (size_s1990949619at_nat @ p2))),
% 0.78/0.42 inference(rectify,[],[f14])).
% 0.78/0.42 thf(f606,plain,(
% 0.78/0.42 (((ord_less_nat @ (size_s1990949619at_nat @ p) @ (size_s1990949619at_nat @ p2))) = $true)),
% 0.78/0.42 inference(fool_elimination,[],[f605])).
% 0.78/0.42 thf(f715,plain,(
% 0.78/0.42 ~ ! [X0 : list_P559422087at_nat] : ((isPath_b @ c2 @ s @ X0 @ t) => (((size_s1990949619at_nat @ X0)) != ((min_dist_b @ c2 @ s @ t))))),
% 0.78/0.42 inference(rectify,[],[f28])).
% 0.78/0.42 thf(f716,plain,(
% 0.78/0.42 ~ ! [X0 : list_P559422087at_nat] : ((((isPath_b @ c2 @ s @ X0 @ t)) = $true) => (((min_dist_b @ c2 @ s @ t)) != ((size_s1990949619at_nat @ X0))))),
% 0.78/0.42 inference(fool_elimination,[],[f715])).
% 0.78/0.42 thf(f901,plain,(
% 0.78/0.42 ! [X0 : nat,X1 : nat] : ((ord_less_eq_nat @ X1 @ X0) => ((ord_less_eq_nat @ X0 @ X1) => (X0 = X1)))),
% 0.78/0.42 inference(rectify,[],[f97])).
% 0.78/0.42 thf(f902,plain,(
% 0.78/0.42 ! [X0 : nat,X1 : nat] : ((((ord_less_eq_nat @ X1 @ X0)) = $true) => ((((ord_less_eq_nat @ X0 @ X1)) = $true) => (X0 = X1)))),
% 0.78/0.42 inference(fool_elimination,[],[f901])).
% 0.78/0.42 thf(f940,plain,(
% 0.78/0.42 ! [X0 : nat] : (((ord_less_nat @ X0 @ X0)) != $true)),
% 0.78/0.42 inference(flattening,[],[f372])).
% 0.78/0.42 thf(f1019,plain,(
% 0.78/0.42 ! [X0 : nat,X1 : nat] : ((((ord_less_eq_nat @ X0 @ X1)) = $true) | ((((ord_less_nat @ X0 @ X1)) != $true) & (X0 != X1)))),
% 0.78/0.42 inference(ennf_transformation,[],[f491])).
% 0.78/0.42 thf(f1042,plain,(
% 0.78/0.42 ? [X0 : list_P559422087at_nat] : ((((min_dist_b @ c2 @ s @ t)) = ((size_s1990949619at_nat @ X0))) & (((isPath_b @ c2 @ s @ X0 @ t)) = $true))),
% 0.78/0.42 inference(ennf_transformation,[],[f716])).
% 0.78/0.42 thf(f1166,plain,(
% 0.78/0.42 ! [X0 : nat,X1 : nat] : (((X0 = X1) | (((ord_less_eq_nat @ X0 @ X1)) != $true)) | (((ord_less_eq_nat @ X1 @ X0)) != $true))),
% 0.78/0.42 inference(ennf_transformation,[],[f902])).
% 0.78/0.42 thf(f1167,plain,(
% 0.78/0.42 ! [X0 : nat,X1 : nat] : ((((ord_less_eq_nat @ X1 @ X0)) != $true) | (((ord_less_eq_nat @ X0 @ X1)) != $true) | (X0 = X1))),
% 0.78/0.42 inference(flattening,[],[f1166])).
% 0.78/0.42 thf(f1429,plain,(
% 0.78/0.42 (((min_dist_b @ c2 @ s @ t)) = ((size_s1990949619at_nat @ sK56))) & ($true = ((isPath_b @ c2 @ s @ sK56 @ t)))),
% 0.78/0.42 inference(skolemize,[status(esa),new_symbols(skolem,[sK56]),skolemize(X0,sK56)],[f1042])).
% 0.78/0.42 thf(f1450,plain,(
% 0.78/0.42 (((ord_less_nat @ (size_s1990949619at_nat @ p) @ (size_s1990949619at_nat @ p2))) = $true)),
% 0.78/0.42 inference(cnf_transformation,[],[f606])).
% 0.78/0.42 thf(f1560,plain,(
% 0.78/0.42 (((ord_less_nat @ (min_dist_b @ c2 @ s @ t) @ (min_dist_a @ c @ s @ t))) = $true)),
% 0.78/0.42 inference(cnf_transformation,[],[f466])).
% 0.78/0.42 thf(f1562,plain,(
% 0.78/0.42 ( ! [X0 : nat,X1 : nat] : ((((ord_less_eq_nat @ X0 @ X1)) = $true) | (((ord_less_nat @ X0 @ X1)) != $true)) )),
% 0.78/0.42 inference(cnf_transformation,[],[f1019])).
% 0.78/0.42 thf(f1631,plain,(
% 0.78/0.42 (((size_s1990949619at_nat @ p)) = ((min_dist_a @ c @ s @ t)))),
% 0.78/0.42 inference(cnf_transformation,[],[f2])).
% 0.78/0.42 thf(f1669,plain,(
% 0.78/0.42 (((size_s1990949619at_nat @ p2)) = ((min_dist_b @ c2 @ s @ t)))),
% 0.78/0.42 inference(cnf_transformation,[],[f3])).
% 0.78/0.42 thf(f1765,plain,(
% 0.78/0.42 ( ! [X0 : nat] : ((((ord_less_nat @ X0 @ X0)) != $true)) )),
% 0.78/0.42 inference(cnf_transformation,[],[f940])).
% 0.78/0.42 thf(f1831,plain,(
% 0.78/0.42 ( ! [X0 : nat,X1 : nat] : ((((ord_less_eq_nat @ X1 @ X0)) != $true) | (((ord_less_eq_nat @ X0 @ X1)) != $true) | (X0 = X1)) )),
% 0.78/0.42 inference(cnf_transformation,[],[f1167])).
% 0.78/0.42 thf(f1869,plain,(
% 0.78/0.42 (((min_dist_b @ c2 @ s @ t)) = ((size_s1990949619at_nat @ sK56)))),
% 0.78/0.42 inference(cnf_transformation,[],[f1429])).
% 0.78/0.42 thf(f2009,definition,(
% 0.78/0.42 spl62_9 <=> (((ord_less_nat @ (size_s1990949619at_nat @ p) @ (size_s1990949619at_nat @ p2))) = $true)),
% 0.78/0.42 introduced(definition,[new_symbols(definition,[spl62_9])],[avatar_definition])).
% 0.78/0.42 thf(f2011,plain,(
% 0.78/0.42 (((ord_less_nat @ (size_s1990949619at_nat @ p) @ (size_s1990949619at_nat @ p2))) = $true) | ~spl62_9),
% 0.78/0.42 inference(avatar_component_clause,[],[f2009])).
% 0.78/0.42 thf(f2012,plain,(
% 0.78/0.42 spl62_9),
% 0.78/0.42 inference(avatar_split_clause,[],[f1450,f2009])).
% 0.78/0.42 thf(f2124,definition,(
% 0.78/0.42 spl62_32 <=> (((size_s1990949619at_nat @ p2)) = ((min_dist_b @ c2 @ s @ t)))),
% 0.78/0.42 introduced(definition,[new_symbols(definition,[spl62_32])],[avatar_definition])).
% 0.78/0.42 thf(f2126,plain,(
% 0.78/0.42 (((size_s1990949619at_nat @ p2)) = ((min_dist_b @ c2 @ s @ t))) | ~spl62_32),
% 0.78/0.42 inference(avatar_component_clause,[],[f2124])).
% 0.78/0.42 thf(f2127,plain,(
% 0.78/0.42 spl62_32),
% 0.78/0.42 inference(avatar_split_clause,[],[f1669,f2124])).
% 0.78/0.42 thf(f2143,definition,(
% 0.78/0.42 spl62_36 <=> (((size_s1990949619at_nat @ p)) = ((min_dist_a @ c @ s @ t)))),
% 0.78/0.42 introduced(definition,[new_symbols(definition,[spl62_36])],[avatar_definition])).
% 0.78/0.42 thf(f2145,plain,(
% 0.78/0.42 (((size_s1990949619at_nat @ p)) = ((min_dist_a @ c @ s @ t))) | ~spl62_36),
% 0.78/0.42 inference(avatar_component_clause,[],[f2143])).
% 0.78/0.42 thf(f2146,plain,(
% 0.78/0.42 spl62_36),
% 0.78/0.42 inference(avatar_split_clause,[],[f1631,f2143])).
% 0.78/0.42 thf(f2250,definition,(
% 0.78/0.42 spl62_57 <=> (((ord_less_nat @ (min_dist_b @ c2 @ s @ t) @ (min_dist_a @ c @ s @ t))) = $true)),
% 0.78/0.42 introduced(definition,[new_symbols(definition,[spl62_57])],[avatar_definition])).
% 0.78/0.42 thf(f2252,plain,(
% 0.78/0.42 (((ord_less_nat @ (min_dist_b @ c2 @ s @ t) @ (min_dist_a @ c @ s @ t))) = $true) | ~spl62_57),
% 0.78/0.42 inference(avatar_component_clause,[],[f2250])).
% 0.78/0.42 thf(f2253,plain,(
% 0.78/0.42 spl62_57),
% 0.78/0.42 inference(avatar_split_clause,[],[f1560,f2250])).
% 0.78/0.42 thf(f2255,definition,(
% 0.78/0.42 spl62_58 <=> (((min_dist_b @ c2 @ s @ t)) = ((size_s1990949619at_nat @ sK56)))),
% 0.78/0.42 introduced(definition,[new_symbols(definition,[spl62_58])],[avatar_definition])).
% 0.78/0.42 thf(f2257,plain,(
% 0.78/0.42 (((min_dist_b @ c2 @ s @ t)) = ((size_s1990949619at_nat @ sK56))) | ~spl62_58),
% 0.78/0.42 inference(avatar_component_clause,[],[f2255])).
% 0.78/0.42 thf(f2258,plain,(
% 0.78/0.42 spl62_58),
% 0.78/0.42 inference(avatar_split_clause,[],[f1869,f2255])).
% 0.78/0.42 thf(f2537,plain,(
% 0.78/0.42 ( ! [X0 : nat,X1 : nat] : ((((ord_less_eq_nat @ X1 @ X0)) != $true) | (((ord_less_nat @ X0 @ X1)) != $true) | (X0 = X1) | ($true != $true)) )),
% 0.78/0.42 inference(superposition,[],[f1831,f1562])).
% 0.78/0.42 thf(f2538,plain,(
% 0.78/0.42 ( ! [X0 : nat,X1 : nat] : ((((ord_less_eq_nat @ X1 @ X0)) != $true) | (((ord_less_nat @ X0 @ X1)) != $true) | (X0 = X1)) )),
% 0.78/0.42 inference(trivial_inequality_removal,[],[f2537])).
% 0.78/0.42 thf(f2571,plain,(
% 0.78/0.42 ( ! [X0 : nat,X1 : nat] : ((((ord_less_nat @ X0 @ X1)) != $true) | ($true != $true) | (X0 = X1) | (((ord_less_nat @ X1 @ X0)) != $true)) )),
% 0.78/0.42 inference(superposition,[],[f2538,f1562])).
% 0.78/0.42 thf(f2572,plain,(
% 0.78/0.42 ( ! [X0 : nat,X1 : nat] : ((((ord_less_nat @ X1 @ X0)) != $true) | (((ord_less_nat @ X0 @ X1)) != $true) | (X0 = X1)) )),
% 0.78/0.42 inference(trivial_inequality_removal,[],[f2571])).
% 0.78/0.42 thf(f3010,plain,(
% 0.78/0.42 ($true != $true) | (((size_s1990949619at_nat @ p)) = ((size_s1990949619at_nat @ p2))) | (((ord_less_nat @ (size_s1990949619at_nat @ p2) @ (size_s1990949619at_nat @ p))) != $true) | ~spl62_9),
% 0.78/0.42 inference(superposition,[],[f2572,f2011])).
% 0.78/0.42 thf(f3019,plain,(
% 0.78/0.42 (((ord_less_nat @ (size_s1990949619at_nat @ p2) @ (size_s1990949619at_nat @ p))) != $true) | (((size_s1990949619at_nat @ p)) = ((size_s1990949619at_nat @ p2))) | ~spl62_9),
% 0.78/0.42 inference(trivial_inequality_removal,[],[f3010])).
% 0.78/0.42 thf(f3023,plain,(
% 0.78/0.42 (((ord_less_nat @ (min_dist_b @ c2 @ s @ t) @ (size_s1990949619at_nat @ p))) != $true) | (((size_s1990949619at_nat @ p)) = ((size_s1990949619at_nat @ p2))) | (~spl62_9 | ~spl62_32)),
% 0.78/0.42 inference(forward_demodulation,[],[f3019,f2126])).
% 0.78/0.42 thf(f3024,plain,(
% 0.78/0.42 (((ord_less_nat @ (size_s1990949619at_nat @ sK56) @ (size_s1990949619at_nat @ p))) != $true) | (((size_s1990949619at_nat @ p)) = ((size_s1990949619at_nat @ p2))) | (~spl62_9 | ~spl62_32 | ~spl62_58)),
% 0.78/0.42 inference(forward_demodulation,[],[f3023,f2257])).
% 0.78/0.42 thf(f3025,plain,(
% 0.78/0.42 (((size_s1990949619at_nat @ p)) = ((size_s1990949619at_nat @ p2))) | (((ord_less_nat @ (size_s1990949619at_nat @ sK56) @ (min_dist_a @ c @ s @ t))) != $true) | (~spl62_9 | ~spl62_32 | ~spl62_36 | ~spl62_58)),
% 0.78/0.42 inference(forward_demodulation,[],[f3024,f2145])).
% 0.78/0.42 thf(f3026,plain,(
% 0.78/0.42 (((size_s1990949619at_nat @ p)) = ((min_dist_b @ c2 @ s @ t))) | (((ord_less_nat @ (size_s1990949619at_nat @ sK56) @ (min_dist_a @ c @ s @ t))) != $true) | (~spl62_9 | ~spl62_32 | ~spl62_36 | ~spl62_58)),
% 0.78/0.42 inference(forward_demodulation,[],[f3025,f2126])).
% 0.78/0.42 thf(f3027,plain,(
% 0.78/0.42 (((ord_less_nat @ (size_s1990949619at_nat @ sK56) @ (min_dist_a @ c @ s @ t))) != $true) | (((size_s1990949619at_nat @ p)) = ((size_s1990949619at_nat @ sK56))) | (~spl62_9 | ~spl62_32 | ~spl62_36 | ~spl62_58)),
% 0.78/0.42 inference(forward_demodulation,[],[f3026,f2257])).
% 0.78/0.42 thf(f3028,plain,(
% 0.78/0.42 (((ord_less_nat @ (size_s1990949619at_nat @ sK56) @ (min_dist_a @ c @ s @ t))) != $true) | (((min_dist_a @ c @ s @ t)) = ((size_s1990949619at_nat @ sK56))) | (~spl62_9 | ~spl62_32 | ~spl62_36 | ~spl62_58)),
% 0.78/0.42 inference(forward_demodulation,[],[f3027,f2145])).
% 0.78/0.42 thf(f3030,definition,(
% 0.78/0.42 spl62_89 <=> (((min_dist_a @ c @ s @ t)) = ((size_s1990949619at_nat @ sK56)))),
% 0.78/0.42 introduced(definition,[new_symbols(definition,[spl62_89])],[avatar_definition])).
% 0.78/0.42 thf(f3032,plain,(
% 0.78/0.42 (((min_dist_a @ c @ s @ t)) = ((size_s1990949619at_nat @ sK56))) | ~spl62_89),
% 0.78/0.42 inference(avatar_component_clause,[],[f3030])).
% 0.78/0.42 thf(f3034,definition,(
% 0.78/0.42 spl62_90 <=> (((ord_less_nat @ (size_s1990949619at_nat @ sK56) @ (min_dist_a @ c @ s @ t))) = $true)),
% 0.78/0.42 introduced(definition,[new_symbols(definition,[spl62_90])],[avatar_definition])).
% 0.78/0.42 thf(f3037,plain,(
% 0.78/0.42 spl62_89 | ~spl62_90 | ~spl62_9 | ~spl62_32 | ~spl62_36 | ~spl62_58),
% 0.78/0.42 inference(avatar_split_clause,[],[f3028,f2255,f2143,f2124,f2009,f3034,f3030])).
% 0.78/0.42 thf(f3038,definition,(
% 0.78/0.42 (((min_dist_b @ c2 @ s @ t)) != ((size_s1990949619at_nat @ sK56))) | (((ord_less_nat @ (min_dist_b @ c2 @ s @ t) @ (min_dist_a @ c @ s @ t))) != $true) | (((ord_less_nat @ (size_s1990949619at_nat @ sK56) @ (min_dist_a @ c @ s @ t))) = $true)),
% 0.78/0.42 introduced(theory,[theory_tautology_sat_conflict])).
% 0.78/0.42 thf(f3307,plain,(
% 0.78/0.42 (((ord_less_nat @ (size_s1990949619at_nat @ sK56) @ (min_dist_a @ c @ s @ t))) = $true) | (~spl62_57 | ~spl62_58)),
% 0.78/0.42 inference(forward_demodulation,[],[f2252,f2257])).
% 0.78/0.42 thf(f3308,plain,(
% 0.78/0.42 ($true = ((ord_less_nat @ (size_s1990949619at_nat @ sK56) @ (size_s1990949619at_nat @ sK56)))) | (~spl62_57 | ~spl62_58 | ~spl62_89)),
% 0.78/0.42 inference(forward_demodulation,[],[f3307,f3032])).
% 0.78/0.42 thf(f3309,plain,(
% 0.78/0.42 $false | (~spl62_57 | ~spl62_58 | ~spl62_89)),
% 0.78/0.42 inference(forward_subsumption_resolution,[],[f3308,f1765])).
% 0.78/0.42 thf(f3310,plain,(
% 0.78/0.42 ~spl62_57 | ~spl62_58 | ~spl62_89),
% 0.78/0.42 inference(avatar_contradiction_clause,[],[f3309])).
% 0.78/0.42 cnf(s9, plain, spl62_9, inference(sat_conversion,[],[f2012])).
% 0.78/0.42 cnf(s34, plain, spl62_32, inference(sat_conversion,[],[f2127])).
% 0.78/0.42 cnf(s38, plain, spl62_36, inference(sat_conversion,[],[f2146])).
% 0.78/0.42 cnf(s68, plain, spl62_57, inference(sat_conversion,[],[f2253])).
% 0.78/0.42 cnf(s69, plain, spl62_58, inference(sat_conversion,[],[f2258])).
% 0.78/0.42 cnf(s96, plain, ~spl62_9 | ~spl62_32 | ~spl62_36 | ~spl62_58 | spl62_89 | ~spl62_90, inference(sat_conversion,[],[f3037])).
% 0.78/0.42 cnf(s97, plain, ~spl62_57 | ~spl62_58 | spl62_90, inference(sat_conversion,[],[f3038])).
% 0.78/0.42 cnf(s109, plain, ~spl62_57 | ~spl62_58 | ~spl62_89, inference(sat_conversion,[],[f3310])).
% 0.78/0.42 cnf(s112, plain, ~spl62_89, inference(rat,[],[s109,s69,s68])).
% 0.78/0.42 cnf(s113, plain, spl62_90, inference(rat,[],[s97,s69,s68])).
% 0.78/0.42 cnf(s120, plain, ~spl62_9, inference(rat,[],[s96,s113,s112,s69,s38,s34])).
% 0.78/0.42 cnf(s124, plain, $false, inference(rat,[],[s9,s120])).
% 0.78/0.42 thf(f3311,plain,(
% 0.78/0.42 $false),
% 0.78/0.42 inference(avatar_sat_refutation,[],[s124])).
% 0.78/0.42 % SZS output end Proof for theBenchmark
% 0.78/0.42 % (554933)------------------------------
% 0.78/0.42 % (554933)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.42 % (554933)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.42 % (554933)CaDiCaL version: 2.1.3
% 0.78/0.42 % (554933)Termination reason: Refutation
% 0.78/0.42 % (554933)Time elapsed: 0.093 s
% 0.78/0.42 % (554933)Peak memory usage: 15 MB
% 0.78/0.42 % (554933)Instructions burned: 227 (million)
% 0.78/0.42 % (554925)Success in time 0.148 s
% 0.78/0.42 % Vampire exiting
%------------------------------------------------------------------------------