%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM664^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 08:18:27 AM UTC 2026
% Result : Theorem 0.18s 0.27s
% Output : Refutation 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM664^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n007.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 12:31:56 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.09/0.22 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
% 0.18/0.27 % (3292787)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.18/0.27 % (3292795)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=2542823705: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)
% 0.18/0.27 % (3292795) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3292787-3292795"...
% 0.18/0.27 % (3292795)...printing done.
% 0.18/0.27 % (3292795)Refutation found. Thanks to Tanya!
% 0.18/0.27 % SZS status Theorem for theBenchmark
% 0.18/0.27 % SZS output start Proof for theBenchmark
% 0.18/0.27 thf(type_def_5, type, nat: $tType).
% 0.18/0.27 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.18/0.27 thf(func_def_0, type, x: nat).
% 0.18/0.27 thf(func_def_1, type, y: nat).
% 0.18/0.27 thf(func_def_2, type, z: nat).
% 0.18/0.27 thf(func_def_3, type, less: (nat > nat > $o)).
% 0.18/0.27 thf(f1,axiom,(
% 0.18/0.27 (less @ x @ y)),
% 0.18/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p',l)).
% 0.18/0.27 thf(f2,axiom,(
% 0.18/0.27 ~(less @ y @ z) => (y = z)),
% 0.18/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p',k)).
% 0.18/0.27 thf(f4,axiom,(
% 0.18/0.27 ! [X1 : nat,X0 : nat,X2 : nat] : ((less @ X0 @ X1) => ((less @ X1 @ X2) => (less @ X0 @ X2)))),
% 0.18/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz15)).
% 0.18/0.27 thf(f5,conjecture,(
% 0.18/0.27 (less @ x @ z)),
% 0.18/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz16b)).
% 0.18/0.27 thf(f6,negated_conjecture,(
% 0.18/0.27 ~(less @ x @ z)),
% 0.18/0.27 inference(negated_conjecture,[status(cth)],[f5])).
% 0.18/0.27 thf(f7,plain,(
% 0.18/0.27 (less @ x @ y)),
% 0.18/0.27 inference(rectify,[],[f1])).
% 0.18/0.27 thf(f8,plain,(
% 0.18/0.27 (((less @ x @ y)) = $true)),
% 0.18/0.27 inference(fool_elimination,[],[f7])).
% 0.18/0.27 thf(f11,plain,(
% 0.18/0.27 ~(less @ x @ z)),
% 0.18/0.27 inference(rectify,[],[f6])).
% 0.18/0.27 thf(f12,plain,(
% 0.18/0.27 ~ (((less @ x @ z)) = $true)),
% 0.18/0.27 inference(fool_elimination,[],[f11])).
% 0.18/0.27 thf(f13,plain,(
% 0.18/0.27 ~(less @ y @ z) => (y = z)),
% 0.18/0.27 inference(rectify,[],[f2])).
% 0.18/0.27 thf(f14,plain,(
% 0.18/0.27 ~ (((less @ y @ z)) = $true) => (y = z)),
% 0.18/0.27 inference(fool_elimination,[],[f13])).
% 0.18/0.27 thf(f15,plain,(
% 0.18/0.27 ! [X0 : nat,X1 : nat,X2 : nat] : ((less @ X1 @ X0) => ((less @ X0 @ X2) => (less @ X1 @ X2)))),
% 0.18/0.27 inference(rectify,[],[f4])).
% 0.18/0.27 thf(f16,plain,(
% 0.18/0.27 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = ((less @ X1 @ X0))) => ((((less @ X0 @ X2)) = $true) => (((less @ X1 @ X2)) = $true)))),
% 0.18/0.27 inference(fool_elimination,[],[f15])).
% 0.18/0.27 thf(f18,plain,(
% 0.18/0.27 (((less @ x @ z)) != $true)),
% 0.18/0.27 inference(flattening,[],[f12])).
% 0.18/0.27 thf(f19,plain,(
% 0.18/0.27 (((less @ y @ z)) != $true) => (y = z)),
% 0.18/0.27 inference(flattening,[],[f14])).
% 0.18/0.27 thf(f20,plain,(
% 0.18/0.27 (y = z) | (((less @ y @ z)) = $true)),
% 0.18/0.27 inference(ennf_transformation,[],[f19])).
% 0.18/0.27 thf(f22,plain,(
% 0.18/0.27 ! [X0 : nat,X1 : nat,X2 : nat] : (((((less @ X1 @ X2)) = $true) | (((less @ X0 @ X2)) != $true)) | ($true != ((less @ X1 @ X0))))),
% 0.18/0.27 inference(ennf_transformation,[],[f16])).
% 0.18/0.27 thf(f23,plain,(
% 0.18/0.27 ! [X2 : nat,X0 : nat,X1 : nat] : ((((less @ X0 @ X2)) != $true) | ($true != ((less @ X1 @ X0))) | (((less @ X1 @ X2)) = $true))),
% 0.18/0.27 inference(flattening,[],[f22])).
% 0.18/0.27 thf(f24,plain,(
% 0.18/0.27 ! [X0 : nat,X1 : nat,X2 : nat] : (($true != ((less @ X1 @ X0))) | ($true != ((less @ X2 @ X1))) | ($true = ((less @ X2 @ X0))))),
% 0.18/0.27 inference(rectify,[],[f23])).
% 0.18/0.27 thf(f25,plain,(
% 0.18/0.27 (((less @ x @ y)) = $true)),
% 0.18/0.27 inference(cnf_transformation,[],[f8])).
% 0.18/0.27 thf(f27,plain,(
% 0.18/0.27 (((less @ y @ z)) = $true) | (y = z)),
% 0.18/0.27 inference(cnf_transformation,[],[f20])).
% 0.18/0.27 thf(f28,plain,(
% 0.18/0.27 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = ((less @ X2 @ X0))) | ($true != ((less @ X2 @ X1))) | ($true != ((less @ X1 @ X0)))) )),
% 0.18/0.27 inference(cnf_transformation,[],[f24])).
% 0.18/0.27 thf(f29,plain,(
% 0.18/0.27 (((less @ x @ z)) != $true)),
% 0.18/0.27 inference(cnf_transformation,[],[f18])).
% 0.18/0.27 thf(f33,definition,(
% 0.18/0.27 spl0_1 <=> (((less @ x @ y)) = $true)),
% 0.18/0.27 introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition])).
% 0.18/0.27 thf(f35,plain,(
% 0.18/0.27 (((less @ x @ y)) = $true) | ~spl0_1),
% 0.18/0.27 inference(avatar_component_clause,[],[f33])).
% 0.18/0.27 thf(f36,plain,(
% 0.18/0.27 spl0_1),
% 0.18/0.27 inference(avatar_split_clause,[],[f25,f33])).
% 0.18/0.27 thf(f38,definition,(
% 0.18/0.27 spl0_2 <=> (((less @ y @ z)) = $true)),
% 0.18/0.27 introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition])).
% 0.18/0.27 thf(f40,plain,(
% 0.18/0.27 (((less @ y @ z)) = $true) | ~spl0_2),
% 0.18/0.27 inference(avatar_component_clause,[],[f38])).
% 0.18/0.27 thf(f42,definition,(
% 0.18/0.27 spl0_3 <=> (y = z)),
% 0.18/0.27 introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition])).
% 0.18/0.27 thf(f45,plain,(
% 0.18/0.27 spl0_2 | spl0_3),
% 0.18/0.27 inference(avatar_split_clause,[],[f27,f42,f38])).
% 0.18/0.27 thf(f47,definition,(
% 0.18/0.27 spl0_4 <=> (((less @ x @ z)) = $true)),
% 0.18/0.27 introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition])).
% 0.18/0.27 thf(f49,plain,(
% 0.18/0.27 (((less @ x @ z)) != $true) | spl0_4),
% 0.18/0.27 inference(avatar_component_clause,[],[f47])).
% 0.18/0.27 thf(f50,plain,(
% 0.18/0.27 ~spl0_4),
% 0.18/0.27 inference(avatar_split_clause,[],[f29,f47])).
% 0.18/0.27 thf(f51,definition,(
% 0.18/0.27 (y != z) | (((less @ x @ y)) != $true) | (((less @ x @ z)) = $true)),
% 0.18/0.27 introduced(theory,[theory_tautology_sat_conflict])).
% 0.18/0.27 thf(f52,plain,(
% 0.18/0.27 ( ! [X0 : nat] : (($true != ((less @ x @ X0))) | ($true != ((less @ X0 @ z))) | ($true != $true)) ) | spl0_4),
% 0.18/0.27 inference(superposition,[],[f49,f28])).
% 0.18/0.27 thf(f53,plain,(
% 0.18/0.27 ( ! [X0 : nat] : (($true != ((less @ x @ X0))) | ($true != ((less @ X0 @ z)))) ) | spl0_4),
% 0.18/0.27 inference(trivial_inequality_removal,[],[f52])).
% 0.18/0.27 thf(f54,plain,(
% 0.18/0.27 ($true != $true) | (((less @ y @ z)) != $true) | (~spl0_1 | spl0_4)),
% 0.18/0.27 inference(superposition,[],[f53,f35])).
% 0.18/0.27 thf(f56,plain,(
% 0.18/0.27 (((less @ y @ z)) != $true) | (~spl0_1 | spl0_4)),
% 0.18/0.27 inference(trivial_inequality_removal,[],[f54])).
% 0.18/0.27 thf(f58,plain,(
% 0.18/0.27 $false | (~spl0_1 | ~spl0_2 | spl0_4)),
% 0.18/0.27 inference(forward_subsumption_resolution,[],[f56,f40])).
% 0.18/0.27 thf(f59,plain,(
% 0.18/0.27 ~spl0_1 | ~spl0_2 | spl0_4),
% 0.18/0.27 inference(avatar_contradiction_clause,[],[f58])).
% 0.18/0.27 cnf(s1, plain, spl0_1, inference(sat_conversion,[],[f36])).
% 0.18/0.27 cnf(s2, plain, spl0_2 | spl0_3, inference(sat_conversion,[],[f45])).
% 0.18/0.27 cnf(s3, plain, ~spl0_4, inference(sat_conversion,[],[f50])).
% 0.18/0.27 cnf(s4, plain, ~spl0_1 | ~spl0_3 | spl0_4, inference(sat_conversion,[],[f51])).
% 0.18/0.27 cnf(s5, plain, ~spl0_1 | ~spl0_2 | spl0_4, inference(sat_conversion,[],[f59])).
% 0.18/0.27 cnf(s6, plain, ~spl0_2, inference(rat,[],[s5,s3,s1])).
% 0.18/0.27 cnf(s7, plain, ~spl0_3, inference(rat,[],[s4,s3,s1])).
% 0.18/0.27 cnf(s8, plain, $false, inference(rat,[],[s2,s7,s6])).
% 0.18/0.27 thf(f60,plain,(
% 0.18/0.27 $false),
% 0.18/0.27 inference(avatar_sat_refutation,[],[s8])).
% 0.18/0.27 % SZS output end Proof for theBenchmark
% 0.18/0.27 % (3292795)------------------------------
% 0.18/0.27 % (3292795)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.27 % (3292795)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.27 % (3292795)CaDiCaL version: 2.1.3
% 0.18/0.27 % (3292795)Termination reason: Refutation
% 0.18/0.27 % (3292795)Time elapsed: 0.002 s
% 0.18/0.27 % (3292795)Peak memory usage: 13 MB
% 0.18/0.27 % (3292795)Instructions burned: 3 (million)
% 0.18/0.27 % (3292787)Success in time 0.032 s
% 0.18/0.27 % Vampire exiting
%------------------------------------------------------------------------------