%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO317^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:47:26 AM UTC 2026
% Result : Theorem 0.22s 0.26s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO317^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n016.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 16:50:05 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.23 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
% 0.22/0.26 % (601943)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.26 % (601951)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=59676372: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)
% 0.22/0.26 % (601954)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.26 % (601954)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
% 0.22/0.26 % (601951) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-601943-601951"...
% 0.22/0.26 % (601951)...printing done.
% 0.22/0.26 % (601949)lrs+10_16_si=on:nwc=1.5:random_seed=1139064523:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.26 % (601951)Refutation found. Thanks to Tanya!
% 0.22/0.26 % SZS status Theorem for theBenchmark
% 0.22/0.26 % SZS output start Proof for theBenchmark
% 0.22/0.26 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.26 thf(func_def_0, type, cP: ($i > $o)).
% 0.22/0.26 thf(func_def_1, type, f: ($i > $i)).
% 0.22/0.26 thf(func_def_2, type, cEQ: ($i > $i > $o)).
% 0.22/0.26 thf(func_def_7, type, sK0: (($i > $o) > $i)).
% 0.22/0.26 thf(func_def_8, type, vNOT: ($o > $o)).
% 0.22/0.26 thf(func_def_10, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.22/0.26 thf(func_def_11, type, db0: !>[X0: $tType]:(X0)).
% 0.22/0.26 thf(func_def_12, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.22/0.26 thf(f1,conjecture,(
% 0.22/0.26 (! [X0 : $i] : (cEQ @ X0 @ X0) & ! [X1 : $i,X0 : $i] : (((cP @ X0) & (cEQ @ X0 @ X1)) => (cP @ X1)) & (cP @ a) & ! [X2 : $i,X1 : $i] : ((cEQ @ (f @ X1) @ (f @ X2)) => (cEQ @ X1 @ X2))) => ? [X3 : ($i > $o)] : (? [X2 : $i] : (X3 @ X2) & ! [X0 : $i] : ((X3 @ (f @ X0)) => (cP @ X0)))),
% 0.22/0.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM304)).
% 0.22/0.26 thf(f2,negated_conjecture,(
% 0.22/0.26 ~((! [X0 : $i] : (cEQ @ X0 @ X0) & ! [X1 : $i,X0 : $i] : (((cP @ X0) & (cEQ @ X0 @ X1)) => (cP @ X1)) & (cP @ a) & ! [X2 : $i,X1 : $i] : ((cEQ @ (f @ X1) @ (f @ X2)) => (cEQ @ X1 @ X2))) => ? [X3 : ($i > $o)] : (? [X2 : $i] : (X3 @ X2) & ! [X0 : $i] : ((X3 @ (f @ X0)) => (cP @ X0))))),
% 0.22/0.26 inference(negated_conjecture,[status(cth)],[f1])).
% 0.22/0.26 thf(f3,plain,(
% 0.22/0.26 ~((! [X0 : $i] : (cEQ @ X0 @ X0) & ! [X1 : $i,X2 : $i] : (((cP @ X2) & (cEQ @ X2 @ X1)) => (cP @ X1)) & (cP @ a) & ! [X3 : $i,X4 : $i] : ((cEQ @ (f @ X4) @ (f @ X3)) => (cEQ @ X4 @ X3))) => ? [X5 : ($i > $o)] : (? [X6 : $i] : (X5 @ X6) & ! [X7 : $i] : ((X5 @ (f @ X7)) => (cP @ X7))))),
% 0.22/0.26 inference(rectify,[],[f2])).
% 0.22/0.26 thf(f4,plain,(
% 0.22/0.26 ~((! [X4 : $i,X3 : $i] : (($true = ((cEQ @ (f @ X4) @ (f @ X3)))) => (((cEQ @ X4 @ X3)) = $true)) & ! [X2 : $i,X1 : $i] : ((($true = ((cP @ X2))) & (((cEQ @ X2 @ X1)) = $true)) => (((cP @ X1)) = $true)) & (((cP @ a)) = $true) & ! [X0 : $i] : (((cEQ @ X0 @ X0)) = $true)) => ? [X5 : ($i > $o)] : (! [X7 : $i] : (($true = ((X5 @ (f @ X7)))) => ($true = ((cP @ X7)))) & ? [X6 : $i] : (((X5 @ X6)) = $true)))),
% 0.22/0.26 inference(fool_elimination,[],[f3])).
% 0.22/0.26 thf(f5,plain,(
% 0.22/0.26 ! [X5 : ($i > $o)] : (! [X6 : $i] : (((X5 @ X6)) != $true) | ? [X7 : $i] : (($true != ((cP @ X7))) & ($true = ((X5 @ (f @ X7)))))) & (! [X4 : $i,X3 : $i] : ((((cEQ @ X4 @ X3)) = $true) | ($true != ((cEQ @ (f @ X4) @ (f @ X3))))) & ! [X2 : $i,X1 : $i] : ((((cP @ X1)) = $true) | (($true != ((cP @ X2))) | (((cEQ @ X2 @ X1)) != $true))) & (((cP @ a)) = $true) & ! [X0 : $i] : (((cEQ @ X0 @ X0)) = $true))),
% 0.22/0.26 inference(ennf_transformation,[],[f4])).
% 0.22/0.26 thf(f6,plain,(
% 0.22/0.26 ! [X4 : $i,X3 : $i] : ((((cEQ @ X4 @ X3)) = $true) | ($true != ((cEQ @ (f @ X4) @ (f @ X3))))) & (((cP @ a)) = $true) & ! [X2 : $i,X1 : $i] : (($true != ((cP @ X2))) | (((cP @ X1)) = $true) | (((cEQ @ X2 @ X1)) != $true)) & ! [X5 : ($i > $o)] : (! [X6 : $i] : (((X5 @ X6)) != $true) | ? [X7 : $i] : (($true != ((cP @ X7))) & ($true = ((X5 @ (f @ X7)))))) & ! [X0 : $i] : (((cEQ @ X0 @ X0)) = $true)),
% 0.22/0.26 inference(flattening,[],[f5])).
% 0.22/0.26 thf(f7,plain,(
% 0.22/0.26 ! [X0 : $i,X1 : $i] : ((((cEQ @ X0 @ X1)) = $true) | ($true != ((cEQ @ (f @ X0) @ (f @ X1))))) & (((cP @ a)) = $true) & ! [X2 : $i,X3 : $i] : (($true != ((cP @ X2))) | ($true = ((cP @ X3))) | ($true != ((cEQ @ X2 @ X3)))) & ! [X4 : ($i > $o)] : (! [X5 : $i] : ($true != ((X4 @ X5))) | ? [X6 : $i] : ((((cP @ X6)) != $true) & ($true = ((X4 @ (f @ X6)))))) & ! [X7 : $i] : ($true = ((cEQ @ X7 @ X7)))),
% 0.22/0.26 inference(rectify,[],[f6])).
% 0.22/0.26 thf(f8,plain,(
% 0.22/0.26 ! [X0 : $i,X1 : $i] : ((((cEQ @ X0 @ X1)) = $true) | ($true != ((cEQ @ (f @ X0) @ (f @ X1))))) & (((cP @ a)) = $true) & ! [X2 : $i,X3 : $i] : (($true != ((cP @ X2))) | ($true = ((cP @ X3))) | ($true != ((cEQ @ X2 @ X3)))) & ! [X4 : ($i > $o)] : (! [X5 : $i] : ($true != ((X4 @ X5))) | ((((cP @ (sK0 @ X4))) != $true) & ($true = ((X4 @ (f @ (sK0 @ X4))))))) & ! [X7 : $i] : ($true = ((cEQ @ X7 @ X7)))),
% 0.22/0.26 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X6,sK0 @ X4)],[f7])).
% 0.22/0.26 thf(f9,plain,(
% 0.22/0.26 ( ! [X7 : $i] : (($true = ((cEQ @ X7 @ X7)))) )),
% 0.22/0.26 inference(cnf_transformation,[],[f8])).
% 0.22/0.26 thf(f10,plain,(
% 0.22/0.26 ( ! [X4 : ($i > $o),X5 : $i] : (($true = ((X4 @ (f @ (sK0 @ X4))))) | ($true != ((X4 @ X5)))) )),
% 0.22/0.26 inference(cnf_transformation,[],[f8])).
% 0.22/0.26 thf(f11,plain,(
% 0.22/0.26 ( ! [X4 : ($i > $o),X5 : $i] : ((((cP @ (sK0 @ X4))) != $true) | ($true != ((X4 @ X5)))) )),
% 0.22/0.26 inference(cnf_transformation,[],[f8])).
% 0.22/0.26 thf(f12,plain,(
% 0.22/0.26 ( ! [X2 : $i,X3 : $i] : (($true != ((cEQ @ X2 @ X3))) | ($true != ((cP @ X2))) | ($true = ((cP @ X3)))) )),
% 0.22/0.26 inference(cnf_transformation,[],[f8])).
% 0.22/0.26 thf(f13,plain,(
% 0.22/0.26 (((cP @ a)) = $true)),
% 0.22/0.26 inference(cnf_transformation,[],[f8])).
% 0.22/0.26 thf(f14,plain,(
% 0.22/0.26 ( ! [X0 : $i,X1 : $i] : (($true != ((cEQ @ (f @ X0) @ (f @ X1)))) | (((cEQ @ X0 @ X1)) = $true)) )),
% 0.22/0.26 inference(cnf_transformation,[],[f8])).
% 0.22/0.26 thf(f17,definition,(
% 0.22/0.26 spl1_1 <=> (((cP @ a)) = $true)),
% 0.22/0.26 introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition])).
% 0.22/0.26 thf(f19,plain,(
% 0.22/0.26 (((cP @ a)) = $true) | ~spl1_1),
% 0.22/0.26 inference(avatar_component_clause,[],[f17])).
% 0.22/0.26 thf(f20,plain,(
% 0.22/0.26 spl1_1),
% 0.22/0.26 inference(avatar_split_clause,[],[f13,f17])).
% 0.22/0.26 thf(f29,plain,(
% 0.22/0.26 ( ! [X0 : $i,X1 : $i] : ((((cEQ @ X0 @ (sK0 @ (cEQ @ (f @ X0))))) = $true) | ($true != $true) | ($true != ((cEQ @ (f @ X0) @ X1)))) )),
% 0.22/0.26 inference(superposition,[],[f14,f10])).
% 0.22/0.26 thf(f34,plain,(
% 0.22/0.26 ( ! [X0 : $i,X1 : $i] : ((((cEQ @ X0 @ (sK0 @ (cEQ @ (f @ X0))))) = $true) | ($true != ((cEQ @ (f @ X0) @ X1)))) )),
% 0.22/0.26 inference(trivial_inequality_removal,[],[f29])).
% 0.22/0.26 thf(f43,plain,(
% 0.22/0.26 ( ! [X0 : $i,X1 : $i] : ((((cP @ X0)) != $true) | ($true != $true) | (((cP @ (sK0 @ (cEQ @ (f @ X0))))) = $true) | ($true != ((cEQ @ (f @ X0) @ X1)))) )),
% 0.22/0.26 inference(superposition,[],[f12,f34])).
% 0.22/0.26 thf(f44,plain,(
% 0.22/0.26 ( ! [X0 : $i,X1 : $i] : ((((cP @ (sK0 @ (cEQ @ (f @ X0))))) = $true) | (((cP @ X0)) != $true) | ($true != ((cEQ @ (f @ X0) @ X1)))) )),
% 0.22/0.26 inference(trivial_inequality_removal,[],[f43])).
% 0.22/0.26 thf(f45,plain,(
% 0.22/0.26 ( ! [X0 : $i,X1 : $i] : (($true != ((cEQ @ (f @ X0) @ X1))) | (((cP @ X0)) != $true)) )),
% 0.22/0.26 inference(forward_subsumption_resolution,[],[f44,f11])).
% 0.22/0.26 thf(f74,plain,(
% 0.22/0.26 ( ! [X0 : $i] : ((((cP @ X0)) != $true) | ($true != $true)) )),
% 0.22/0.26 inference(superposition,[],[f45,f9])).
% 0.22/0.26 thf(f80,plain,(
% 0.22/0.26 ( ! [X0 : $i] : ((((cP @ X0)) != $true)) )),
% 0.22/0.26 inference(trivial_inequality_removal,[],[f74])).
% 0.22/0.26 thf(f194,plain,(
% 0.22/0.26 ($true != $true) | ~spl1_1),
% 0.22/0.26 inference(superposition,[],[f80,f19])).
% 0.22/0.26 thf(f202,plain,(
% 0.22/0.26 $false | ~spl1_1),
% 0.22/0.26 inference(trivial_inequality_removal,[],[f194])).
% 0.22/0.26 thf(f203,plain,(
% 0.22/0.26 ~spl1_1),
% 0.22/0.26 inference(avatar_contradiction_clause,[],[f202])).
% 0.22/0.26 cnf(s1, plain, spl1_1, inference(sat_conversion,[],[f20])).
% 0.22/0.26 cnf(s2, plain, ~spl1_1, inference(sat_conversion,[],[f203])).
% 0.22/0.26 cnf(s3, plain, $false, inference(rat,[],[s1,s2])).
% 0.22/0.26 thf(f206,plain,(
% 0.22/0.26 $false),
% 0.22/0.26 inference(avatar_sat_refutation,[],[s3])).
% 0.22/0.26 % SZS output end Proof for theBenchmark
% 0.22/0.26 % (601951)------------------------------
% 0.22/0.26 % (601951)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.26 % (601951)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.26 % (601951)CaDiCaL version: 2.1.3
% 0.22/0.26 % (601951)Termination reason: Refutation
% 0.22/0.26 % (601951)Time elapsed: 0.006 s
% 0.22/0.26 % (601951)Peak memory usage: 13 MB
% 0.22/0.26 % (601951)Instructions burned: 17 (million)
% 0.22/0.26 % (601943)Success in time 0.021 s
% 0.22/0.26 % Vampire exiting
%------------------------------------------------------------------------------