%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO261^5 : 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 : n005.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 08:47:18 AM UTC 2026
% Result : Theorem 0.19s 0.26s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO261^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n005.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 16:41:47 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
% 0.08/0.22 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
% 0.19/0.26 % (1894340)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.26 % (1894350)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2772107612:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.19/0.26 % (1894351)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.19/0.26 % (1894351)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
% 0.19/0.26 % (1894350) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1894340-1894350"...
% 0.19/0.26 % (1894350)...printing done.
% 0.19/0.26 % (1894345)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3190794317:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.19/0.26 % (1894350)Refutation found. Thanks to Tanya!
% 0.19/0.26 % SZS status Theorem for theBenchmark
% 0.19/0.26 % SZS output start Proof for theBenchmark
% 0.19/0.26 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.19/0.26 thf(func_def_1, type, cP: ($i > $o)).
% 0.19/0.26 thf(func_def_2, type, c1_plus: ($i > $i)).
% 0.19/0.26 thf(func_def_7, type, sK0: (($i > $o) > $i)).
% 0.19/0.26 thf(func_def_8, type, vNOT: ($o > $o)).
% 0.19/0.26 thf(func_def_9, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.19/0.26 thf(func_def_10, type, db0: !>[X0: $tType]:(X0)).
% 0.19/0.26 thf(func_def_11, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.19/0.26 thf(f1,conjecture,(
% 0.19/0.26 (! [X1 : $i] : ((cP @ X1) => (cP @ (c1_plus @ X1))) & ! [X0 : ($i > $o)] : ((! [X1 : $i] : ((X0 @ X1) => (X0 @ (c1_plus @ X1))) & (X0 @ cO)) => (X0 @ n)) & (cP @ cO)) => (cP @ n)),
% 0.19/0.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBLEDSOE_FENG_SV_I1)).
% 0.19/0.26 thf(f2,negated_conjecture,(
% 0.19/0.26 ~((! [X1 : $i] : ((cP @ X1) => (cP @ (c1_plus @ X1))) & ! [X0 : ($i > $o)] : ((! [X1 : $i] : ((X0 @ X1) => (X0 @ (c1_plus @ X1))) & (X0 @ cO)) => (X0 @ n)) & (cP @ cO)) => (cP @ n))),
% 0.19/0.26 inference(negated_conjecture,[status(cth)],[f1])).
% 0.19/0.26 thf(f3,plain,(
% 0.19/0.26 ~((! [X0 : $i] : ((cP @ X0) => (cP @ (c1_plus @ X0))) & ! [X1 : ($i > $o)] : ((! [X2 : $i] : ((X1 @ X2) => (X1 @ (c1_plus @ X2))) & (X1 @ cO)) => (X1 @ n)) & (cP @ cO)) => (cP @ n))),
% 0.19/0.26 inference(rectify,[],[f2])).
% 0.19/0.26 thf(f4,plain,(
% 0.19/0.26 ~(((((cP @ cO)) = $true) & ! [X1 : ($i > $o)] : ((! [X2 : $i] : (($true = ((X1 @ X2))) => ($true = ((X1 @ (c1_plus @ X2))))) & ($true = ((X1 @ cO)))) => ($true = ((X1 @ n)))) & ! [X0 : $i] : (($true = ((cP @ X0))) => (((cP @ (c1_plus @ X0))) = $true))) => (((cP @ n)) = $true))),
% 0.19/0.26 inference(fool_elimination,[],[f3])).
% 0.19/0.26 thf(f5,plain,(
% 0.19/0.26 (((cP @ n)) != $true) & ((((cP @ cO)) = $true) & ! [X1 : ($i > $o)] : (($true = ((X1 @ n))) | (? [X2 : $i] : (($true != ((X1 @ (c1_plus @ X2)))) & ($true = ((X1 @ X2)))) | ($true != ((X1 @ cO))))) & ! [X0 : $i] : ((((cP @ (c1_plus @ X0))) = $true) | ($true != ((cP @ X0)))))),
% 0.19/0.26 inference(ennf_transformation,[],[f4])).
% 0.19/0.26 thf(f6,plain,(
% 0.19/0.26 ! [X1 : ($i > $o)] : (($true != ((X1 @ cO))) | ($true = ((X1 @ n))) | ? [X2 : $i] : (($true != ((X1 @ (c1_plus @ X2)))) & ($true = ((X1 @ X2))))) & ! [X0 : $i] : ((((cP @ (c1_plus @ X0))) = $true) | ($true != ((cP @ X0)))) & (((cP @ n)) != $true) & (((cP @ cO)) = $true)),
% 0.19/0.26 inference(flattening,[],[f5])).
% 0.19/0.26 thf(f7,plain,(
% 0.19/0.26 ! [X0 : ($i > $o)] : ((((X0 @ cO)) != $true) | (((X0 @ n)) = $true) | ? [X1 : $i] : ((((X0 @ (c1_plus @ X1))) != $true) & (((X0 @ X1)) = $true))) & ! [X2 : $i] : ((((cP @ (c1_plus @ X2))) = $true) | (((cP @ X2)) != $true)) & (((cP @ n)) != $true) & (((cP @ cO)) = $true)),
% 0.19/0.26 inference(rectify,[],[f6])).
% 0.19/0.26 thf(f8,plain,(
% 0.19/0.26 ! [X0 : ($i > $o)] : ((((X0 @ cO)) != $true) | (((X0 @ n)) = $true) | ((((X0 @ (c1_plus @ (sK0 @ X0)))) != $true) & ($true = ((X0 @ (sK0 @ X0)))))) & ! [X2 : $i] : ((((cP @ (c1_plus @ X2))) = $true) | (((cP @ X2)) != $true)) & (((cP @ n)) != $true) & (((cP @ cO)) = $true)),
% 0.19/0.26 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X1,sK0 @ X0)],[f7])).
% 0.19/0.26 thf(f9,plain,(
% 0.19/0.26 (((cP @ cO)) = $true)),
% 0.19/0.26 inference(cnf_transformation,[],[f8])).
% 0.19/0.26 thf(f10,plain,(
% 0.19/0.26 (((cP @ n)) != $true)),
% 0.19/0.26 inference(cnf_transformation,[],[f8])).
% 0.19/0.26 thf(f11,plain,(
% 0.19/0.26 ( ! [X2 : $i] : ((((cP @ X2)) != $true) | (((cP @ (c1_plus @ X2))) = $true)) )),
% 0.19/0.26 inference(cnf_transformation,[],[f8])).
% 0.19/0.26 thf(f12,plain,(
% 0.19/0.26 ( ! [X0 : ($i > $o)] : ((((X0 @ cO)) != $true) | (((X0 @ n)) = $true) | ($true = ((X0 @ (sK0 @ X0))))) )),
% 0.19/0.26 inference(cnf_transformation,[],[f8])).
% 0.19/0.26 thf(f13,plain,(
% 0.19/0.26 ( ! [X0 : ($i > $o)] : ((((X0 @ (c1_plus @ (sK0 @ X0)))) != $true) | (((X0 @ cO)) != $true) | (((X0 @ n)) = $true)) )),
% 0.19/0.26 inference(cnf_transformation,[],[f8])).
% 0.19/0.26 thf(f23,plain,(
% 0.19/0.26 ($true = (((^[Y0 : $i]: (cP @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ (sK0 @ (^[Y0 : $i]: (cP @ ((^[Y1 : $i]: (Y1)) @ Y0))))))) | ($true != $true) | ($true = (((^[Y0 : $i]: (cP @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ n)))),
% 0.19/0.26 inference(constrained_superposition,[],[f12,f9])).
% 0.19/0.26 thf(f37,plain,(
% 0.19/0.26 ($true = (((^[Y0 : $i]: (cP @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ (sK0 @ (^[Y0 : $i]: (cP @ ((^[Y1 : $i]: (Y1)) @ Y0))))))) | ($true = (((^[Y0 : $i]: (cP @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ n)))),
% 0.19/0.26 inference(trivial_inequality_removal,[],[f23])).
% 0.19/0.26 thf(f38,plain,(
% 0.19/0.26 ($true = ((cP @ (sK0 @ cP)))) | (((cP @ n)) = $true)),
% 0.19/0.26 inference(beta-eta_normalization,[],[f37])).
% 0.19/0.26 thf(f52,plain,(
% 0.19/0.26 ($true = ((cP @ (sK0 @ cP))))),
% 0.19/0.26 inference(forward_subsumption_resolution,[],[f38,f10])).
% 0.19/0.26 thf(f122,plain,(
% 0.19/0.26 (((cP @ (c1_plus @ (sK0 @ cP)))) = $true) | ($true != $true)),
% 0.19/0.26 inference(constrained_superposition,[],[f11,f52])).
% 0.19/0.26 thf(f125,plain,(
% 0.19/0.26 (((cP @ (c1_plus @ (sK0 @ cP)))) = $true)),
% 0.19/0.26 inference(trivial_inequality_removal,[],[f122])).
% 0.19/0.26 thf(f238,plain,(
% 0.19/0.26 ($true != (((^[Y0 : $i]: (cP @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ cO))) | ($true != $true) | ($true = (((^[Y0 : $i]: (cP @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ n)))),
% 0.19/0.26 inference(constrained_superposition,[],[f13,f125])).
% 0.19/0.26 thf(f250,plain,(
% 0.19/0.26 ($true != (((^[Y0 : $i]: (cP @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ cO))) | ($true = (((^[Y0 : $i]: (cP @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ n)))),
% 0.19/0.26 inference(trivial_inequality_removal,[],[f238])).
% 0.19/0.26 thf(f251,plain,(
% 0.19/0.26 (((cP @ cO)) != $true) | (((cP @ n)) = $true)),
% 0.19/0.26 inference(beta-eta_normalization,[],[f250])).
% 0.19/0.26 thf(f253,plain,(
% 0.19/0.26 (((cP @ n)) = $true)),
% 0.19/0.26 inference(forward_subsumption_resolution,[],[f251,f9])).
% 0.19/0.26 thf(f254,plain,(
% 0.19/0.26 $false),
% 0.19/0.26 inference(forward_subsumption_resolution,[],[f253,f10])).
% 0.19/0.26 % SZS output end Proof for theBenchmark
% 0.19/0.26 % (1894350)------------------------------
% 0.19/0.26 % (1894350)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.26 % (1894350)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.26 % (1894350)CaDiCaL version: 2.1.3
% 0.19/0.26 % (1894350)Termination reason: Refutation
% 0.19/0.26 % (1894350)Time elapsed: 0.006 s
% 0.19/0.26 % (1894350)Peak memory usage: 12 MB
% 0.19/0.26 % (1894350)Instructions burned: 17 (million)
% 0.19/0.26 % (1894340)Success in time 0.03 s
% 0.19/0.26 % Vampire exiting
%------------------------------------------------------------------------------