%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO261^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n009.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 08:49:37 AM UTC 2026
% Result : Theorem 0.18s 0.26s
% Output : Refutation 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO261^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n009.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % 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 16:42:01 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.26 % (40882)Will run a generic schedule for satisfiability detection.
% 0.18/0.26 % (40892)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4083175533:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.26 % (40888)% WARNING: option uhcvi not known.
% 0.18/0.26 % (40892) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-40882-40892"...
% 0.18/0.26 % (40892)...printing done.
% 0.18/0.26 % (40891)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1826496177:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.26 % (40887)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2946599029_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.26 % (40888)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1278271408:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.26 % (40889)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4059209146:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.26 % (40890)dis+10_1_sil=32000:sp=arity:random_seed=3562263406:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.26 % (40891)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.18/0.26 % (40892)Refutation found. Thanks to Tanya!
% 0.18/0.26 % SZS status Theorem for theBenchmark
% 0.18/0.26 % SZS output start Proof for theBenchmark
% 0.18/0.26 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.18/0.26 thf(func_def_1, type, cP: ($i > $o)).
% 0.18/0.26 thf(func_def_2, type, c1_plus: ($i > $i)).
% 0.18/0.26 thf(func_def_7, type, sK0: (($i > $o) > $i)).
% 0.18/0.26 thf(func_def_8, type, vNOT: ($o > $o)).
% 0.18/0.26 thf(func_def_9, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.18/0.26 thf(func_def_10, type, db0: !>[X0: $tType]:(X0)).
% 0.18/0.26 thf(func_def_11, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.18/0.26 thf(f1,conjecture,(
% 0.18/0.26 (! [X1 : $i] : ((cP @ X1) => (cP @ (c1_plus @ X1))) & (cP @ cO) & ! [X0 : ($i > $o)] : ((! [X1 : $i] : ((X0 @ X1) => (X0 @ (c1_plus @ X1))) & (X0 @ cO)) => (X0 @ n))) => (cP @ n)),
% 0.18/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cBLEDSOE_FENG_SV_I1)).
% 0.18/0.26 thf(f2,negated_conjecture,(
% 0.18/0.26 ~((! [X1 : $i] : ((cP @ X1) => (cP @ (c1_plus @ X1))) & (cP @ cO) & ! [X0 : ($i > $o)] : ((! [X1 : $i] : ((X0 @ X1) => (X0 @ (c1_plus @ X1))) & (X0 @ cO)) => (X0 @ n))) => (cP @ n))),
% 0.18/0.26 inference(negated_conjecture,[status(cth)],[f1])).
% 0.18/0.26 thf(f3,plain,(
% 0.18/0.26 ~((! [X0 : $i] : ((cP @ X0) => (cP @ (c1_plus @ X0))) & (cP @ cO) & ! [X1 : ($i > $o)] : ((! [X2 : $i] : ((X1 @ X2) => (X1 @ (c1_plus @ X2))) & (X1 @ cO)) => (X1 @ n))) => (cP @ n))),
% 0.18/0.26 inference(rectify,[],[f2])).
% 0.18/0.26 thf(f4,plain,(
% 0.18/0.26 ~((! [X0 : $i] : ((((cP @ X0)) = $true) => (((cP @ (c1_plus @ X0))) = $true)) & (((cP @ cO)) = $true) & ! [X1 : ($i > $o)] : ((! [X2 : $i] : ((((X1 @ X2)) = $true) => (((X1 @ (c1_plus @ X2))) = $true)) & (((X1 @ cO)) = $true)) => (((X1 @ n)) = $true))) => (((cP @ n)) = $true))),
% 0.18/0.26 inference(fool_elimination,[],[f3])).
% 0.18/0.26 thf(f5,plain,(
% 0.18/0.26 (((cP @ n)) != $true) & (! [X0 : $i] : ((((cP @ (c1_plus @ X0))) = $true) | (((cP @ X0)) != $true)) & (((cP @ cO)) = $true) & ! [X1 : ($i > $o)] : ((((X1 @ n)) = $true) | (? [X2 : $i] : ((((X1 @ (c1_plus @ X2))) != $true) & (((X1 @ X2)) = $true)) | (((X1 @ cO)) != $true))))),
% 0.18/0.26 inference(ennf_transformation,[],[f4])).
% 0.18/0.26 thf(f6,plain,(
% 0.18/0.26 (((cP @ n)) != $true) & ! [X0 : $i] : ((((cP @ (c1_plus @ X0))) = $true) | (((cP @ X0)) != $true)) & (((cP @ cO)) = $true) & ! [X1 : ($i > $o)] : ((((X1 @ n)) = $true) | ? [X2 : $i] : ((((X1 @ (c1_plus @ X2))) != $true) & (((X1 @ X2)) = $true)) | (((X1 @ cO)) != $true))),
% 0.18/0.26 inference(flattening,[],[f5])).
% 0.18/0.26 thf(f7,plain,(
% 0.18/0.26 (((cP @ n)) != $true) & ! [X0 : $i] : ((((cP @ (c1_plus @ X0))) = $true) | (((cP @ X0)) != $true)) & (((cP @ cO)) = $true) & ! [X1 : ($i > $o)] : ((((X1 @ n)) = $true) | (($true != ((X1 @ (c1_plus @ (sK0 @ X1))))) & ($true = ((X1 @ (sK0 @ X1))))) | (((X1 @ cO)) != $true))),
% 0.18/0.26 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X2,sK0 @ X1)],[f6])).
% 0.18/0.26 thf(f8,plain,(
% 0.18/0.26 ( ! [X1 : ($i > $o)] : ((((X1 @ cO)) != $true) | ($true = ((X1 @ (sK0 @ X1)))) | (((X1 @ n)) = $true)) )),
% 0.18/0.26 inference(cnf_transformation,[],[f7])).
% 0.18/0.26 thf(f9,plain,(
% 0.18/0.26 ( ! [X1 : ($i > $o)] : (($true != ((X1 @ (c1_plus @ (sK0 @ X1))))) | (((X1 @ n)) = $true) | (((X1 @ cO)) != $true)) )),
% 0.18/0.26 inference(cnf_transformation,[],[f7])).
% 0.18/0.26 thf(f10,plain,(
% 0.18/0.26 (((cP @ cO)) = $true)),
% 0.18/0.26 inference(cnf_transformation,[],[f7])).
% 0.18/0.26 thf(f11,plain,(
% 0.18/0.26 ( ! [X0 : $i] : ((((cP @ X0)) != $true) | (((cP @ (c1_plus @ X0))) = $true)) )),
% 0.18/0.26 inference(cnf_transformation,[],[f7])).
% 0.18/0.26 thf(f12,plain,(
% 0.18/0.26 (((cP @ n)) != $true)),
% 0.18/0.26 inference(cnf_transformation,[],[f7])).
% 0.18/0.26 thf(f14,definition,(
% 0.18/0.26 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.18/0.26 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.18/0.26 thf(f21,plain,(
% 0.18/0.26 ($true != $true) | ($true = (((^[Y0 : $i]: (cP @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ (sK0 @ (^[Y0 : $i]: (cP @ ((^[Y1 : $i]: (Y1)) @ Y0))))))) | ($true = (((^[Y0 : $i]: (cP @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ n)))),
% 0.18/0.26 inference(constrained_superposition,[],[f8,f10])).
% 0.18/0.26 thf(f29,plain,(
% 0.18/0.26 ($true = (((^[Y0 : $i]: (cP @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ (sK0 @ (^[Y0 : $i]: (cP @ ((^[Y1 : $i]: (Y1)) @ Y0))))))) | ($true = (((^[Y0 : $i]: (cP @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ n)))),
% 0.18/0.26 inference(trivial_inequality_removal,[],[f21])).
% 0.18/0.26 thf(f30,plain,(
% 0.18/0.26 ($true = ((cP @ (sK0 @ cP)))) | (((cP @ n)) = $true)),
% 0.18/0.26 inference(beta-eta_normalization,[],[f29])).
% 0.18/0.26 thf(f40,plain,(
% 0.18/0.26 ($true = ((cP @ (sK0 @ cP))))),
% 0.18/0.26 inference(forward_subsumption_resolution,[],[f30,f12])).
% 0.18/0.26 thf(f100,plain,(
% 0.18/0.26 ( ! [X0 : $i] : (($true != $true) | (((cP @ (c1_plus @ X0))) = $true) | (((cP @ X0)) = $false)) )),
% 0.18/0.26 inference(constrained_superposition,[],[f11,f14])).
% 0.18/0.26 thf(f108,plain,(
% 0.18/0.26 ( ! [X0 : $i] : ((((cP @ (c1_plus @ X0))) = $true) | (((cP @ X0)) = $false)) )),
% 0.18/0.26 inference(trivial_inequality_removal,[],[f100])).
% 0.18/0.26 thf(f141,plain,(
% 0.18/0.26 ( ! [X0 : $i] : (($true != $true) | ($true = (((^[Y0 : $i]: (cP @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ n))) | ($true != (((^[Y0 : $i]: (cP @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ cO))) | (((cP @ X0)) = $false) | (((sK0 @ cP)) != X0)) )),
% 0.18/0.26 inference(constrained_superposition,[],[f9,f108])).
% 0.18/0.26 thf(f145,plain,(
% 0.18/0.26 ( ! [X0 : $i] : (($true = (((^[Y0 : $i]: (cP @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ n))) | ($true != (((^[Y0 : $i]: (cP @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ cO))) | (((cP @ X0)) = $false) | (((sK0 @ cP)) != X0)) )),
% 0.18/0.26 inference(trivial_inequality_removal,[],[f141])).
% 0.18/0.26 thf(f146,plain,(
% 0.18/0.26 ( ! [X0 : $i] : ((((cP @ n)) = $true) | (((cP @ cO)) != $true) | (((cP @ X0)) = $false) | (((sK0 @ cP)) != X0)) )),
% 0.18/0.26 inference(beta-eta_normalization,[],[f145])).
% 0.18/0.26 thf(f150,plain,(
% 0.18/0.26 ( ! [X0 : $i] : ((((cP @ cO)) != $true) | (((cP @ X0)) = $false) | (((sK0 @ cP)) != X0)) )),
% 0.18/0.26 inference(forward_subsumption_resolution,[],[f146,f12])).
% 0.18/0.26 thf(f151,plain,(
% 0.18/0.26 ( ! [X0 : $i] : ((((sK0 @ cP)) != X0) | (((cP @ X0)) = $false)) )),
% 0.18/0.26 inference(forward_subsumption_resolution,[],[f150,f10])).
% 0.18/0.26 thf(f152,plain,(
% 0.18/0.26 ($false = ((cP @ (sK0 @ cP))))),
% 0.18/0.26 inference(equality_resolution,[],[f151])).
% 0.18/0.26 thf(f212,plain,(
% 0.18/0.26 ($true = $false)),
% 0.18/0.26 inference(constrained_superposition,[],[f40,f152])).
% 0.18/0.26 thf(f223,plain,(
% 0.18/0.26 $false),
% 0.18/0.26 inference(trivial_inequality_removal,[],[f212])).
% 0.18/0.26 % SZS output end Proof for theBenchmark
% 0.18/0.26 % (40892)------------------------------
% 0.18/0.26 % (40892)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.26 % (40892)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.26 % (40892)CaDiCaL version: 2.1.3
% 0.18/0.26 % (40892)Termination reason: Refutation
% 0.18/0.26 % (40892)Time elapsed: 0.005 s
% 0.18/0.26 % (40892)Peak memory usage: 12 MB
% 0.18/0.26 % (40892)Instructions burned: 14 (million)
% 0.18/0.26 % (40882)Success in time 0.031 s
% 0.18/0.26 % Vampire exiting
%------------------------------------------------------------------------------