%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL727^5 : 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 : 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 08:15:09 AM UTC 2026
% Result : Theorem 0.25s 0.31s
% Output : Refutation 0.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL727^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.20 % Computer : n007.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 09:56:56 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.25 Running first-order model finding
% 0.08/0.25 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
% 0.25/0.31 % (3155058)Will run a generic schedule for satisfiability detection.
% 0.25/0.31 % (3155065)% WARNING: option uhcvi not known.
% 0.25/0.31 % (3155065)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3849353814:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.25/0.31 % (3155065)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.25/0.31 % (3155065)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.25/0.31 % (3155070)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1122108665:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.25/0.31 % (3155064)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3284200570_2999 on theBenchmark for (2999ds/0Mi)
% 0.25/0.31 % (3155066)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1942798378:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.25/0.31 % (3155067)dis+10_1_sil=32000:sp=arity:random_seed=171530402:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.25/0.31 % (3155068)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1991542431:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.25/0.31 % Exception at run slice level
% 0.25/0.31 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.25/0.31 % (3155069)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=336800167:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.25/0.31 % (3155068)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.25/0.31 % (3155066) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3155058-3155066"...
% 0.25/0.31 % (3155066)...printing done.
% 0.25/0.31 % (3155066)Refutation found. Thanks to Tanya!
% 0.25/0.31 % SZS status Theorem for theBenchmark
% 0.25/0.31 % SZS output start Proof for theBenchmark
% 0.25/0.31 thf(type_def_5, type, a: $tType).
% 0.25/0.31 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.25/0.31 thf(func_def_3, type, sK0: ((a > $o) > $o)).
% 0.25/0.31 thf(func_def_4, type, sK1: (((a > $o) > a) > a > $o)).
% 0.25/0.31 thf(func_def_5, type, sK2: ((a > $o) > a)).
% 0.25/0.31 thf(func_def_6, type, sK3: (((a > $o) > a > $o) > (a > $o) > a)).
% 0.25/0.31 thf(func_def_7, type, vNOT: ($o > $o)).
% 0.25/0.31 thf(func_def_9, type, db0: !>[X0: $tType]:(X0)).
% 0.25/0.31 thf(func_def_10, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.25/0.31 thf(func_def_11, type, db1: !>[X0: $tType]:(X0)).
% 0.25/0.31 thf(func_def_12, type, sK5: (((a > $o) > a > a) > a)).
% 0.25/0.31 thf(f1,conjecture,(
% 0.25/0.31 ! [X0 : ((a > $o) > a > $o)] : ? [X1 : ((a > $o) > a)] : ! [X2 : (a > $o)] : (? [X3 : a] : (X0 @ X2 @ X3) => (X0 @ X2 @ (X1 @ X2))) => ! [X4 : ((a > $o) > $o)] : (! [X5 : (a > $o)] : ((X4 @ X5) => ? [X6 : a] : (X5 @ X6)) => ? [X7 : ((a > $o) > a)] : ! [X5 : (a > $o)] : ((X4 @ X5) => (X5 @ (X7 @ X5))))),
% 0.25/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM533)).
% 0.25/0.31 thf(f2,negated_conjecture,(
% 0.25/0.31 ~(! [X0 : ((a > $o) > a > $o)] : ? [X1 : ((a > $o) > a)] : ! [X2 : (a > $o)] : (? [X3 : a] : (X0 @ X2 @ X3) => (X0 @ X2 @ (X1 @ X2))) => ! [X4 : ((a > $o) > $o)] : (! [X5 : (a > $o)] : ((X4 @ X5) => ? [X6 : a] : (X5 @ X6)) => ? [X7 : ((a > $o) > a)] : ! [X5 : (a > $o)] : ((X4 @ X5) => (X5 @ (X7 @ X5)))))),
% 0.25/0.31 inference(negated_conjecture,[status(cth)],[f1])).
% 0.25/0.31 thf(f3,plain,(
% 0.25/0.31 ~(! [X0 : ((a > $o) > a > $o)] : ? [X1 : ((a > $o) > a)] : ! [X2 : (a > $o)] : (? [X3 : a] : (X0 @ X2 @ X3) => (X0 @ X2 @ (X1 @ X2))) => ! [X4 : ((a > $o) > $o)] : (! [X5 : (a > $o)] : ((X4 @ X5) => ? [X6 : a] : (X5 @ X6)) => ? [X7 : ((a > $o) > a)] : ! [X8 : (a > $o)] : ((X4 @ X8) => (X8 @ (X7 @ X8)))))),
% 0.25/0.31 inference(rectify,[],[f2])).
% 0.25/0.31 thf(f4,plain,(
% 0.25/0.31 ~(! [X0 : ((a > $o) > a > $o)] : ? [X1 : ((a > $o) > a)] : ! [X2 : (a > $o)] : (? [X3 : a] : (((X0 @ X2 @ X3)) = $true) => (((X0 @ X2 @ (X1 @ X2))) = $true)) => ! [X4 : ((a > $o) > $o)] : (! [X5 : (a > $o)] : ((((X4 @ X5)) = $true) => ? [X6 : a] : (((X5 @ X6)) = $true)) => ? [X7 : ((a > $o) > a)] : ! [X8 : (a > $o)] : ((((X4 @ X8)) = $true) => (((X8 @ (X7 @ X8))) = $true))))),
% 0.25/0.31 inference(fool_elimination,[],[f3])).
% 0.25/0.31 thf(f5,plain,(
% 0.25/0.31 ? [X4 : ((a > $o) > $o)] : (! [X7 : ((a > $o) > a)] : ? [X8 : (a > $o)] : ((((X8 @ (X7 @ X8))) != $true) & (((X4 @ X8)) = $true)) & ! [X5 : (a > $o)] : (? [X6 : a] : (((X5 @ X6)) = $true) | (((X4 @ X5)) != $true))) & ! [X0 : ((a > $o) > a > $o)] : ? [X1 : ((a > $o) > a)] : ! [X2 : (a > $o)] : ((((X0 @ X2 @ (X1 @ X2))) = $true) | ! [X3 : a] : (((X0 @ X2 @ X3)) != $true))),
% 0.25/0.31 inference(ennf_transformation,[],[f4])).
% 0.25/0.31 thf(f6,plain,(
% 0.25/0.31 ? [X0 : ((a > $o) > $o)] : (! [X1 : ((a > $o) > a)] : ? [X2 : (a > $o)] : (($true != ((X2 @ (X1 @ X2)))) & ($true = ((X0 @ X2)))) & ! [X3 : (a > $o)] : (? [X4 : a] : ($true = ((X3 @ X4))) | ($true != ((X0 @ X3))))) & ! [X5 : ((a > $o) > a > $o)] : ? [X6 : ((a > $o) > a)] : ! [X7 : (a > $o)] : (($true = ((X5 @ X7 @ (X6 @ X7)))) | ! [X8 : a] : ($true != ((X5 @ X7 @ X8))))),
% 0.25/0.31 inference(rectify,[],[f5])).
% 0.25/0.31 thf(f7,plain,(
% 0.25/0.31 (! [X1 : ((a > $o) > a)] : (($true != ((sK1 @ X1 @ (X1 @ (sK1 @ X1))))) & ($true = ((sK0 @ (sK1 @ X1))))) & ! [X3 : (a > $o)] : (($true = ((X3 @ (sK2 @ X3)))) | ($true != ((sK0 @ X3))))) & ! [X5 : ((a > $o) > a > $o)] : ! [X7 : (a > $o)] : (($true = ((X5 @ X7 @ (sK3 @ X5 @ X7)))) | ! [X8 : a] : ($true != ((X5 @ X7 @ X8))))),
% 0.25/0.31 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,vAPP,vAPP,vAPP]),skolemize(X0,sK0),skolemize(X6,sK3 @ X5),skolemize(X6,sK3 @ X5),skolemize(X6,sK3 @ X5)],[f6])).
% 0.25/0.31 thf(f9,plain,(
% 0.25/0.31 ( ! [X3 : (a > $o)] : (($true != ((sK0 @ X3))) | ($true = ((X3 @ (sK2 @ X3))))) )),
% 0.25/0.31 inference(cnf_transformation,[],[f7])).
% 0.25/0.31 thf(f10,plain,(
% 0.25/0.31 ( ! [X1 : ((a > $o) > a)] : (($true = ((sK0 @ (sK1 @ X1))))) )),
% 0.25/0.31 inference(cnf_transformation,[],[f7])).
% 0.25/0.31 thf(f11,plain,(
% 0.25/0.31 ( ! [X1 : ((a > $o) > a)] : (($true != ((sK1 @ X1 @ (X1 @ (sK1 @ X1)))))) )),
% 0.25/0.31 inference(cnf_transformation,[],[f7])).
% 0.25/0.31 thf(f20,plain,(
% 0.25/0.31 ( ! [X0 : ((a > $o) > a)] : (($true != $true) | ($true = ((sK1 @ X0 @ (sK2 @ (sK1 @ X0)))))) )),
% 0.25/0.31 inference(constrained_superposition,[],[f9,f10])).
% 0.25/0.31 thf(f21,plain,(
% 0.25/0.31 ( ! [X0 : ((a > $o) > a)] : (($true = ((sK1 @ X0 @ (sK2 @ (sK1 @ X0)))))) )),
% 0.25/0.31 inference(trivial_inequality_removal,[],[f20])).
% 0.25/0.31 thf(f40,plain,(
% 0.25/0.31 ( ! [X0 : ((a > $o) > a > a)] : (($true != $true) | ((^[Y0 : a]: ((^[Y1 : a > $o]: (sK2 @ ((^[Y2 : a > $o]: ((^[Y3 : a]: (Y2 @ (X0 @ Y2 @ Y3))))) @ Y1))))) != (^[Y0 : a]: ((^[Y1 : a > $o]: (sK2 @ (^[Y2 : a]: (Y1 @ (X0 @ Y1 @ Y2)))))))) | ((^[Y0 : a]: (Y0)) != ((X0 @ (sK1 @ (^[Y0 : a > $o]: (sK2 @ (^[Y1 : a]: (Y0 @ (X0 @ Y0 @ Y1)))))))))) )),
% 0.25/0.31 inference(constrained_superposition,[],[f11,f21])).
% 0.25/0.31 thf(f44,plain,(
% 0.25/0.31 ( ! [X0 : ((a > $o) > a > a)] : (((^[Y0 : a]: ((^[Y1 : a > $o]: (sK2 @ ((^[Y2 : a > $o]: ((^[Y3 : a]: (Y2 @ (X0 @ Y2 @ Y3))))) @ Y1))))) != (^[Y0 : a]: ((^[Y1 : a > $o]: (sK2 @ (^[Y2 : a]: (Y1 @ (X0 @ Y1 @ Y2)))))))) | ((^[Y0 : a]: (Y0)) != ((X0 @ (sK1 @ (^[Y0 : a > $o]: (sK2 @ (^[Y1 : a]: (Y0 @ (X0 @ Y0 @ Y1)))))))))) )),
% 0.25/0.31 inference(trivial_inequality_removal,[],[f40])).
% 0.25/0.31 thf(f45,plain,(
% 0.25/0.31 ( ! [X0 : ((a > $o) > a > a)] : (((^[Y0 : a]: ((^[Y1 : a > $o]: (sK2 @ (^[Y2 : a]: (Y1 @ (X0 @ Y1 @ Y2))))))) != (^[Y0 : a]: ((^[Y1 : a > $o]: (sK2 @ (^[Y2 : a]: (Y1 @ (X0 @ Y1 @ Y2)))))))) | ((^[Y0 : a]: (Y0)) != ((X0 @ (sK1 @ (^[Y0 : a > $o]: (sK2 @ (^[Y1 : a]: (Y0 @ (X0 @ Y0 @ Y1)))))))))) )),
% 0.25/0.31 inference(beta-eta_normalization,[],[f44])).
% 0.25/0.31 thf(f46,plain,(
% 0.25/0.31 ( ! [X0 : ((a > $o) > a > a)] : (((^[Y0 : a]: (Y0)) != ((X0 @ (sK1 @ (^[Y0 : a > $o]: (sK2 @ (^[Y1 : a]: (Y0 @ (X0 @ Y0 @ Y1)))))))))) )),
% 0.25/0.31 inference(trivial_inequality_removal,[],[f45])).
% 0.25/0.31 thf(f48,plain,(
% 0.25/0.31 $false),
% 0.25/0.31 inference(equality_resolution,[],[f46])).
% 0.25/0.31 % SZS output end Proof for theBenchmark
% 0.25/0.31 % (3155066)------------------------------
% 0.25/0.31 % (3155066)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.31 % (3155066)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.31 % (3155066)CaDiCaL version: 2.1.3
% 0.25/0.31 % (3155066)Termination reason: Refutation
% 0.25/0.31 % (3155066)Time elapsed: 0.007 s
% 0.25/0.31 % (3155066)Peak memory usage: 12 MB
% 0.25/0.31 % (3155066)Instructions burned: 6 (million)
% 0.25/0.31 % (3155058)Success in time 0.045 s
% 0.25/0.31 % Vampire exiting
%------------------------------------------------------------------------------