%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV273^5 : TPTP v9.3.1. Released v4.0.0.
% 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 08:38:10 AM UTC 2026
% Result : Theorem 0.32s 0.26s
% Output : Refutation 0.32s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV273^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.05/0.17 % Computer : n007.cluster.edu
% 0.05/0.17 % Model : x86_64 x86_64
% 0.05/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.17 % Memory : 8046.5625MB
% 0.05/0.17 % OS : Linux 6.8.0-71-generic
% 0.05/0.17 % CPULimit : 300
% 0.05/0.17 % WCLimit : 300
% 0.05/0.17 % DateTime : Tue Sep 29 15:28:58 UTC 2026
% 0.05/0.17 % CPUTime :
% 0.05/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.05/0.20 Running higher-order theorem proving
% 0.05/0.22 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
% 0.32/0.26 % (3506266)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.32/0.26 % (3506275)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2995893682:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.32/0.26 % (3506277)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.32/0.26 % (3506277)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
% 0.32/0.26 % (3506275) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3506266-3506275"...
% 0.32/0.26 % (3506275)...printing done.
% 0.32/0.26 % (3506271)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=683834415:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.32/0.26 % (3506272)lrs+10_16_si=on:nwc=1.5:random_seed=716671146:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.32/0.26 % (3506273)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3001885675:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.32/0.26 % (3506275)Refutation found. Thanks to Tanya!
% 0.32/0.26 % SZS status Theorem for theBenchmark
% 0.32/0.26 % SZS output start Proof for theBenchmark
% 0.32/0.26 thf(type_def_5, type, a: $tType).
% 0.32/0.26 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.32/0.26 thf(func_def_0, type, cR: (a > a > $o)).
% 0.32/0.26 thf(func_def_4, type, sK0: a).
% 0.32/0.26 thf(func_def_5, type, sK1: ((a > $o) > a)).
% 0.32/0.26 thf(func_def_6, type, sK2: (a > (a > $o) > a)).
% 0.32/0.26 thf(func_def_7, type, vNOT: ($o > $o)).
% 0.32/0.26 thf(func_def_8, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.32/0.26 thf(func_def_9, type, db0: !>[X0: $tType]:(X0)).
% 0.32/0.26 thf(func_def_10, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.32/0.26 thf(f1,conjecture,(
% 0.32/0.26 ! [X0 : (a > $o)] : (? [X1 : a] : (X0 @ X1) => ? [X1 : a] : (! [X3 : a] : ((! [X2 : a] : ((X0 @ X2) => (cR @ X3 @ X2)) & (X0 @ X3)) => (X3 = X1)) & ! [X2 : a] : ((X0 @ X2) => (cR @ X1 @ X2)) & (X0 @ X1))) => ! [X2 : a] : (cR @ X2 @ X2)),
% 0.32/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM542_pme)).
% 0.32/0.26 thf(f2,negated_conjecture,(
% 0.32/0.26 ~(! [X0 : (a > $o)] : (? [X1 : a] : (X0 @ X1) => ? [X1 : a] : (! [X3 : a] : ((! [X2 : a] : ((X0 @ X2) => (cR @ X3 @ X2)) & (X0 @ X3)) => (X3 = X1)) & ! [X2 : a] : ((X0 @ X2) => (cR @ X1 @ X2)) & (X0 @ X1))) => ! [X2 : a] : (cR @ X2 @ X2))),
% 0.32/0.26 inference(negated_conjecture,[status(cth)],[f1])).
% 0.32/0.26 thf(f3,plain,(
% 0.32/0.26 ~(! [X0 : (a > $o)] : (? [X1 : a] : (X0 @ X1) => ? [X2 : a] : (! [X3 : a] : ((! [X4 : a] : ((X0 @ X4) => (cR @ X3 @ X4)) & (X0 @ X3)) => (X2 = X3)) & ! [X5 : a] : ((X0 @ X5) => (cR @ X2 @ X5)) & (X0 @ X2))) => ! [X6 : a] : (cR @ X6 @ X6))),
% 0.32/0.26 inference(rectify,[],[f2])).
% 0.32/0.26 thf(f4,plain,(
% 0.32/0.26 ~(! [X0 : (a > $o)] : (? [X1 : a] : (((X0 @ X1)) = $true) => ? [X2 : a] : (! [X3 : a] : ((! [X4 : a] : ((((X0 @ X4)) = $true) => ($true = ((cR @ X3 @ X4)))) & (((X0 @ X3)) = $true)) => (X2 = X3)) & ! [X5 : a] : ((((X0 @ X5)) = $true) => (((cR @ X2 @ X5)) = $true)) & (((X0 @ X2)) = $true))) => ! [X6 : a] : (((cR @ X6 @ X6)) = $true))),
% 0.32/0.26 inference(fool_elimination,[],[f3])).
% 0.32/0.26 thf(f5,plain,(
% 0.32/0.26 ? [X6 : a] : (((cR @ X6 @ X6)) != $true) & ! [X0 : (a > $o)] : (? [X2 : a] : (! [X3 : a] : ((X2 = X3) | (? [X4 : a] : (($true != ((cR @ X3 @ X4))) & (((X0 @ X4)) = $true)) | (((X0 @ X3)) != $true))) & ! [X5 : a] : ((((X0 @ X5)) != $true) | (((cR @ X2 @ X5)) = $true)) & (((X0 @ X2)) = $true)) | ! [X1 : a] : (((X0 @ X1)) != $true))),
% 0.32/0.26 inference(ennf_transformation,[],[f4])).
% 0.32/0.26 thf(f6,plain,(
% 0.32/0.26 ? [X6 : a] : (((cR @ X6 @ X6)) != $true) & ! [X0 : (a > $o)] : (? [X2 : a] : ((((X0 @ X2)) = $true) & ! [X5 : a] : ((((X0 @ X5)) != $true) | (((cR @ X2 @ X5)) = $true)) & ! [X3 : a] : ((X2 = X3) | ? [X4 : a] : (($true != ((cR @ X3 @ X4))) & (((X0 @ X4)) = $true)) | (((X0 @ X3)) != $true))) | ! [X1 : a] : (((X0 @ X1)) != $true))),
% 0.32/0.26 inference(flattening,[],[f5])).
% 0.32/0.26 thf(f7,plain,(
% 0.32/0.26 ? [X0 : a] : (((cR @ X0 @ X0)) != $true) & ! [X1 : (a > $o)] : (? [X2 : a] : (($true = ((X1 @ X2))) & ! [X3 : a] : ((((X1 @ X3)) != $true) | (((cR @ X2 @ X3)) = $true)) & ! [X4 : a] : ((X2 = X4) | ? [X5 : a] : ((((cR @ X4 @ X5)) != $true) & (((X1 @ X5)) = $true)) | (((X1 @ X4)) != $true))) | ! [X6 : a] : (((X1 @ X6)) != $true))),
% 0.32/0.26 inference(rectify,[],[f6])).
% 0.32/0.26 thf(f8,plain,(
% 0.32/0.26 (((cR @ sK0 @ sK0)) != $true) & ! [X1 : (a > $o)] : (((((X1 @ (sK1 @ X1))) = $true) & ! [X3 : a] : ((((X1 @ X3)) != $true) | (((cR @ (sK1 @ X1) @ X3)) = $true)) & ! [X4 : a] : ((((sK1 @ X1)) = X4) | (($true != ((cR @ X4 @ (sK2 @ X4 @ X1)))) & (((X1 @ (sK2 @ X4 @ X1))) = $true)) | (((X1 @ X4)) != $true))) | ! [X6 : a] : (((X1 @ X6)) != $true))),
% 0.32/0.26 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,vAPP,vAPP]),skolemize(X0,sK0),skolemize(X5,sK2 @ X4 @ X1),skolemize(X5,sK2 @ X4 @ X1)],[f7])).
% 0.32/0.26 thf(f11,plain,(
% 0.32/0.26 ( ! [X3 : a,X1 : (a > $o),X6 : a] : ((((X1 @ X3)) != $true) | (((X1 @ X6)) != $true) | (((cR @ (sK1 @ X1) @ X3)) = $true)) )),
% 0.32/0.26 inference(cnf_transformation,[],[f8])).
% 0.32/0.26 thf(f12,plain,(
% 0.32/0.26 ( ! [X1 : (a > $o),X6 : a] : ((((X1 @ X6)) != $true) | (((X1 @ (sK1 @ X1))) = $true)) )),
% 0.32/0.26 inference(cnf_transformation,[],[f8])).
% 0.32/0.26 thf(f13,plain,(
% 0.32/0.26 (((cR @ sK0 @ sK0)) != $true)),
% 0.32/0.26 inference(cnf_transformation,[],[f8])).
% 0.32/0.26 thf(f18,plain,(
% 0.32/0.26 ( ! [X6 : a,X7 : (a > $o)] : (((((^[Y0 : a]: (~ (X7 @ Y0))) @ X6)) != $true) | ((((^[Y0 : a]: (~ (X7 @ Y0))) @ (sK1 @ (^[Y0 : a]: (~ (X7 @ Y0)))))) = $true)) )),
% 0.32/0.26 inference(primitive_instantiation,[],[f12])).
% 0.32/0.26 thf(f20,plain,(
% 0.32/0.26 ( ! [X6 : a,X7 : (a > $o)] : ((((~ (X7 @ (sK1 @ (^[Y0 : a]: (~ (X7 @ Y0))))))) = $true) | (((~ (X7 @ X6))) != $true)) )),
% 0.32/0.26 inference(beta-eta_normalization,[],[f18])).
% 0.32/0.26 thf(f21,plain,(
% 0.32/0.26 ( ! [X6 : a,X7 : (a > $o)] : ((((X7 @ (sK1 @ (^[Y0 : a]: (~ (X7 @ Y0)))))) = $false) | (((~ (X7 @ X6))) != $true)) )),
% 0.32/0.26 inference(not_proxy_clausification,[],[f20])).
% 0.32/0.26 thf(f22,plain,(
% 0.32/0.26 ( ! [X6 : a,X7 : (a > $o)] : ((((X7 @ (sK1 @ (^[Y0 : a]: (~ (X7 @ Y0)))))) = $false) | (((X7 @ X6)) = $true)) )),
% 0.32/0.26 inference(not_proxy_clausification,[],[f21])).
% 0.32/0.26 thf(f26,plain,(
% 0.32/0.26 ( ! [X0 : a] : ((((sK1 @ (^[Y0 : a]: (~ ((^[Y1 : a]: (~ (Y1 = X0))) @ Y0))))) = X0)) )),
% 0.32/0.26 inference(leibniz_equality_elimination,[],[f22])).
% 0.32/0.26 thf(f32,plain,(
% 0.32/0.26 ( ! [X8 : (a > $o),X6 : a] : (((((^[Y0 : a]: (~ (X8 @ Y0))) @ X6)) = $true) | ((((^[Y0 : a]: (~ (X8 @ Y0))) @ (sK1 @ (^[Y0 : a]: (~ ((^[Y1 : a]: (~ (X8 @ Y1))) @ Y0)))))) = $false)) )),
% 0.32/0.26 inference(primitive_instantiation,[],[f22])).
% 0.32/0.26 thf(f38,plain,(
% 0.32/0.26 ( ! [X0 : a] : ((((sK1 @ (^[Y0 : a]: (~ (~ (Y0 = X0)))))) = X0)) )),
% 0.32/0.26 inference(beta-eta_normalization,[],[f26])).
% 0.32/0.26 thf(f39,plain,(
% 0.32/0.26 ( ! [X0 : a] : ((((sK1 @ (^[Y0 : a]: (Y0 = X0)))) = X0)) )),
% 0.32/0.26 inference(boolean_simplification,[],[f38])).
% 0.32/0.26 thf(f43,plain,(
% 0.32/0.26 ( ! [X8 : (a > $o),X6 : a] : ((((~ (X8 @ X6))) = $true) | (((~ (X8 @ (sK1 @ (^[Y0 : a]: (~ (~ (X8 @ Y0)))))))) = $false)) )),
% 0.32/0.26 inference(beta-eta_normalization,[],[f32])).
% 0.32/0.26 thf(f44,plain,(
% 0.32/0.26 ( ! [X8 : (a > $o),X6 : a] : ((((~ (X8 @ (sK1 @ (^[Y0 : a]: (~ (~ (X8 @ Y0)))))))) = $false) | ($false = ((X8 @ X6)))) )),
% 0.32/0.26 inference(not_proxy_clausification,[],[f43])).
% 0.32/0.26 thf(f45,plain,(
% 0.32/0.26 ( ! [X8 : (a > $o),X6 : a] : (($false = ((X8 @ X6))) | (((X8 @ (sK1 @ (^[Y0 : a]: (~ (~ (X8 @ Y0))))))) = $true)) )),
% 0.32/0.26 inference(not_proxy_clausification,[],[f44])).
% 0.32/0.26 thf(f46,plain,(
% 0.32/0.26 ( ! [X8 : (a > $o),X6 : a] : (($false = ((X8 @ X6))) | (((X8 @ (sK1 @ (^[Y0 : a]: (X8 @ Y0))))) = $true)) )),
% 0.32/0.26 inference(boolean_simplification,[],[f45])).
% 0.32/0.26 thf(f47,plain,(
% 0.32/0.26 ( ! [X8 : (a > $o),X6 : a] : ((((X8 @ (sK1 @ X8))) = $true) | ($false = ((X8 @ X6)))) )),
% 0.32/0.26 inference(beta-eta_normalization,[],[f46])).
% 0.32/0.26 thf(f87,plain,(
% 0.32/0.26 ( ! [X2 : a,X0 : (a > $o),X1 : a] : ((((X0 @ X1)) != $true) | ($true = ((cR @ (sK1 @ X0) @ (sK1 @ X0)))) | ($true != $true) | (((X0 @ X2)) = $false)) )),
% 0.32/0.26 inference(superposition,[],[f11,f47])).
% 0.32/0.26 thf(f102,plain,(
% 0.32/0.26 ( ! [X2 : a,X0 : (a > $o),X1 : a] : ((((X0 @ X1)) != $true) | (((X0 @ X2)) = $false) | ($true = ((cR @ (sK1 @ X0) @ (sK1 @ X0))))) )),
% 0.32/0.26 inference(trivial_inequality_removal,[],[f87])).
% 0.32/0.26 thf(f170,plain,(
% 0.32/0.26 ( ! [X2 : a,X0 : (a > $o),X1 : a] : ((((X0 @ X1)) = $false) | (((X0 @ X2)) = $false) | ($true != $true) | ($true = ((cR @ (sK1 @ X0) @ (sK1 @ X0))))) )),
% 0.32/0.26 inference(superposition,[],[f102,f47])).
% 0.32/0.26 thf(f175,plain,(
% 0.32/0.26 ( ! [X2 : a,X0 : (a > $o),X1 : a] : ((((X0 @ X2)) = $false) | ($true = ((cR @ (sK1 @ X0) @ (sK1 @ X0)))) | (((X0 @ X1)) = $false)) )),
% 0.32/0.26 inference(trivial_inequality_removal,[],[f170])).
% 0.32/0.26 thf(f195,plain,(
% 0.32/0.26 ( ! [X2 : a,X0 : a,X1 : a] : ((((cR @ X0 @ X0)) = $true) | ($false = (((^[Y0 : a]: (Y0 = X0)) @ X2))) | ($false = (((^[Y0 : a]: (Y0 = X0)) @ X1)))) )),
% 0.32/0.26 inference(superposition,[],[f175,f39])).
% 0.32/0.26 thf(f238,plain,(
% 0.32/0.26 ( ! [X2 : a,X0 : a,X1 : a] : (($false = ((X2 = X0))) | (((X1 = X0)) = $false) | (((cR @ X0 @ X0)) = $true)) )),
% 0.32/0.26 inference(beta-eta_normalization,[],[f195])).
% 0.32/0.26 thf(f239,plain,(
% 0.32/0.26 ( ! [X2 : a,X0 : a,X1 : a] : ((((X1 = X0)) = $false) | (((cR @ X0 @ X0)) = $true) | (X0 != X2)) )),
% 0.32/0.26 inference(equality_proxy_clausification,[],[f238])).
% 0.32/0.26 thf(f240,plain,(
% 0.32/0.26 ( ! [X2 : a,X0 : a,X1 : a] : ((((cR @ X0 @ X0)) = $true) | (X0 != X1) | (X0 != X2)) )),
% 0.32/0.26 inference(equality_proxy_clausification,[],[f239])).
% 0.32/0.26 thf(f268,plain,(
% 0.32/0.26 ( ! [X0 : a,X1 : a] : (($true != $true) | (sK0 != X1) | (sK0 != X0)) )),
% 0.32/0.26 inference(superposition,[],[f13,f240])).
% 0.32/0.26 thf(f273,plain,(
% 0.32/0.26 ( ! [X0 : a,X1 : a] : ((sK0 != X0) | (sK0 != X1)) )),
% 0.32/0.26 inference(trivial_inequality_removal,[],[f268])).
% 0.32/0.26 thf(f288,plain,(
% 0.32/0.26 ( ! [X0 : a] : ((sK0 != X0)) )),
% 0.32/0.26 inference(equality_resolution,[],[f273])).
% 0.32/0.26 thf(f290,plain,(
% 0.32/0.26 (sK0 != sK0)),
% 0.32/0.26 inference(imitation,[],[f288])).
% 0.32/0.26 thf(f292,plain,(
% 0.32/0.26 $false),
% 0.32/0.26 inference(trivial_inequality_removal,[],[f290])).
% 0.32/0.26 % SZS output end Proof for theBenchmark
% 0.32/0.26 % (3506275)------------------------------
% 0.32/0.26 % (3506275)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.32/0.26 % (3506275)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/0.26 % (3506275)CaDiCaL version: 2.1.3
% 0.32/0.26 % (3506275)Termination reason: Refutation
% 0.32/0.26 % (3506275)Time elapsed: 0.006 s
% 0.32/0.26 % (3506275)Peak memory usage: 12 MB
% 0.32/0.26 % (3506275)Instructions burned: 18 (million)
% 0.32/0.26 % (3506266)Success in time 0.032 s
% 0.32/0.26 % Vampire exiting
%------------------------------------------------------------------------------