%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV195^5 : 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 : n020.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 08:38:00 AM UTC 2026
% Result : Theorem 0.21s 0.31s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV195^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n020.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Sep 29 15:21:05 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running higher-order theorem proving
% 0.09/0.26 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
% 0.21/0.31 % (1181796)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.31 % (1181807)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.31 % (1181807)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
% 0.21/0.31 % (1181803)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2717374625:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.31 % (1181802)lrs+10_16_si=on:nwc=1.5:random_seed=2333180165:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.31 % (1181806)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=869501606:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.31 % (1181801)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2757702502:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.31 % (1181805)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=932871196:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.31 % (1181804)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=1887768006: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)
% 0.21/0.31 % (1181807)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=115417989:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.31 % (1181803)Instruction limit reached!
% 0.21/0.31 % (1181803)------------------------------
% 0.21/0.31 % (1181803)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (1181803)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (1181803)CaDiCaL version: 2.1.3
% 0.21/0.31 % (1181803)Termination reason: Instruction limit
% 0.21/0.31 % (1181803)Termination phase: Saturation
% 0.21/0.31 % (1181803)Time elapsed: 0.003 s
% 0.21/0.31 % (1181803)Peak memory usage: 12 MB
% 0.21/0.31 % (1181803)Instructions burned: 4 (million)
% 0.21/0.31 % (1181807)Refutation not found, incomplete strategy
% 0.21/0.31 % (1181807)------------------------------
% 0.21/0.31 % (1181807)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (1181807)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (1181807)CaDiCaL version: 2.1.3
% 0.21/0.31 % (1181807)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.31 % (1181807)Time elapsed: 0.005 s
% 0.21/0.31 % (1181807)Peak memory usage: 12 MB
% 0.21/0.31 % (1181807)Instructions burned: 7 (million)
% 0.21/0.31 % (1181807)------------------------------
% 0.21/0.31 % (1181807)------------------------------
% 0.21/0.31 % (1181804) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1181796-1181804"...
% 0.21/0.31 % (1181804)...printing done.
% 0.21/0.31 % (1181801) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1181796-1181801"...
% 0.21/0.31 % (1181805) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1181796-1181805"...
% 0.21/0.31 % (1181804)Refutation found. Thanks to Tanya!
% 0.21/0.31 % SZS status Theorem for theBenchmark
% 0.21/0.31 % SZS output start Proof for theBenchmark
% 0.21/0.31 thf(type_def_5, type, a: $tType).
% 0.21/0.31 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.31 thf(func_def_0, type, cP: (a > a > a)).
% 0.21/0.31 thf(func_def_1, type, cZ: a).
% 0.21/0.31 thf(func_def_5, type, sK0: ((a > $o) > a)).
% 0.21/0.31 thf(func_def_6, type, sK1: ((a > $o) > a)).
% 0.21/0.31 thf(func_def_7, type, sK2: a).
% 0.21/0.31 thf(func_def_8, type, vNOT: ($o > $o)).
% 0.21/0.31 thf(func_def_10, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.21/0.31 thf(func_def_11, type, db0: !>[X0: $tType]:(X0)).
% 0.21/0.31 thf(func_def_12, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.21/0.31 thf(f1,conjecture,(
% 0.21/0.31 (! [X4 : (a > $o)] : (((X4 @ cZ) & ! [X1 : a,X0 : a] : (((X4 @ X1) & (X4 @ X0)) => (X4 @ (cP @ X0 @ X1)))) => ! [X0 : a] : (X4 @ X0)) & ! [X1 : a,X2 : a,X3 : a,X0 : a] : ((((cP @ X0 @ X2)) = ((cP @ X1 @ X3))) => ((X0 = X1) & (X2 = X3))) & ! [X0 : a,X1 : a] : (((cP @ X0 @ X1)) != cZ)) => ! [X0 : a] : ((X0 = cZ) | ? [X1 : a,X5 : a] : (X0 = ((cP @ X1 @ X5))))),
% 0.21/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cS_LEM1D_pme)).
% 0.21/0.31 thf(f2,negated_conjecture,(
% 0.21/0.31 ~((! [X4 : (a > $o)] : (((X4 @ cZ) & ! [X1 : a,X0 : a] : (((X4 @ X1) & (X4 @ X0)) => (X4 @ (cP @ X0 @ X1)))) => ! [X0 : a] : (X4 @ X0)) & ! [X1 : a,X2 : a,X3 : a,X0 : a] : ((((cP @ X0 @ X2)) = ((cP @ X1 @ X3))) => ((X0 = X1) & (X2 = X3))) & ! [X0 : a,X1 : a] : (((cP @ X0 @ X1)) != cZ)) => ! [X0 : a] : ((X0 = cZ) | ? [X1 : a,X5 : a] : (X0 = ((cP @ X1 @ X5)))))),
% 0.21/0.31 inference(negated_conjecture,[status(cth)],[f1])).
% 0.21/0.31 thf(f3,plain,(
% 0.21/0.31 ~((! [X0 : (a > $o)] : (((X0 @ cZ) & ! [X1 : a,X2 : a] : (((X0 @ X1) & (X0 @ X2)) => (X0 @ (cP @ X2 @ X1)))) => ! [X3 : a] : (X0 @ X3)) & ! [X4 : a,X5 : a,X6 : a,X7 : a] : ((((cP @ X4 @ X6)) = ((cP @ X7 @ X5))) => ((X4 = X7) & (X5 = X6))) & ! [X8 : a,X9 : a] : (cZ != ((cP @ X8 @ X9)))) => ! [X10 : a] : ((cZ = X10) | ? [X11 : a,X12 : a] : (((cP @ X11 @ X12)) = X10)))),
% 0.21/0.31 inference(rectify,[],[f2])).
% 0.21/0.31 thf(f4,plain,(
% 0.21/0.31 ~((! [X8 : a,X9 : a] : (cZ != ((cP @ X8 @ X9))) & ! [X0 : (a > $o)] : ((($true = ((X0 @ cZ))) & ! [X2 : a,X1 : a] : ((($true = ((X0 @ X1))) & ($true = ((X0 @ X2)))) => ($true = ((X0 @ (cP @ X2 @ X1)))))) => ! [X3 : a] : ($true = ((X0 @ X3)))) & ! [X7 : a,X5 : a,X4 : a,X6 : a] : ((((cP @ X4 @ X6)) = ((cP @ X7 @ X5))) => ((X5 = X6) & (X4 = X7)))) => ! [X10 : a] : (? [X11 : a,X12 : a] : (((cP @ X11 @ X12)) = X10) | (cZ = X10)))),
% 0.21/0.31 inference(fool_elimination,[],[f3])).
% 0.21/0.31 thf(f5,plain,(
% 0.21/0.31 ? [X10 : a] : (! [X11 : a,X12 : a] : (((cP @ X11 @ X12)) != X10) & (cZ != X10)) & (! [X8 : a,X9 : a] : (cZ != ((cP @ X8 @ X9))) & ! [X0 : (a > $o)] : (! [X3 : a] : ($true = ((X0 @ X3))) | (($true != ((X0 @ cZ))) | ? [X2 : a,X1 : a] : (($true != ((X0 @ (cP @ X2 @ X1)))) & (($true = ((X0 @ X1))) & ($true = ((X0 @ X2))))))) & ! [X4 : a,X7 : a,X6 : a,X5 : a] : ((((cP @ X4 @ X6)) != ((cP @ X7 @ X5))) | ((X5 = X6) & (X4 = X7))))),
% 0.21/0.31 inference(ennf_transformation,[],[f4])).
% 0.21/0.31 thf(f6,plain,(
% 0.21/0.31 ! [X0 : (a > $o)] : (($true != ((X0 @ cZ))) | ! [X3 : a] : ($true = ((X0 @ X3))) | ? [X1 : a,X2 : a] : (($true = ((X0 @ X2))) & ($true = ((X0 @ X1))) & ($true != ((X0 @ (cP @ X2 @ X1)))))) & ! [X8 : a,X9 : a] : (cZ != ((cP @ X8 @ X9))) & ! [X4 : a,X7 : a,X6 : a,X5 : a] : ((((cP @ X4 @ X6)) != ((cP @ X7 @ X5))) | ((X5 = X6) & (X4 = X7))) & ? [X10 : a] : (! [X11 : a,X12 : a] : (((cP @ X11 @ X12)) != X10) & (cZ != X10))),
% 0.21/0.31 inference(flattening,[],[f5])).
% 0.21/0.31 thf(f7,plain,(
% 0.21/0.31 ! [X0 : (a > $o)] : (($true != ((X0 @ cZ))) | ! [X1 : a] : ($true = ((X0 @ X1))) | ? [X2 : a,X3 : a] : (($true = ((X0 @ X3))) & ($true = ((X0 @ X2))) & ($true != ((X0 @ (cP @ X3 @ X2)))))) & ! [X4 : a,X5 : a] : (cZ != ((cP @ X4 @ X5))) & ! [X6 : a,X7 : a,X8 : a,X9 : a] : ((((cP @ X6 @ X8)) != ((cP @ X7 @ X9))) | ((X8 = X9) & (X6 = X7))) & ? [X10 : a] : (! [X11 : a,X12 : a] : (((cP @ X11 @ X12)) != X10) & (cZ != X10))),
% 0.21/0.31 inference(rectify,[],[f6])).
% 0.21/0.31 thf(f8,plain,(
% 0.21/0.31 ! [X0 : (a > $o)] : (($true != ((X0 @ cZ))) | ! [X1 : a] : ($true = ((X0 @ X1))) | (($true = ((X0 @ (sK1 @ X0)))) & (((X0 @ (sK0 @ X0))) = $true) & ($true != ((X0 @ (cP @ (sK1 @ X0) @ (sK0 @ X0))))))) & ! [X4 : a,X5 : a] : (cZ != ((cP @ X4 @ X5))) & ! [X6 : a,X7 : a,X8 : a,X9 : a] : ((((cP @ X6 @ X8)) != ((cP @ X7 @ X9))) | ((X8 = X9) & (X6 = X7))) & (! [X11 : a,X12 : a] : (((cP @ X11 @ X12)) != sK2) & (cZ != sK2))),
% 0.21/0.31 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,sK2]),skolemize(X3,sK1 @ X0),skolemize(X3,sK1 @ X0),skolemize(X10,sK2)],[f7])).
% 0.21/0.31 thf(f9,plain,(
% 0.21/0.31 (cZ != sK2)),
% 0.21/0.31 inference(cnf_transformation,[],[f8])).
% 0.21/0.31 thf(f10,plain,(
% 0.21/0.31 ( ! [X11 : a,X12 : a] : ((((cP @ X11 @ X12)) != sK2)) )),
% 0.21/0.31 inference(cnf_transformation,[],[f8])).
% 0.21/0.31 thf(f14,plain,(
% 0.21/0.31 ( ! [X0 : (a > $o),X1 : a] : (($true != ((X0 @ (cP @ (sK1 @ X0) @ (sK0 @ X0))))) | ($true = ((X0 @ X1))) | ($true != ((X0 @ cZ)))) )),
% 0.21/0.31 inference(cnf_transformation,[],[f8])).
% 0.21/0.31 thf(f19,definition,(
% 0.21/0.31 spl3_1 <=> (cZ = sK2)),
% 0.21/0.31 introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition])).
% 0.21/0.31 thf(f21,plain,(
% 0.21/0.31 (cZ != sK2) | spl3_1),
% 0.21/0.31 inference(avatar_component_clause,[],[f19])).
% 0.21/0.31 thf(f22,plain,(
% 0.21/0.31 ~spl3_1),
% 0.21/0.31 inference(avatar_split_clause,[],[f9,f19])).
% 0.21/0.31 thf(f66,plain,(
% 0.21/0.31 ( ! [X0 : a] : ((((cP @ (sK1 @ (^[Y0 : a]: (~ (Y0 = X0)))) @ (sK0 @ (^[Y0 : a]: (~ (Y0 = X0)))))) = X0) | ($true != (((^[Y0 : a]: (~ (Y0 = X0))) @ cZ)))) )),
% 0.21/0.31 inference(leibniz_equality_elimination,[],[f14])).
% 0.21/0.31 thf(f73,plain,(
% 0.21/0.31 ( ! [X0 : a] : (($true != ((~ (cZ = X0)))) | (((cP @ (sK1 @ (^[Y0 : a]: (~ (Y0 = X0)))) @ (sK0 @ (^[Y0 : a]: (~ (Y0 = X0)))))) = X0)) )),
% 0.21/0.31 inference(beta-eta_normalization,[],[f66])).
% 0.21/0.31 thf(f74,plain,(
% 0.21/0.31 ( ! [X0 : a] : (($true = ((cZ = X0))) | (((cP @ (sK1 @ (^[Y0 : a]: (~ (Y0 = X0)))) @ (sK0 @ (^[Y0 : a]: (~ (Y0 = X0)))))) = X0)) )),
% 0.21/0.31 inference(not_proxy_clausification,[],[f73])).
% 0.21/0.31 thf(f75,plain,(
% 0.21/0.31 ( ! [X0 : a] : ((((cP @ (sK1 @ (^[Y0 : a]: (~ (Y0 = X0)))) @ (sK0 @ (^[Y0 : a]: (~ (Y0 = X0)))))) = X0) | (cZ = X0)) )),
% 0.21/0.31 inference(equality_proxy_clausification,[],[f74])).
% 0.21/0.31 thf(f189,plain,(
% 0.21/0.31 ( ! [X0 : a] : ((cZ = X0) | (sK2 != X0)) )),
% 0.21/0.31 inference(superposition,[],[f10,f75])).
% 0.21/0.31 thf(f202,plain,(
% 0.21/0.31 ( ! [X0 : a] : ((sK2 != X0) | (sK2 != X0)) ) | spl3_1),
% 0.21/0.31 inference(superposition,[],[f21,f189])).
% 0.21/0.31 thf(f203,plain,(
% 0.21/0.31 ( ! [X0 : a] : ((sK2 != X0)) ) | spl3_1),
% 0.21/0.31 inference(duplicate_literal_removal,[],[f202])).
% 0.21/0.31 thf(f220,plain,(
% 0.21/0.31 (sK2 != sK2) | spl3_1),
% 0.21/0.31 inference(imitation,[],[f203])).
% 0.21/0.31 thf(f223,plain,(
% 0.21/0.31 $false | spl3_1),
% 0.21/0.31 inference(trivial_inequality_removal,[],[f220])).
% 0.21/0.31 thf(f224,plain,(
% 0.21/0.31 spl3_1),
% 0.21/0.31 inference(avatar_contradiction_clause,[],[f223])).
% 0.21/0.31 cnf(s1, plain, ~spl3_1, inference(sat_conversion,[],[f22])).
% 0.21/0.31 cnf(s8, plain, spl3_1, inference(sat_conversion,[],[f224])).
% 0.21/0.31 cnf(s9, plain, $false, inference(rat,[],[s1,s8])).
% 0.21/0.31 thf(f225,plain,(
% 0.21/0.31 $false),
% 0.21/0.31 inference(avatar_sat_refutation,[],[s9])).
% 0.21/0.31 % SZS output end Proof for theBenchmark
% 0.21/0.31 % (1181804)------------------------------
% 0.21/0.31 % (1181804)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (1181804)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (1181804)CaDiCaL version: 2.1.3
% 0.21/0.31 % (1181804)Termination reason: Refutation
% 0.21/0.31 % (1181804)Time elapsed: 0.008 s
% 0.21/0.31 % (1181804)Peak memory usage: 13 MB
% 0.21/0.31 % (1181804)Instructions burned: 10 (million)
% 0.21/0.31 % (1181796)Success in time 0.044 s
% 0.21/0.31 % Vampire exiting
%------------------------------------------------------------------------------