%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT288^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 07:48:42 AM UTC 2026
% Result : Theorem 0.22s 0.30s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT288^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n018.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 18:22:41 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.24 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
% 0.22/0.30 % (459454)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.30 % (459465)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.30 % (459465)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
% 0.22/0.30 % (459460)lrs+10_16_si=on:nwc=1.5:random_seed=712734738:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.30 % (459459)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1086029178:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.30 % (459461)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1483940579:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.30 % (459463)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2159776033:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.30 % (459462)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=3266064688: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)
% 0.22/0.30 % (459464)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=630498490:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.30 % (459465)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=3543966564:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.30 % (459461)Instruction limit reached!
% 0.22/0.30 % (459461)------------------------------
% 0.22/0.30 % (459461)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (459461)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (459461)CaDiCaL version: 2.1.3
% 0.22/0.30 % (459461)Termination reason: Instruction limit
% 0.22/0.30 % (459461)Termination phase: Saturation
% 0.22/0.30 % (459461)Time elapsed: 0.004 s
% 0.22/0.30 % (459461)Peak memory usage: 12 MB
% 0.22/0.30 % (459461)Instructions burned: 5 (million)
% 0.22/0.30 % (459462) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-459454-459462"...
% 0.22/0.30 % (459460)Instruction limit reached!
% 0.22/0.30 % (459460)------------------------------
% 0.22/0.30 % (459460)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (459460)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (459460)CaDiCaL version: 2.1.3
% 0.22/0.30 % (459460)Termination reason: Instruction limit
% 0.22/0.30 % (459460)Termination phase: Saturation
% 0.22/0.30 % (459460)Time elapsed: 0.010 s
% 0.22/0.30 % (459460)Peak memory usage: 12 MB
% 0.22/0.30 % (459460)Instructions burned: 19 (million)
% 0.22/0.30 % (459462)...printing done.
% 0.22/0.30 % (459462)Refutation found. Thanks to Tanya!
% 0.22/0.30 % SZS status Theorem for theBenchmark
% 0.22/0.30 % SZS output start Proof for theBenchmark
% 0.22/0.30 thf(type_def_5, type, 'type/ind_types/list': $tType > $tType).
% 0.22/0.30 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.30 thf(type_def_7, type, sK0: $tType).
% 0.22/0.30 thf(func_def_0, type, 'const/ind_types/NIL': !>[X0: $tType]:('type/ind_types/list' @ X0)).
% 0.22/0.30 thf(func_def_1, type, 'const/ind_types/CONS': !>[X0: $tType]:((X0 > 'type/ind_types/list' @ X0 > 'type/ind_types/list' @ X0))).
% 0.22/0.30 thf(func_def_5, type, sK1: 'type/ind_types/list' @ sK0).
% 0.22/0.30 thf(func_def_6, type, sK2: !>[X0: $tType]:((('type/ind_types/list' @ X0 > $o) > 'type/ind_types/list' @ X0))).
% 0.22/0.30 thf(func_def_7, type, sK3: !>[X0: $tType]:((('type/ind_types/list' @ X0 > $o) > X0))).
% 0.22/0.30 thf(func_def_8, type, vNOT: ($o > $o)).
% 0.22/0.30 thf(func_def_10, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.22/0.30 thf(func_def_11, type, db0: !>[X0: $tType]:(X0)).
% 0.22/0.30 thf(func_def_12, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.22/0.30 thf(f1,axiom,(
% 0.22/0.30 ! [X0 : $tType,X1 : ('type/ind_types/list' @ X0 > $o)] : (((X1 @ 'const/ind_types/NIL' @ X0) & ! [X2 : X0,X3 : 'type/ind_types/list' @ X0] : ((X1 @ X3) => (X1 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3)))) => ! [X2 : 'type/ind_types/list' @ X0] : (X1 @ X2))),
% 0.22/0.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/ind_types/list_INDUCT_')).
% 0.22/0.30 thf(f4,conjecture,(
% 0.22/0.30 ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : ((X1 = 'const/ind_types/NIL' @ X0) | ? [X3 : 'type/ind_types/list' @ X0,X2 : X0] : (X1 = (('const/ind_types/CONS' @ X0 @ X2 @ X3))))),
% 0.22/0.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/lists/list_CASES_')).
% 0.22/0.30 thf(f5,negated_conjecture,(
% 0.22/0.30 ~ ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : ((X1 = 'const/ind_types/NIL' @ X0) | ? [X3 : 'type/ind_types/list' @ X0,X2 : X0] : (X1 = (('const/ind_types/CONS' @ X0 @ X2 @ X3))))),
% 0.22/0.30 inference(negated_conjecture,[status(cth)],[f4])).
% 0.22/0.30 thf(f8,plain,(
% 0.22/0.30 ! [X0 : $tType,X1 : ('type/ind_types/list' @ X0 > $o)] : (((X1 @ 'const/ind_types/NIL' @ X0) & ! [X2 : X0,X3 : 'type/ind_types/list' @ X0] : ((X1 @ X3) => (X1 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3)))) => ! [X4 : 'type/ind_types/list' @ X0] : (X1 @ X4))),
% 0.22/0.30 inference(rectify,[],[f1])).
% 0.22/0.30 thf(f9,plain,(
% 0.22/0.30 ! [X0 : $tType,X1 : ('type/ind_types/list' @ X0 > $o)] : ((! [X3 : 'type/ind_types/list' @ X0,X2 : X0] : ((((X1 @ X3)) = $true) => (((X1 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3))) = $true)) & (((X1 @ 'const/ind_types/NIL' @ X0)) = $true)) => ! [X4 : 'type/ind_types/list' @ X0] : ($true = ((X1 @ X4))))),
% 0.22/0.30 inference(fool_elimination,[],[f8])).
% 0.22/0.30 thf(f11,plain,(
% 0.22/0.30 ~ ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : ((X1 = 'const/ind_types/NIL' @ X0) | ? [X2 : 'type/ind_types/list' @ X0,X3 : X0] : ((('const/ind_types/CONS' @ X0 @ X3 @ X2)) = X1))),
% 0.22/0.30 inference(rectify,[],[f5])).
% 0.22/0.30 thf(f12,plain,(
% 0.22/0.30 ? [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (! [X3 : X0,X2 : 'type/ind_types/list' @ X0] : ((('const/ind_types/CONS' @ X0 @ X3 @ X2)) != X1) & ('const/ind_types/NIL' @ X0 != X1))),
% 0.22/0.30 inference(ennf_transformation,[],[f11])).
% 0.22/0.30 thf(f13,plain,(
% 0.22/0.30 ! [X0 : $tType,X1 : ('type/ind_types/list' @ X0 > $o)] : (! [X4 : 'type/ind_types/list' @ X0] : ($true = ((X1 @ X4))) | (? [X3 : 'type/ind_types/list' @ X0,X2 : X0] : ((((X1 @ X3)) = $true) & (((X1 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3))) != $true)) | (((X1 @ 'const/ind_types/NIL' @ X0)) != $true)))),
% 0.22/0.30 inference(ennf_transformation,[],[f9])).
% 0.22/0.30 thf(f14,plain,(
% 0.22/0.30 ! [X0 : $tType,X1 : ('type/ind_types/list' @ X0 > $o)] : (! [X4 : 'type/ind_types/list' @ X0] : ($true = ((X1 @ X4))) | ? [X3 : 'type/ind_types/list' @ X0,X2 : X0] : ((((X1 @ X3)) = $true) & (((X1 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3))) != $true)) | (((X1 @ 'const/ind_types/NIL' @ X0)) != $true))),
% 0.22/0.30 inference(flattening,[],[f13])).
% 0.22/0.30 thf(f18,plain,(
% 0.22/0.30 ? [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (! [X2 : X0,X3 : 'type/ind_types/list' @ X0] : ((('const/ind_types/CONS' @ X0 @ X2 @ X3)) != X1) & ('const/ind_types/NIL' @ X0 != X1))),
% 0.22/0.30 inference(rectify,[],[f12])).
% 0.22/0.30 thf(f19,plain,(
% 0.22/0.30 ! [X2 : sK0,X3 : 'type/ind_types/list' @ sK0] : ((('const/ind_types/CONS' @ sK0 @ X2 @ X3)) != sK1) & ('const/ind_types/NIL' @ sK0 != sK1)),
% 0.22/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f18])).
% 0.22/0.30 thf(f20,plain,(
% 0.22/0.30 ! [X0 : $tType,X1 : ('type/ind_types/list' @ X0 > $o)] : (! [X2 : 'type/ind_types/list' @ X0] : (((X1 @ X2)) = $true) | ? [X3 : 'type/ind_types/list' @ X0,X4 : X0] : ((((X1 @ X3)) = $true) & (((X1 @ ('const/ind_types/CONS' @ X0 @ X4 @ X3))) != $true)) | (((X1 @ 'const/ind_types/NIL' @ X0)) != $true))),
% 0.22/0.30 inference(rectify,[],[f14])).
% 0.22/0.30 thf(f21,plain,(
% 0.22/0.30 ! [X0 : $tType,X1 : ('type/ind_types/list' @ X0 > $o)] : (! [X2 : 'type/ind_types/list' @ X0] : (((X1 @ X2)) = $true) | ((((X1 @ (sK2 @ X0 @ X1))) = $true) & (((X1 @ ('const/ind_types/CONS' @ X0 @ (sK3 @ X0 @ X1) @ (sK2 @ X0 @ X1)))) != $true)) | (((X1 @ 'const/ind_types/NIL' @ X0)) != $true))),
% 0.22/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X4,sK3 @ X0 @ X1),skolemize(X4,sK3 @ X0 @ X1)],[f20])).
% 0.22/0.30 thf(f25,plain,(
% 0.22/0.30 ('const/ind_types/NIL' @ sK0 != sK1)),
% 0.22/0.30 inference(cnf_transformation,[],[f19])).
% 0.22/0.30 thf(f26,plain,(
% 0.22/0.30 ( ! [X2 : sK0,X3 : 'type/ind_types/list' @ sK0] : (((('const/ind_types/CONS' @ sK0 @ X2 @ X3)) != sK1)) )),
% 0.22/0.30 inference(cnf_transformation,[],[f19])).
% 0.22/0.30 thf(f28,plain,(
% 0.22/0.30 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : ('type/ind_types/list' @ X0 > $o)] : ((((X1 @ ('const/ind_types/CONS' @ X0 @ (sK3 @ X0 @ X1) @ (sK2 @ X0 @ X1)))) != $true) | (((X1 @ 'const/ind_types/NIL' @ X0)) != $true) | (((X1 @ X2)) = $true)) )),
% 0.22/0.30 inference(cnf_transformation,[],[f21])).
% 0.22/0.30 thf(f34,definition,(
% 0.22/0.30 spl4_1 <=> ('const/ind_types/NIL' @ sK0 = sK1)),
% 0.22/0.30 introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition])).
% 0.22/0.30 thf(f36,plain,(
% 0.22/0.30 ('const/ind_types/NIL' @ sK0 != sK1) | spl4_1),
% 0.22/0.30 inference(avatar_component_clause,[],[f34])).
% 0.22/0.30 thf(f37,plain,(
% 0.22/0.30 ~spl4_1),
% 0.22/0.30 inference(avatar_split_clause,[],[f25,f34])).
% 0.22/0.30 thf(f65,plain,(
% 0.22/0.30 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (($true != (((^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1))) @ 'const/ind_types/NIL' @ X0))) | ((('const/ind_types/CONS' @ X0 @ (sK3 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))) @ (sK2 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))))) = X1)) )),
% 0.22/0.30 inference(leibniz_equality_elimination,[],[f28])).
% 0.22/0.30 thf(f74,plain,(
% 0.22/0.30 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (((('const/ind_types/CONS' @ X0 @ (sK3 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))) @ (sK2 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))))) = X1) | (((~ ('const/ind_types/NIL' @ X0 = X1))) != $true)) )),
% 0.22/0.30 inference(beta-eta_normalization,[],[f65])).
% 0.22/0.30 thf(f75,plain,(
% 0.22/0.30 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (((('const/ind_types/CONS' @ X0 @ (sK3 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))) @ (sK2 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))))) = X1) | ($true = (('const/ind_types/NIL' @ X0 = X1)))) )),
% 0.22/0.30 inference(not_proxy_clausification,[],[f74])).
% 0.22/0.30 thf(f76,plain,(
% 0.22/0.30 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (((('const/ind_types/CONS' @ X0 @ (sK3 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))) @ (sK2 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))))) = X1) | ('const/ind_types/NIL' @ X0 = X1)) )),
% 0.22/0.30 inference(equality_proxy_clausification,[],[f75])).
% 0.22/0.30 thf(f264,plain,(
% 0.22/0.30 ( ! [X0 : 'type/ind_types/list' @ sK0] : (('const/ind_types/NIL' @ sK0 = X0) | (sK1 != X0)) )),
% 0.22/0.30 inference(superposition,[],[f26,f76])).
% 0.22/0.30 thf(f266,plain,(
% 0.22/0.30 ( ! [X0 : 'type/ind_types/list' @ sK0] : ((sK1 != X0) | (sK1 != X0)) ) | spl4_1),
% 0.22/0.30 inference(superposition,[],[f36,f264])).
% 0.22/0.30 thf(f271,plain,(
% 0.22/0.30 ( ! [X0 : 'type/ind_types/list' @ sK0] : ((sK1 != X0)) ) | spl4_1),
% 0.22/0.30 inference(duplicate_literal_removal,[],[f266])).
% 0.22/0.30 thf(f275,plain,(
% 0.22/0.30 $false | spl4_1),
% 0.22/0.30 inference(equality_resolution,[],[f271])).
% 0.22/0.30 thf(f278,plain,(
% 0.22/0.30 spl4_1),
% 0.22/0.30 inference(avatar_contradiction_clause,[],[f275])).
% 0.22/0.30 cnf(s1, plain, ~spl4_1, inference(sat_conversion,[],[f37])).
% 0.22/0.30 cnf(s3, plain, spl4_1, inference(sat_conversion,[],[f278])).
% 0.22/0.30 cnf(s4, plain, $false, inference(rat,[],[s1,s3])).
% 0.22/0.30 thf(f279,plain,(
% 0.22/0.30 $false),
% 0.22/0.30 inference(avatar_sat_refutation,[],[s4])).
% 0.22/0.30 % SZS output end Proof for theBenchmark
% 0.22/0.30 % (459462)------------------------------
% 0.22/0.30 % (459462)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (459462)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (459462)CaDiCaL version: 2.1.3
% 0.22/0.30 % (459462)Termination reason: Refutation
% 0.22/0.30 % (459462)Time elapsed: 0.010 s
% 0.22/0.30 % (459462)Peak memory usage: 13 MB
% 0.22/0.30 % (459462)Instructions burned: 15 (million)
% 0.22/0.30 % (459454)Success in time 0.048 s
% 0.22/0.30 % Vampire exiting
%------------------------------------------------------------------------------