%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT324^1 : 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 : n010.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 07:48:46 AM UTC 2026
% Result : Theorem 0.22s 0.28s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT324^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n010.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.20 % CPULimit : 300
% 0.07/0.20 % WCLimit : 300
% 0.07/0.20 % DateTime : Tue Sep 29 18:27:49 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.07/0.24 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
% 0.22/0.28 % (3242978)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.28 % (3242986)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=344400940: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)
% 0.22/0.28 % (3242986) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3242978-3242986"...
% 0.22/0.28 % (3242986)...printing done.
% 0.22/0.28 % (3242989)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.28 % (3242989)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
% 0.22/0.28 % (3242986)Refutation found. Thanks to Tanya!
% 0.22/0.28 % SZS status Theorem for theBenchmark
% 0.22/0.28 % SZS output start Proof for theBenchmark
% 0.22/0.28 thf(type_def_5, type, 'type/nums/num': $tType).
% 0.22/0.28 thf(type_def_6, type, 'type/ind_types/list': $tType > $tType).
% 0.22/0.28 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.28 thf(type_def_8, type, sK0: $tType).
% 0.22/0.28 thf(func_def_0, type, 'const/sets/set_of_list': !>[X0: $tType]:(('type/ind_types/list' @ X0 > X0 > $o))).
% 0.22/0.28 thf(func_def_1, type, 'const/sets/list_of_set': !>[X0: $tType]:(((X0 > $o) > 'type/ind_types/list' @ X0))).
% 0.22/0.28 thf(func_def_2, type, 'const/sets/FINITE': !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.22/0.28 thf(func_def_3, type, 'const/sets/CARD': !>[X0: $tType]:(((X0 > $o) > 'type/nums/num'))).
% 0.22/0.28 thf(func_def_4, type, 'const/lists/LENGTH': !>[X0: $tType]:(('type/ind_types/list' @ X0 > 'type/nums/num'))).
% 0.22/0.28 thf(func_def_8, type, sK1: (sK0 > $o)).
% 0.22/0.28 thf(f1,axiom,(
% 0.22/0.28 ! [X0 : $tType,X1 : (X0 > $o)] : (('const/sets/FINITE' @ X0 @ X1) => (((('const/lists/LENGTH' @ X0 @ ('const/sets/list_of_set' @ X0 @ X1))) = (('const/sets/CARD' @ X0 @ X1))) & ((('const/sets/set_of_list' @ X0 @ ('const/sets/list_of_set' @ X0 @ X1))) = X1)))),
% 0.22/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/LIST_OF_SET_PROPERTIES_')).
% 0.22/0.28 thf(f2,conjecture,(
% 0.22/0.28 ! [X0 : $tType,X1 : (X0 > $o)] : (('const/sets/FINITE' @ X0 @ X1) => ((('const/lists/LENGTH' @ X0 @ ('const/sets/list_of_set' @ X0 @ X1))) = (('const/sets/CARD' @ X0 @ X1))))),
% 0.22/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/LENGTH_LIST_OF_SET_')).
% 0.22/0.28 thf(f3,negated_conjecture,(
% 0.22/0.28 ~ ! [X0 : $tType,X1 : (X0 > $o)] : (('const/sets/FINITE' @ X0 @ X1) => ((('const/lists/LENGTH' @ X0 @ ('const/sets/list_of_set' @ X0 @ X1))) = (('const/sets/CARD' @ X0 @ X1))))),
% 0.22/0.28 inference(negated_conjecture,[status(cth)],[f2])).
% 0.22/0.28 thf(f4,plain,(
% 0.22/0.28 ~ ! [X0 : $tType,X1 : (X0 > $o)] : (('const/sets/FINITE' @ X0 @ X1) => ((('const/lists/LENGTH' @ X0 @ ('const/sets/list_of_set' @ X0 @ X1))) = (('const/sets/CARD' @ X0 @ X1))))),
% 0.22/0.28 inference(rectify,[],[f3])).
% 0.22/0.28 thf(f5,plain,(
% 0.22/0.28 ~ ! [X0 : $tType,X1 : (X0 > $o)] : (((('const/sets/FINITE' @ X0 @ X1)) = $true) => ((('const/lists/LENGTH' @ X0 @ ('const/sets/list_of_set' @ X0 @ X1))) = (('const/sets/CARD' @ X0 @ X1))))),
% 0.22/0.28 inference(fool_elimination,[],[f4])).
% 0.22/0.28 thf(f6,plain,(
% 0.22/0.28 ! [X0 : $tType,X1 : (X0 > $o)] : (('const/sets/FINITE' @ X0 @ X1) => (((('const/lists/LENGTH' @ X0 @ ('const/sets/list_of_set' @ X0 @ X1))) = (('const/sets/CARD' @ X0 @ X1))) & ((('const/sets/set_of_list' @ X0 @ ('const/sets/list_of_set' @ X0 @ X1))) = X1)))),
% 0.22/0.28 inference(rectify,[],[f1])).
% 0.22/0.28 thf(f7,plain,(
% 0.22/0.28 ! [X0 : $tType,X1 : (X0 > $o)] : (((('const/sets/FINITE' @ X0 @ X1)) = $true) => (((('const/sets/set_of_list' @ X0 @ ('const/sets/list_of_set' @ X0 @ X1))) = X1) & ((('const/lists/LENGTH' @ X0 @ ('const/sets/list_of_set' @ X0 @ X1))) = (('const/sets/CARD' @ X0 @ X1)))))),
% 0.22/0.28 inference(fool_elimination,[],[f6])).
% 0.22/0.28 thf(f8,plain,(
% 0.22/0.28 ! [X0 : $tType,X1 : (X0 > $o)] : ((((('const/sets/set_of_list' @ X0 @ ('const/sets/list_of_set' @ X0 @ X1))) = X1) & ((('const/lists/LENGTH' @ X0 @ ('const/sets/list_of_set' @ X0 @ X1))) = (('const/sets/CARD' @ X0 @ X1)))) | ((('const/sets/FINITE' @ X0 @ X1)) != $true))),
% 0.22/0.28 inference(ennf_transformation,[],[f7])).
% 0.22/0.28 thf(f9,plain,(
% 0.22/0.28 ? [X0 : $tType,X1 : (X0 > $o)] : (((('const/sets/FINITE' @ X0 @ X1)) = $true) & ((('const/lists/LENGTH' @ X0 @ ('const/sets/list_of_set' @ X0 @ X1))) != (('const/sets/CARD' @ X0 @ X1))))),
% 0.22/0.28 inference(ennf_transformation,[],[f5])).
% 0.22/0.28 thf(f10,plain,(
% 0.22/0.28 ((('const/sets/FINITE' @ sK0 @ sK1)) = $true) & ((('const/sets/CARD' @ sK0 @ sK1)) != (('const/lists/LENGTH' @ sK0 @ ('const/sets/list_of_set' @ sK0 @ sK1))))),
% 0.22/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f9])).
% 0.22/0.28 thf(f11,plain,(
% 0.22/0.28 ((('const/sets/CARD' @ sK0 @ sK1)) != (('const/lists/LENGTH' @ sK0 @ ('const/sets/list_of_set' @ sK0 @ sK1))))),
% 0.22/0.28 inference(cnf_transformation,[],[f10])).
% 0.22/0.28 thf(f12,plain,(
% 0.22/0.28 ((('const/sets/FINITE' @ sK0 @ sK1)) = $true)),
% 0.22/0.28 inference(cnf_transformation,[],[f10])).
% 0.22/0.28 thf(f13,plain,(
% 0.22/0.28 ( ! [X0 : $tType,X1 : (X0 > $o)] : (((('const/lists/LENGTH' @ X0 @ ('const/sets/list_of_set' @ X0 @ X1))) = (('const/sets/CARD' @ X0 @ X1))) | ((('const/sets/FINITE' @ X0 @ X1)) != $true)) )),
% 0.22/0.28 inference(cnf_transformation,[],[f8])).
% 0.22/0.28 thf(f17,definition,(
% 0.22/0.28 spl2_1 <=> ((('const/sets/FINITE' @ sK0 @ sK1)) = $true)),
% 0.22/0.28 introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition])).
% 0.22/0.28 thf(f19,plain,(
% 0.22/0.28 ((('const/sets/FINITE' @ sK0 @ sK1)) = $true) | ~spl2_1),
% 0.22/0.28 inference(avatar_component_clause,[],[f17])).
% 0.22/0.28 thf(f20,plain,(
% 0.22/0.28 spl2_1),
% 0.22/0.28 inference(avatar_split_clause,[],[f12,f17])).
% 0.22/0.28 thf(f22,definition,(
% 0.22/0.28 spl2_2 <=> ((('const/sets/CARD' @ sK0 @ sK1)) = (('const/lists/LENGTH' @ sK0 @ ('const/sets/list_of_set' @ sK0 @ sK1))))),
% 0.22/0.28 introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition])).
% 0.22/0.28 thf(f24,plain,(
% 0.22/0.28 ((('const/sets/CARD' @ sK0 @ sK1)) != (('const/lists/LENGTH' @ sK0 @ ('const/sets/list_of_set' @ sK0 @ sK1)))) | spl2_2),
% 0.22/0.28 inference(avatar_component_clause,[],[f22])).
% 0.22/0.28 thf(f25,plain,(
% 0.22/0.28 ~spl2_2),
% 0.22/0.28 inference(avatar_split_clause,[],[f11,f22])).
% 0.22/0.28 thf(f29,plain,(
% 0.22/0.28 ((('const/sets/FINITE' @ sK0 @ sK1)) != $true) | ((('const/sets/CARD' @ sK0 @ sK1)) != (('const/sets/CARD' @ sK0 @ sK1))) | spl2_2),
% 0.22/0.28 inference(superposition,[],[f24,f13])).
% 0.22/0.28 thf(f30,plain,(
% 0.22/0.28 ((('const/sets/FINITE' @ sK0 @ sK1)) != $true) | spl2_2),
% 0.22/0.28 inference(trivial_inequality_removal,[],[f29])).
% 0.22/0.28 thf(f31,plain,(
% 0.22/0.28 $false | (~spl2_1 | spl2_2)),
% 0.22/0.28 inference(forward_subsumption_resolution,[],[f30,f19])).
% 0.22/0.28 thf(f32,plain,(
% 0.22/0.28 ~spl2_1 | spl2_2),
% 0.22/0.28 inference(avatar_contradiction_clause,[],[f31])).
% 0.22/0.28 cnf(s1, plain, spl2_1, inference(sat_conversion,[],[f20])).
% 0.22/0.28 cnf(s2, plain, ~spl2_2, inference(sat_conversion,[],[f25])).
% 0.22/0.28 cnf(s3, plain, ~spl2_1 | spl2_2, inference(sat_conversion,[],[f32])).
% 0.22/0.28 cnf(s4, plain, ~spl2_1, inference(rat,[],[s3,s2])).
% 0.22/0.28 cnf(s5, plain, $false, inference(rat,[],[s1,s4])).
% 0.22/0.28 thf(f33,plain,(
% 0.22/0.28 $false),
% 0.22/0.28 inference(avatar_sat_refutation,[],[s5])).
% 0.22/0.28 % SZS output end Proof for theBenchmark
% 0.22/0.28 % (3242986)------------------------------
% 0.22/0.28 % (3242986)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.28 % (3242986)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.28 % (3242986)CaDiCaL version: 2.1.3
% 0.22/0.28 % (3242986)Termination reason: Refutation
% 0.22/0.28 % (3242986)Time elapsed: 0.002 s
% 0.22/0.28 % (3242986)Peak memory usage: 13 MB
% 0.22/0.28 % (3242986)Instructions burned: 3 (million)
% 0.22/0.28 % (3242978)Success in time 0.03 s
% 0.22/0.28 % Vampire exiting
%------------------------------------------------------------------------------