%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT280^1 : 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 : n026.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 07:48:41 AM UTC 2026
% Result : Theorem 0.20s 0.27s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT280^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n026.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 18:22:12 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running higher-order theorem proving
% 0.07/0.23 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
% 0.20/0.27 % (975631)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.27 % (975638)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3960954348:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.27 % (975638) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-975631-975638"...
% 0.20/0.27 % (975638)...printing done.
% 0.20/0.27 % (975638)Refutation found. Thanks to Tanya!
% 0.20/0.27 % SZS status Theorem for theBenchmark
% 0.20/0.27 % SZS output start Proof for theBenchmark
% 0.20/0.27 thf(type_def_5, type, 'type/ind_types/list': $tType > $tType).
% 0.20/0.27 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.27 thf(type_def_7, type, sK0: $tType).
% 0.20/0.27 thf(type_def_8, type, sK1: $tType).
% 0.20/0.27 thf(type_def_9, type, sK2: $tType).
% 0.20/0.27 thf(func_def_0, type, 'const/lists/ITLIST2': !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2 > X2) > 'type/ind_types/list' @ X0 > 'type/ind_types/list' @ X1 > X2 > X2))).
% 0.20/0.27 thf(func_def_1, type, 'const/ind_types/NIL': !>[X0: $tType]:('type/ind_types/list' @ X0)).
% 0.20/0.27 thf(func_def_3, type, sK3: sK1).
% 0.20/0.27 thf(func_def_4, type, sK4: (sK2 > sK0 > sK1 > sK1)).
% 0.20/0.27 thf(f1,axiom,(
% 0.20/0.27 ! [X0 : $tType,X2 : $tType,X1 : $tType,X5 : X2,X4 : 'type/ind_types/list' @ X1,X3 : (X0 > X1 > X2 > X2)] : ((('const/lists/ITLIST2' @ X0 @ X1 @ X2 @ X3 @ 'const/ind_types/NIL' @ X0 @ X4 @ X5)) = X5)),
% 0.20/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/lists/ITLIST2_DEF_0')).
% 0.20/0.27 thf(f2,conjecture,(
% 0.20/0.27 ! [X2 : $tType,X1 : $tType,X0 : $tType,X3 : (X0 > X1 > X2 > X2),X4 : X2] : ((('const/lists/ITLIST2' @ X0 @ X1 @ X2 @ X3 @ 'const/ind_types/NIL' @ X0 @ 'const/ind_types/NIL' @ X1 @ X4)) = X4)),
% 0.20/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/lists/ITLIST2_0')).
% 0.20/0.27 thf(f3,negated_conjecture,(
% 0.20/0.27 ~ ! [X2 : $tType,X1 : $tType,X0 : $tType,X3 : (X0 > X1 > X2 > X2),X4 : X2] : ((('const/lists/ITLIST2' @ X0 @ X1 @ X2 @ X3 @ 'const/ind_types/NIL' @ X0 @ 'const/ind_types/NIL' @ X1 @ X4)) = X4)),
% 0.20/0.27 inference(negated_conjecture,[status(cth)],[f2])).
% 0.20/0.27 thf(f4,plain,(
% 0.20/0.27 ~ ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : (X2 > X1 > X0 > X0),X4 : X0] : ((('const/lists/ITLIST2' @ X2 @ X1 @ X0 @ X3 @ 'const/ind_types/NIL' @ X2 @ 'const/ind_types/NIL' @ X1 @ X4)) = X4)),
% 0.20/0.27 inference(rectify,[],[f3])).
% 0.20/0.27 thf(f5,plain,(
% 0.20/0.27 ~ ! [X1 : $tType,X2 : $tType,X0 : $tType,X4 : X0,X3 : (X2 > X1 > X0 > X0)] : ((('const/lists/ITLIST2' @ X2 @ X1 @ X0 @ X3 @ 'const/ind_types/NIL' @ X2 @ 'const/ind_types/NIL' @ X1 @ X4)) = X4)),
% 0.20/0.27 inference(fool_elimination,[],[f4])).
% 0.20/0.27 thf(f6,plain,(
% 0.20/0.27 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X1,X4 : 'type/ind_types/list' @ X2,X5 : (X0 > X2 > X1 > X1)] : ((('const/lists/ITLIST2' @ X0 @ X2 @ X1 @ X5 @ 'const/ind_types/NIL' @ X0 @ X4 @ X3)) = X3)),
% 0.20/0.27 inference(rectify,[],[f1])).
% 0.20/0.27 thf(f7,plain,(
% 0.20/0.27 ! [X0 : $tType,X1 : $tType,X2 : $tType,X5 : (X0 > X2 > X1 > X1),X4 : 'type/ind_types/list' @ X2,X3 : X1] : ((('const/lists/ITLIST2' @ X0 @ X2 @ X1 @ X5 @ 'const/ind_types/NIL' @ X0 @ X4 @ X3)) = X3)),
% 0.20/0.27 inference(fool_elimination,[],[f6])).
% 0.20/0.27 thf(f8,plain,(
% 0.20/0.27 ? [X1 : $tType,X0 : $tType,X2 : $tType,X4 : X0,X3 : (X2 > X1 > X0 > X0)] : ((('const/lists/ITLIST2' @ X2 @ X1 @ X0 @ X3 @ 'const/ind_types/NIL' @ X2 @ 'const/ind_types/NIL' @ X1 @ X4)) != X4)),
% 0.20/0.27 inference(ennf_transformation,[],[f5])).
% 0.20/0.27 thf(f9,plain,(
% 0.20/0.27 ? [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X1,X4 : (X2 > X0 > X1 > X1)] : ((('const/lists/ITLIST2' @ X2 @ X0 @ X1 @ X4 @ 'const/ind_types/NIL' @ X2 @ 'const/ind_types/NIL' @ X0 @ X3)) != X3)),
% 0.20/0.27 inference(rectify,[],[f8])).
% 0.20/0.27 thf(f10,plain,(
% 0.20/0.27 ((('const/lists/ITLIST2' @ sK2 @ sK0 @ sK1 @ sK4 @ 'const/ind_types/NIL' @ sK2 @ 'const/ind_types/NIL' @ sK0 @ sK3)) != sK3)),
% 0.20/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f9])).
% 0.20/0.27 thf(f11,plain,(
% 0.20/0.27 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : (X0 > X2 > X1 > X1),X4 : 'type/ind_types/list' @ X2,X5 : X1] : ((('const/lists/ITLIST2' @ X0 @ X2 @ X1 @ X3 @ 'const/ind_types/NIL' @ X0 @ X4 @ X5)) = X5)),
% 0.20/0.27 inference(rectify,[],[f7])).
% 0.20/0.27 thf(f12,plain,(
% 0.20/0.27 ((('const/lists/ITLIST2' @ sK2 @ sK0 @ sK1 @ sK4 @ 'const/ind_types/NIL' @ sK2 @ 'const/ind_types/NIL' @ sK0 @ sK3)) != sK3)),
% 0.20/0.27 inference(cnf_transformation,[],[f10])).
% 0.20/0.27 thf(f13,plain,(
% 0.20/0.27 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : (X0 > X2 > X1 > X1),X4 : 'type/ind_types/list' @ X2,X5 : X1] : (((('const/lists/ITLIST2' @ X0 @ X2 @ X1 @ X3 @ 'const/ind_types/NIL' @ X0 @ X4 @ X5)) = X5)) )),
% 0.20/0.27 inference(cnf_transformation,[],[f11])).
% 0.20/0.27 thf(f14,plain,(
% 0.20/0.27 $false),
% 0.20/0.27 inference(forward_subsumption_resolution,[],[f12,f13])).
% 0.20/0.27 % SZS output end Proof for theBenchmark
% 0.20/0.27 % (975638)------------------------------
% 0.20/0.27 % (975638)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (975638)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (975638)CaDiCaL version: 2.1.3
% 0.20/0.27 % (975638)Termination reason: Refutation
% 0.20/0.27 % (975638)Time elapsed: 0.001 s
% 0.20/0.27 % (975638)Peak memory usage: 11 MB
% 0.20/0.27 % (975638)Instructions burned: 1 (million)
% 0.20/0.27 % (975631)Success in time 0.031 s
% 0.20/0.27 % Vampire exiting
%------------------------------------------------------------------------------