%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT319^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 0.08s 0.27s
% Output : Refutation 0.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : DAT319^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n003.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 18:28:59 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.27 % (2878961)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.08/0.27 % (2878971)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=824103890:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.08/0.27 % (2878971) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2878961-2878971"...
% 0.08/0.27 % (2878971)...printing done.
% 0.08/0.27 % (2878971)Refutation found. Thanks to Tanya!
% 0.08/0.27 % SZS status Theorem for theBenchmark
% 0.08/0.27 % SZS output start Proof for theBenchmark
% 0.08/0.27 thf(type_def_5, type, 'type/ind_types/list': $tType > $tType).
% 0.08/0.27 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.08/0.27 thf(type_def_7, type, sK0: $tType).
% 0.08/0.27 thf(func_def_0, type, 'const/lists/APPEND': !>[X0: $tType]:(('type/ind_types/list' @ X0 > 'type/ind_types/list' @ X0 > 'type/ind_types/list' @ X0))).
% 0.08/0.27 thf(func_def_1, type, 'const/ind_types/NIL': !>[X0: $tType]:('type/ind_types/list' @ X0)).
% 0.08/0.27 thf(func_def_2, type, 'const/ind_types/CONS': !>[X0: $tType]:((X0 > 'type/ind_types/list' @ X0 > 'type/ind_types/list' @ X0))).
% 0.08/0.27 thf(func_def_4, type, sK1: sK0).
% 0.08/0.27 thf(func_def_5, type, sK2: 'type/ind_types/list' @ sK0).
% 0.08/0.27 thf(f1,axiom,(
% 0.08/0.27 ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : ((('const/lists/APPEND' @ X0 @ 'const/ind_types/NIL' @ X0 @ X1)) = X1)),
% 0.08/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/lists/APPEND_0')).
% 0.08/0.27 thf(f2,axiom,(
% 0.08/0.27 ! [X0 : $tType,X3 : 'type/ind_types/list' @ X0,X1 : X0,X2 : 'type/ind_types/list' @ X0] : ((('const/lists/APPEND' @ X0 @ ('const/ind_types/CONS' @ X0 @ X1 @ X2) @ X3)) = (('const/ind_types/CONS' @ X0 @ X1 @ ('const/lists/APPEND' @ X0 @ X2 @ X3))))),
% 0.08/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/lists/APPEND_1')).
% 0.08/0.27 thf(f3,conjecture,(
% 0.08/0.27 ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0] : ((('const/lists/APPEND' @ X0 @ ('const/ind_types/CONS' @ X0 @ X1 @ 'const/ind_types/NIL' @ X0) @ X2)) = (('const/ind_types/CONS' @ X0 @ X1 @ X2)))),
% 0.08/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/lists/APPEND_SING_')).
% 0.08/0.27 thf(f4,negated_conjecture,(
% 0.08/0.27 ~ ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0] : ((('const/lists/APPEND' @ X0 @ ('const/ind_types/CONS' @ X0 @ X1 @ 'const/ind_types/NIL' @ X0) @ X2)) = (('const/ind_types/CONS' @ X0 @ X1 @ X2)))),
% 0.08/0.27 inference(negated_conjecture,[status(cth)],[f3])).
% 0.08/0.27 thf(f5,plain,(
% 0.08/0.27 ! [X0 : $tType,X2 : X0,X1 : 'type/ind_types/list' @ X0,X3 : 'type/ind_types/list' @ X0] : ((('const/ind_types/CONS' @ X0 @ X2 @ ('const/lists/APPEND' @ X0 @ X3 @ X1))) = (('const/lists/APPEND' @ X0 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3) @ X1)))),
% 0.08/0.27 inference(rectify,[],[f2])).
% 0.08/0.27 thf(f6,plain,(
% 0.08/0.27 ? [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0] : ((('const/ind_types/CONS' @ X0 @ X1 @ X2)) != (('const/lists/APPEND' @ X0 @ ('const/ind_types/CONS' @ X0 @ X1 @ 'const/ind_types/NIL' @ X0) @ X2)))),
% 0.08/0.27 inference(ennf_transformation,[],[f4])).
% 0.08/0.27 thf(f7,plain,(
% 0.08/0.27 ((('const/lists/APPEND' @ sK0 @ ('const/ind_types/CONS' @ sK0 @ sK1 @ 'const/ind_types/NIL' @ sK0) @ sK2)) != (('const/ind_types/CONS' @ sK0 @ sK1 @ sK2)))),
% 0.08/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f6])).
% 0.08/0.27 thf(f8,plain,(
% 0.08/0.27 ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0,X3 : 'type/ind_types/list' @ X0] : ((('const/ind_types/CONS' @ X0 @ X1 @ ('const/lists/APPEND' @ X0 @ X3 @ X2))) = (('const/lists/APPEND' @ X0 @ ('const/ind_types/CONS' @ X0 @ X1 @ X3) @ X2)))),
% 0.08/0.27 inference(rectify,[],[f5])).
% 0.08/0.27 thf(f9,plain,(
% 0.08/0.27 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (((('const/lists/APPEND' @ X0 @ 'const/ind_types/NIL' @ X0 @ X1)) = X1)) )),
% 0.08/0.27 inference(cnf_transformation,[],[f1])).
% 0.08/0.27 thf(f10,plain,(
% 0.08/0.27 ((('const/lists/APPEND' @ sK0 @ ('const/ind_types/CONS' @ sK0 @ sK1 @ 'const/ind_types/NIL' @ sK0) @ sK2)) != (('const/ind_types/CONS' @ sK0 @ sK1 @ sK2)))),
% 0.08/0.27 inference(cnf_transformation,[],[f7])).
% 0.08/0.27 thf(f11,plain,(
% 0.08/0.27 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X3 : 'type/ind_types/list' @ X0,X1 : X0] : (((('const/ind_types/CONS' @ X0 @ X1 @ ('const/lists/APPEND' @ X0 @ X3 @ X2))) = (('const/lists/APPEND' @ X0 @ ('const/ind_types/CONS' @ X0 @ X1 @ X3) @ X2)))) )),
% 0.08/0.27 inference(cnf_transformation,[],[f8])).
% 0.08/0.27 thf(f12,plain,(
% 0.08/0.27 ((('const/ind_types/CONS' @ sK0 @ sK1 @ ('const/lists/APPEND' @ sK0 @ 'const/ind_types/NIL' @ sK0 @ sK2))) != (('const/ind_types/CONS' @ sK0 @ sK1 @ sK2)))),
% 0.08/0.27 inference(forward_demodulation,[],[f10,f11])).
% 0.08/0.27 thf(f13,plain,(
% 0.08/0.27 ((('const/ind_types/CONS' @ sK0 @ sK1 @ sK2)) != (('const/ind_types/CONS' @ sK0 @ sK1 @ sK2)))),
% 0.08/0.27 inference(forward_demodulation,[],[f12,f9])).
% 0.08/0.27 thf(f14,plain,(
% 0.08/0.27 $false),
% 0.08/0.27 inference(trivial_inequality_removal,[],[f13])).
% 0.08/0.27 % SZS output end Proof for theBenchmark
% 0.08/0.27 % (2878971)------------------------------
% 0.08/0.27 % (2878971)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.27 % (2878971)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.27 % (2878971)CaDiCaL version: 2.1.3
% 0.08/0.27 % (2878971)Termination reason: Refutation
% 0.08/0.27 % (2878971)Time elapsed: 0.001 s
% 0.08/0.27 % (2878971)Peak memory usage: 12 MB
% 0.08/0.27 % (2878971)Instructions burned: 1 (million)
% 0.08/0.27 % (2878961)Success in time 0.026 s
% 0.08/0.28 % Vampire exiting
%------------------------------------------------------------------------------