%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT088_1 : TPTP v9.3.1. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 : Tue Sep 29 09:48:06 AM UTC 2026
% Result : Theorem 0.24s 0.33s
% Output : Refutation 0.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT088_1 : TPTP v9.3.1. Released v6.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.25 % Computer : n020.cluster.edu
% 0.10/0.25 % Model : x86_64 x86_64
% 0.10/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.25 % Memory : 8046.5625MB
% 0.10/0.25 % OS : Linux 6.8.0-71-generic
% 0.10/0.25 % CPULimit : 300
% 0.10/0.25 % WCLimit : 300
% 0.10/0.25 % DateTime : Tue Sep 29 00:09:05 UTC 2026
% 0.10/0.26 % CPUTime :
% 0.10/0.26 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.24/0.29 Running first-order model finding
% 0.24/0.29 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.24/0.33 % (701602)Will run a generic schedule for satisfiability detection.
% 0.24/0.33 % (701611)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1949115521:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.24/0.33 % (701609)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1835260683:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.24/0.33 % (701611) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-701602-701611"...
% 0.24/0.33 % (701611)...printing done.
% 0.24/0.33 % (701611)Refutation found. Thanks to Tanya!
% 0.24/0.33 % SZS status Theorem for theBenchmark
% 0.24/0.33 % SZS output start Proof for theBenchmark
% 0.24/0.33 tff(type_def_5, type, list: $tType).
% 0.24/0.33 tff(func_def_0, type, nil: list).
% 0.24/0.33 tff(func_def_1, type, cons: ($int * list) > list).
% 0.24/0.33 tff(func_def_2, type, head: list > $int).
% 0.24/0.33 tff(func_def_3, type, tail: list > list).
% 0.24/0.33 tff(func_def_5, type, length: list > $int).
% 0.24/0.33 tff(func_def_8, type, count: ($int * list) > $int).
% 0.24/0.33 tff(func_def_9, type, append: (list * list) > list).
% 0.24/0.33 tff(func_def_11, type, sK0: ($int * list) > $int).
% 0.24/0.33 tff(func_def_12, type, sK1: ($int * list) > list).
% 0.24/0.33 tff(func_def_13, type, sK2: ($int * list) > $int).
% 0.24/0.33 tff(func_def_14, type, sK3: ($int * list) > list).
% 0.24/0.33 tff(func_def_15, type, sK4: ($int * list) > $int).
% 0.24/0.33 tff(func_def_16, type, sK5: ($int * list) > list).
% 0.24/0.33 tff(pred_def_1, type, in: ($int * list) > $o).
% 0.24/0.33 tff(pred_def_2, type, inRange: ($int * list) > $o).
% 0.24/0.33 tff(f2,axiom,(
% 0.24/0.33 ! [X0 : $int,X1 : list] : tail(cons(X0,X1)) = X1),
% 0.24/0.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2)).
% 0.24/0.33 tff(f4,axiom,(
% 0.24/0.33 ! [X0 : $int,X1 : list] : cons(X0,X1) != nil),
% 0.24/0.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4)).
% 0.24/0.33 tff(f9,axiom,(
% 0.24/0.33 ! [X0 : $int] : count(X0,nil) = 0),
% 0.24/0.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a)).
% 0.24/0.33 tff(f11,axiom,(
% 0.24/0.33 ! [X0 : $int,X1 : $int,X2 : list,X3 : $int] : (X0 = X1 => count(X0,cons(X1,X2)) = $sum(count(X0,X2),1))),
% 0.24/0.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_4)).
% 0.24/0.33 tff(f15,conjecture,(
% 0.24/0.33 ~ ! [X0 : $int,X1 : list] : (X1 != nil => count(X0,X1) = count(X0,tail(X1)))),
% 0.24/0.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c)).
% 0.24/0.33 tff(f16,negated_conjecture,(
% 0.24/0.33 ~ ~ ! [X0 : $int,X1 : list] : (X1 != nil => count(X0,X1) = count(X0,tail(X1)))),
% 0.24/0.33 inference(negated_conjecture,[status(cth)],[f15])).
% 0.24/0.33 tff(f19,definition,(
% 0.24/0.33 ( ! [X0 : $int,X1 : $int] : ($sum(X0,X1) = $sum(X1,X0)) )),
% 0.24/0.33 introduced(theory,[tha_commutativity])).
% 0.24/0.33 tff(f33,plain,(
% 0.24/0.33 ! [X0 : $int,X1 : $int,X2 : list] : (X0 = X1 => count(X0,cons(X1,X2)) = $sum(count(X0,X2),1))),
% 0.24/0.33 inference(rectify,[],[f11])).
% 0.24/0.33 tff(f34,plain,(
% 0.24/0.33 ! [X0 : $int,X1 : list] : (X1 != nil => count(X0,X1) = count(X0,tail(X1)))),
% 0.24/0.33 inference(flattening,[],[f16])).
% 0.24/0.33 tff(f36,plain,(
% 0.24/0.33 ! [X0 : $int,X1 : $int,X2 : list] : (count(X0,cons(X1,X2)) = $sum(count(X0,X2),1) | X0 != X1)),
% 0.24/0.33 inference(ennf_transformation,[],[f33])).
% 0.24/0.33 tff(f37,plain,(
% 0.24/0.33 ! [X0 : $int,X1 : list] : (count(X0,X1) = count(X0,tail(X1)) | nil = X1)),
% 0.24/0.33 inference(ennf_transformation,[],[f34])).
% 0.24/0.33 tff(f39,plain,(
% 0.24/0.33 ( ! [X0 : $int,X1 : list] : (tail(cons(X0,X1)) = X1) )),
% 0.24/0.33 inference(cnf_transformation,[],[f2])).
% 0.24/0.33 tff(f41,plain,(
% 0.24/0.33 ( ! [X0 : $int,X1 : list] : (cons(X0,X1) != nil) )),
% 0.24/0.33 inference(cnf_transformation,[],[f4])).
% 0.24/0.33 tff(f56,plain,(
% 0.24/0.33 ( ! [X0 : $int] : (0 = count(X0,nil)) )),
% 0.24/0.33 inference(cnf_transformation,[],[f9])).
% 0.24/0.33 tff(f58,plain,(
% 0.24/0.33 ( ! [X2 : list,X0 : $int,X1 : $int] : (X0 != X1 | count(X0,cons(X1,X2)) = $sum(count(X0,X2),1)) )),
% 0.24/0.33 inference(cnf_transformation,[],[f36])).
% 0.24/0.33 tff(f63,plain,(
% 0.24/0.33 ( ! [X0 : $int,X1 : list] : (count(X0,X1) = count(X0,tail(X1)) | nil = X1) )),
% 0.24/0.33 inference(cnf_transformation,[],[f37])).
% 0.24/0.33 tff(f69,plain,(
% 0.24/0.33 ( ! [X2 : list,X1 : $int] : (count(X1,cons(X1,X2)) = $sum(count(X1,X2),1)) )),
% 0.24/0.33 inference(equality_resolution,[],[f58])).
% 0.24/0.33 tff(f72,plain,(
% 0.24/0.33 ( ! [X2 : $int,X0 : list,X1 : $int] : (count(X1,cons(X2,X0)) = count(X1,X0) | nil = cons(X2,X0)) )),
% 0.24/0.33 inference(superposition,[],[f63,f39])).
% 0.24/0.33 tff(f73,plain,(
% 0.24/0.33 ( ! [X2 : $int,X0 : list,X1 : $int] : (count(X1,cons(X2,X0)) = count(X1,X0)) )),
% 0.24/0.33 inference(forward_subsumption_resolution,[],[f72,f41])).
% 0.24/0.33 tff(f284,plain,(
% 0.24/0.33 ( ! [X0 : $int,X1 : list] : (count(X0,X1) = $sum(count(X0,X1),1)) )),
% 0.24/0.33 inference(superposition,[],[f73,f69])).
% 0.24/0.33 tff(f287,plain,(
% 0.24/0.33 ( ! [X0 : $int,X1 : list] : (count(X0,X1) = $sum(1,count(X0,X1))) )),
% 0.24/0.33 inference(forward_demodulation,[],[f284,f19])).
% 0.24/0.33 tff(f292,plain,(
% 0.24/0.33 0 = $sum(1,0)),
% 0.24/0.33 inference(superposition,[],[f287,f56])).
% 0.24/0.33 tff(f301,plain,(
% 0.24/0.33 $false),
% 0.24/0.33 inference(evaluation,[],[f292])).
% 0.24/0.33 % SZS output end Proof for theBenchmark
% 0.24/0.33 % (701611)------------------------------
% 0.24/0.33 % (701611)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.33 % (701611)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.33 % (701611)CaDiCaL version: 2.1.3
% 0.24/0.33 % (701611)Termination reason: Refutation
% 0.24/0.33 % (701611)Time elapsed: 0.007 s
% 0.24/0.33 % (701611)Peak memory usage: 12 MB
% 0.24/0.33 % (701611)Instructions burned: 12 (million)
% 0.24/0.33 % (701602)Success in time 0.029 s
% 0.24/0.33 % Vampire exiting
%------------------------------------------------------------------------------