%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT093_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 : n016.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 09:48:07 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT093_1 : TPTP v9.3.1. Released v6.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n016.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 00:13:04 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 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
% 0.20/0.28 % (4172533)Will run a generic schedule for satisfiability detection.
% 0.20/0.28 % (4172538)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=522014488_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.28 % (4172538)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.20/0.28 % (4172538)Terminated due to inappropriate strategy.
% 0.20/0.28 % (4172538)------------------------------
% 0.20/0.28 % (4172538)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (4172538)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (4172538)CaDiCaL version: 2.1.3
% 0.20/0.28 % (4172538)Termination reason: Inappropriate
% 0.20/0.28 % (4172538)Time elapsed: 0.0000 s
% 0.20/0.28 % (4172538)Peak memory usage: 10 MB
% 0.20/0.28 % (4172538)Instructions burned: 1 (million)
% 0.20/0.28 % (4172538)------------------------------
% 0.20/0.28 % (4172538)------------------------------
% 0.20/0.28 % (4172539)% WARNING: option uhcvi not known.
% 0.20/0.28 % (4172539)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=876810747:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.28 % (4172540)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2828538931:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.28 % (4172543)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3075864552:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.28 % (4172541)dis+10_1_sil=32000:sp=arity:random_seed=4237587442:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.28 % (4172542)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=329633824:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.28 % (4172544)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1416761002:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.28 % (4172543) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4172533-4172543"...
% 0.20/0.28 % (4172542) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4172533-4172542"...
% 0.20/0.28 % (4172544) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4172533-4172544"...
% 0.20/0.28 % (4172539) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4172533-4172539"...
% 0.20/0.28 % (4172541) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4172533-4172541"...
% 0.20/0.28 % (4172543)...printing done.
% 0.20/0.28 % (4172546)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=508861786:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.20/0.28 % (4172542)...printing done.
% 0.20/0.28 % (4172544)...printing done.
% 0.20/0.28 % (4172546)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.20/0.28 % (4172546)Terminated due to inappropriate strategy.
% 0.20/0.28 % (4172546)------------------------------
% 0.20/0.28 % (4172546)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (4172546)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (4172546)CaDiCaL version: 2.1.3
% 0.20/0.28 % (4172546)Termination reason: Inappropriate
% 0.20/0.28 % (4172546)Time elapsed: 0.0000 s
% 0.20/0.28 % (4172546)Peak memory usage: 10 MB
% 0.20/0.28 % (4172546)Instructions burned: 1 (million)
% 0.20/0.28 % (4172543)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% 0.20/0.28 tff(type_def_5, type, list: $tType).
% 0.20/0.28 tff(func_def_0, type, nil: list).
% 0.20/0.28 tff(func_def_1, type, cons: ($int * list) > list).
% 0.20/0.28 tff(func_def_2, type, head: list > $int).
% 0.20/0.28 tff(func_def_3, type, tail: list > list).
% 0.20/0.28 tff(func_def_5, type, length: list > $int).
% 0.20/0.28 tff(func_def_8, type, count: ($int * list) > $int).
% 0.20/0.28 tff(func_def_9, type, append: (list * list) > list).
% 0.20/0.28 tff(func_def_11, type, sK0: ($int * list) > $int).
% 0.20/0.28 tff(func_def_12, type, sK1: ($int * list) > list).
% 0.20/0.28 tff(func_def_13, type, sK2: ($int * list) > $int).
% 0.20/0.28 tff(func_def_14, type, sK3: ($int * list) > list).
% 0.20/0.28 tff(func_def_15, type, sK4: ($int * list) > $int).
% 0.20/0.28 tff(func_def_16, type, sK5: ($int * list) > list).
% 0.20/0.28 tff(pred_def_1, type, in: ($int * list) > $o).
% 0.20/0.28 tff(pred_def_2, type, inRange: ($int * list) > $o).
% 0.20/0.28 tff(f7,axiom,(
% 0.20/0.28 length(nil) = 0),
% 0.20/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l)).
% 0.20/0.28 tff(f12,axiom,(
% 0.20/0.28 ! [X0 : list] : append(nil,X0) = X0),
% 0.20/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l_6)).
% 0.20/0.28 tff(f15,conjecture,(
% 0.20/0.28 ~ ! [X0 : list,X1 : list] : length(append(X0,X1)) = $sum($sum(length(X0),length(X1)),1)),
% 0.20/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c)).
% 0.20/0.28 tff(f16,negated_conjecture,(
% 0.20/0.28 ~ ~ ! [X0 : list,X1 : list] : length(append(X0,X1)) = $sum($sum(length(X0),length(X1)),1)),
% 0.20/0.28 inference(negated_conjecture,[status(cth)],[f15])).
% 0.20/0.28 tff(f19,definition,(
% 0.20/0.28 ( ! [X0 : $int,X1 : $int] : ($sum(X0,X1) = $sum(X1,X0)) )),
% 0.20/0.28 introduced(theory,[tha_commutativity])).
% 0.20/0.28 tff(f34,plain,(
% 0.20/0.28 ! [X0 : list,X1 : list] : length(append(X0,X1)) = $sum($sum(length(X0),length(X1)),1)),
% 0.20/0.28 inference(flattening,[],[f16])).
% 0.20/0.28 tff(f62,plain,(
% 0.20/0.28 0 = length(nil)),
% 0.20/0.28 inference(cnf_transformation,[],[f7])).
% 0.20/0.28 tff(f67,plain,(
% 0.20/0.28 ( ! [X0 : list] : (append(nil,X0) = X0) )),
% 0.20/0.28 inference(cnf_transformation,[],[f12])).
% 0.20/0.28 tff(f71,plain,(
% 0.20/0.28 ( ! [X0 : list,X1 : list] : (length(append(X0,X1)) = $sum($sum(length(X0),length(X1)),1)) )),
% 0.20/0.28 inference(cnf_transformation,[],[f34])).
% 0.20/0.28 tff(f72,plain,(
% 0.20/0.28 ( ! [X0 : list] : (length(X0) = $sum($sum(length(nil),length(X0)),1)) )),
% 0.20/0.28 inference(superposition,[],[f71,f67])).
% 0.20/0.28 tff(f73,plain,(
% 0.20/0.28 ( ! [X0 : list] : (length(X0) = $sum(1,$sum(length(nil),length(X0)))) )),
% 0.20/0.28 inference(forward_demodulation,[],[f72,f19])).
% 0.20/0.28 tff(f74,plain,(
% 0.20/0.28 ( ! [X0 : list] : (length(X0) = $sum(1,$sum(0,length(X0)))) )),
% 0.20/0.28 inference(forward_demodulation,[],[f73,f62])).
% 0.20/0.28 tff(f75,plain,(
% 0.20/0.28 ( ! [X0 : list] : (length(X0) = $sum(1,length(X0))) )),
% 0.20/0.28 inference(evaluation,[],[f74])).
% 0.20/0.28 tff(f77,plain,(
% 0.20/0.28 0 = $sum(1,0)),
% 0.20/0.28 inference(superposition,[],[f75,f62])).
% 0.20/0.28 tff(f78,plain,(
% 0.20/0.28 $false),
% 0.20/0.28 inference(evaluation,[],[f77])).
% 0.20/0.28 % SZS output end Proof for theBenchmark
% 0.20/0.28 % (4172543)------------------------------
% 0.20/0.28 % (4172543)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (4172543)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (4172543)CaDiCaL version: 2.1.3
% 0.20/0.28 % (4172543)Termination reason: Refutation
% 0.20/0.28 % (4172543)Time elapsed: 0.003 s
% 0.20/0.28 % (4172543)Peak memory usage: 12 MB
% 0.20/0.28 % (4172543)Instructions burned: 3 (million)
% 0.20/0.28 % (4172533)Success in time 0.048 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------