%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT089_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 : n011.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 0.19s 0.27s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT089_1 : TPTP v9.3.1. Released v6.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.19 % Computer : n011.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
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 00:08:17 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.22 Running first-order model finding
% 0.07/0.22 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
% 0.19/0.27 % (3916604)Will run a generic schedule for satisfiability detection.
% 0.19/0.27 % (3916610)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3913002222_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.27 % (3916610)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.19/0.27 % (3916610)Terminated due to inappropriate strategy.
% 0.19/0.27 % (3916610)------------------------------
% 0.19/0.27 % (3916610)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (3916610)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (3916610)CaDiCaL version: 2.1.3
% 0.19/0.27 % (3916610)Termination reason: Inappropriate
% 0.19/0.27 % (3916610)Time elapsed: 0.0000 s
% 0.19/0.27 % (3916610)Peak memory usage: 10 MB
% 0.19/0.27 % (3916610)Instructions burned: 1 (million)
% 0.19/0.27 % (3916610)------------------------------
% 0.19/0.27 % (3916610)------------------------------
% 0.19/0.27 % (3916611)% WARNING: option uhcvi not known.
% 0.19/0.27 % (3916612)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3430389256:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.27 % (3916613)dis+10_1_sil=32000:sp=arity:random_seed=833289995:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.27 % (3916611)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2136458107:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.27 % (3916615)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1100173259:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.27 % (3916614)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4088690610:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.27 % (3916616)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1760945152:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.27 % (3916624)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2278648613:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.19/0.27 % (3916624)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.19/0.27 % (3916624)Terminated due to inappropriate strategy.
% 0.19/0.27 % (3916624)------------------------------
% 0.19/0.27 % (3916624)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (3916624)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (3916624)CaDiCaL version: 2.1.3
% 0.19/0.27 % (3916624)Termination reason: Inappropriate
% 0.19/0.27 % (3916624)Time elapsed: 0.0000 s
% 0.19/0.27 % (3916624)Peak memory usage: 10 MB
% 0.19/0.27 % (3916624)Instructions burned: 1 (million)
% 0.19/0.27 % (3916624)------------------------------
% 0.19/0.27 % (3916624)------------------------------
% 0.19/0.27 % (3916611) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3916604-3916611"...
% 0.19/0.27 % (3916611)...printing done.
% 0.19/0.27 % (3916613) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3916604-3916613"...
% 0.19/0.27 % (3916611)Refutation found. Thanks to Tanya!
% 0.19/0.27 % SZS status Theorem for theBenchmark
% 0.19/0.27 % SZS output start Proof for theBenchmark
% 0.19/0.27 tff(type_def_5, type, list: $tType).
% 0.19/0.27 tff(func_def_0, type, nil: list).
% 0.19/0.27 tff(func_def_1, type, cons: ($int * list) > list).
% 0.19/0.27 tff(func_def_2, type, head: list > $int).
% 0.19/0.27 tff(func_def_3, type, tail: list > list).
% 0.19/0.27 tff(func_def_5, type, length: list > $int).
% 0.19/0.27 tff(func_def_8, type, count: ($int * list) > $int).
% 0.19/0.27 tff(func_def_9, type, append: (list * list) > list).
% 0.19/0.27 tff(func_def_11, type, sK0: ($int * list) > $int).
% 0.19/0.27 tff(func_def_12, type, sK1: ($int * list) > list).
% 0.19/0.27 tff(func_def_13, type, sK2: ($int * list) > $int).
% 0.19/0.27 tff(func_def_14, type, sK3: ($int * list) > list).
% 0.19/0.27 tff(func_def_15, type, sK4: ($int * list) > $int).
% 0.19/0.27 tff(func_def_16, type, sK5: ($int * list) > list).
% 0.19/0.27 tff(pred_def_1, type, in: ($int * list) > $o).
% 0.19/0.27 tff(pred_def_2, type, inRange: ($int * list) > $o).
% 0.19/0.27 tff(f7,axiom,(
% 0.19/0.27 length(nil) = 0),
% 0.19/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l)).
% 0.19/0.27 tff(f8,axiom,(
% 0.19/0.27 ! [X0 : $int,X1 : list] : length(cons(X0,X1)) = $sum(1,length(X1))),
% 0.19/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l_1)).
% 0.19/0.27 tff(f9,axiom,(
% 0.19/0.27 ! [X0 : $int] : count(X0,nil) = 0),
% 0.19/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a)).
% 0.19/0.27 tff(f10,axiom,(
% 0.19/0.27 ! [X0 : $int,X1 : $int,X2 : list,X3 : $int] : (X0 != X1 => count(X0,cons(X1,X2)) = count(X0,X2))),
% 0.19/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_3)).
% 0.19/0.27 tff(f15,conjecture,(
% 0.19/0.27 ~ ! [X0 : $int,X1 : list] : $greatereq(count(X0,X1),length(X1))),
% 0.19/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c)).
% 0.19/0.27 tff(f16,negated_conjecture,(
% 0.19/0.27 ~ ~ ! [X0 : $int,X1 : list] : $greatereq(count(X0,X1),length(X1))),
% 0.19/0.27 inference(negated_conjecture,[status(cth)],[f15])).
% 0.19/0.27 tff(f19,plain,(
% 0.19/0.27 ! [X0 : $int,X1 : list] : ~$less(count(X0,X1),length(X1))),
% 0.19/0.27 inference(theory_normalization,[],[f16])).
% 0.19/0.27 tff(f25,definition,(
% 0.19/0.27 ( ! [X0 : $int] : (~$less(X0,X0)) )),
% 0.19/0.27 introduced(theory,[tha_non-reflexivity])).
% 0.19/0.27 tff(f29,definition,(
% 0.19/0.27 ( ! [X0 : $int,X1 : $int] : ($less(X1,$sum(X0,1)) | $less(X0,X1)) )),
% 0.19/0.27 introduced(theory,[tha_order_plus_one_dichotomy])).
% 0.19/0.27 tff(f33,plain,(
% 0.19/0.27 ! [X0 : $int,X1 : $int,X2 : list] : (X0 != X1 => count(X0,cons(X1,X2)) = count(X0,X2))),
% 0.19/0.27 inference(rectify,[],[f10])).
% 0.19/0.27 tff(f35,plain,(
% 0.19/0.27 ! [X0 : $int,X1 : $int,X2 : list] : (count(X0,cons(X1,X2)) = count(X0,X2) | X0 = X1)),
% 0.19/0.27 inference(ennf_transformation,[],[f33])).
% 0.19/0.27 tff(f53,plain,(
% 0.19/0.27 0 = length(nil)),
% 0.19/0.27 inference(cnf_transformation,[],[f7])).
% 0.19/0.27 tff(f54,plain,(
% 0.19/0.27 ( ! [X0 : $int,X1 : list] : (length(cons(X0,X1)) = $sum(1,length(X1))) )),
% 0.19/0.27 inference(cnf_transformation,[],[f8])).
% 0.19/0.27 tff(f55,plain,(
% 0.19/0.27 ( ! [X0 : $int] : (0 = count(X0,nil)) )),
% 0.19/0.27 inference(cnf_transformation,[],[f9])).
% 0.19/0.27 tff(f56,plain,(
% 0.19/0.27 ( ! [X2 : list,X0 : $int,X1 : $int] : (count(X0,cons(X1,X2)) = count(X0,X2) | X0 = X1) )),
% 0.19/0.27 inference(cnf_transformation,[],[f35])).
% 0.19/0.27 tff(f62,plain,(
% 0.19/0.27 ( ! [X0 : $int,X1 : list] : (~$less(count(X0,X1),length(X1))) )),
% 0.19/0.27 inference(cnf_transformation,[],[f19])).
% 0.19/0.27 tff(f99,plain,(
% 0.19/0.27 ( ! [X0 : $int] : ($less(X0,$sum(X0,1))) )),
% 0.19/0.27 inference(resolution,[],[f29,f25])).
% 0.19/0.27 tff(f138,plain,(
% 0.19/0.27 ( ! [X2 : $int,X0 : list,X1 : $int] : (~$less(count(X1,cons(X2,X0)),$sum(1,length(X0)))) )),
% 0.19/0.27 inference(superposition,[],[f62,f54])).
% 0.19/0.27 tff(f165,plain,(
% 0.19/0.27 ( ! [X0 : $int,X1 : $int] : (~$less(count(X0,cons(X1,nil)),$sum(1,0))) )),
% 0.19/0.27 inference(superposition,[],[f138,f53])).
% 0.19/0.27 tff(f167,plain,(
% 0.19/0.27 ( ! [X0 : $int,X1 : $int] : (~$less(count(X0,cons(X1,nil)),1)) )),
% 0.19/0.27 inference(evaluation,[],[f165])).
% 0.19/0.27 tff(f235,plain,(
% 0.19/0.27 ( ! [X0 : $int,X1 : $int] : (~$less(count(X0,nil),1) | X0 = X1) )),
% 0.19/0.27 inference(superposition,[],[f167,f56])).
% 0.19/0.27 tff(f243,plain,(
% 0.19/0.27 ( ! [X0 : $int,X1 : $int] : (~$less(0,1) | X0 = X1) )),
% 0.19/0.27 inference(forward_demodulation,[],[f235,f55])).
% 0.19/0.27 tff(f244,plain,(
% 0.19/0.27 ( ! [X0 : $int,X1 : $int] : (X0 = X1) )),
% 0.19/0.27 inference(evaluation,[],[f243])).
% 0.19/0.27 tff(f270,plain,(
% 0.19/0.27 ( ! [X0 : $int,X1 : $int] : ($less(X1,X0)) )),
% 0.19/0.27 inference(superposition,[],[f99,f244])).
% 0.19/0.27 tff(f368,plain,(
% 0.19/0.27 $false),
% 0.19/0.27 inference(backward_subsumption_resolution,[],[f25,f270])).
% 0.19/0.27 % SZS output end Proof for theBenchmark
% 0.19/0.27 % (3916611)------------------------------
% 0.19/0.27 % (3916611)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (3916611)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (3916611)CaDiCaL version: 2.1.3
% 0.19/0.27 % (3916611)Termination reason: Refutation
% 0.19/0.27 % (3916611)Time elapsed: 0.011 s
% 0.19/0.27 % (3916611)Peak memory usage: 12 MB
% 0.19/0.27 % (3916611)Instructions burned: 13 (million)
% 0.19/0.27 % (3916604)Success in time 0.035 s
% 0.19/0.27 % Vampire exiting
%------------------------------------------------------------------------------