%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT062_1 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n004.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 09:48:03 AM UTC 2026
% Result : Theorem 0.07s 0.26s
% Output : Refutation 0.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT062_1 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.18 % Computer : n004.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 00:07:22 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.21 Running first-order model finding
% 0.07/0.21 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.26 % (915526)Will run a generic schedule for satisfiability detection.
% 0.07/0.26 % (915534)dis+10_1_sil=32000:sp=arity:random_seed=2715685755:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.07/0.26 % (915532)% WARNING: option uhcvi not known.
% 0.07/0.26 % (915534) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-915526-915534"...
% 0.07/0.26 % (915534)...printing done.
% 0.07/0.26 % (915535)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3096584965:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.07/0.26 % (915531)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2732727256_2999 on theBenchmark for (2999ds/0Mi)
% 0.07/0.26 % (915532)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1635354043:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.07/0.26 % (915533)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1702497837:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.07/0.26 % (915537)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4096516145:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.07/0.26 % (915531)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.07/0.26 % (915531)Terminated due to inappropriate strategy.
% 0.07/0.26 % (915531)------------------------------
% 0.07/0.26 % (915531)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.26 % (915531)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.26 % (915531)CaDiCaL version: 2.1.3
% 0.07/0.26 % (915531)Termination reason: Inappropriate
% 0.07/0.26 % (915531)Time elapsed: 0.001 s
% 0.07/0.26 % (915531)Peak memory usage: 10 MB
% 0.07/0.26 % (915531)Instructions burned: 1 (million)
% 0.07/0.26 % (915531)------------------------------
% 0.07/0.26 % (915531)------------------------------
% 0.07/0.26 % (915534)Refutation found. Thanks to Tanya!
% 0.07/0.26 % SZS status Theorem for theBenchmark
% 0.07/0.26 % SZS output start Proof for theBenchmark
% 0.07/0.26 tff(type_def_5, type, heap: $tType).
% 0.07/0.26 tff(func_def_0, type, empty: heap).
% 0.07/0.26 tff(func_def_1, type, get: heap > heap).
% 0.07/0.26 tff(func_def_2, type, app: (heap * $int) > heap).
% 0.07/0.26 tff(func_def_3, type, toop: heap > $int).
% 0.07/0.26 tff(func_def_4, type, length: heap > $int).
% 0.07/0.26 tff(func_def_9, type, sK0: heap).
% 0.07/0.26 tff(func_def_10, type, sK1: $int).
% 0.07/0.26 tff(func_def_11, type, sK2: heap).
% 0.07/0.26 tff(pred_def_1, type, lsls: (heap * heap) > $o).
% 0.07/0.26 tff(f7,axiom,(
% 0.07/0.26 ! [X0 : $int,X1 : heap] : length(app(X1,X0)) = $sum(1,length(X1))),
% 0.07/0.26 file('/export/starexec/sandbox/benchmark/Axioms/DAT005_0.ax',ax_23)).
% 0.07/0.26 tff(f11,axiom,(
% 0.07/0.26 ! [X0 : $int,X1 : heap,X2 : heap] : (lsls(X1,app(X2,X0)) <=> (X1 = X2 | lsls(X1,X2)))),
% 0.07/0.26 file('/export/starexec/sandbox/benchmark/Axioms/DAT005_0.ax',ax_27)).
% 0.07/0.26 tff(f12,conjecture,(
% 0.07/0.26 ! [X0 : heap,X1 : $int] : (~ ! [X2 : heap] : (lsls(X2,X0) => $less(length(X2),length(X0))) | ! [X2 : heap] : (lsls(X2,app(X0,X1)) => $less(length(X2),length(app(X0,X1)))))),
% 0.07/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p',th_lem_1a)).
% 0.07/0.26 tff(f13,negated_conjecture,(
% 0.07/0.26 ~ ! [X0 : heap,X1 : $int] : (~ ! [X2 : heap] : (lsls(X2,X0) => $less(length(X2),length(X0))) | ! [X2 : heap] : (lsls(X2,app(X0,X1)) => $less(length(X2),length(app(X0,X1)))))),
% 0.07/0.26 inference(negated_conjecture,[status(cth)],[f12])).
% 0.07/0.26 tff(f14,definition,(
% 0.07/0.26 ( ! [X0 : $int,X1 : $int] : ($sum(X0,X1) = $sum(X1,X0)) )),
% 0.07/0.26 introduced(theory,[tha_commutativity])).
% 0.07/0.26 tff(f19,definition,(
% 0.07/0.26 ( ! [X0 : $int] : (~$less(X0,X0)) )),
% 0.07/0.26 introduced(theory,[tha_non-reflexivity])).
% 0.07/0.26 tff(f20,definition,(
% 0.07/0.26 ( ! [X2 : $int,X0 : $int,X1 : $int] : (~$less(X1,X2) | ~$less(X0,X1) | $less(X0,X2)) )),
% 0.07/0.26 introduced(theory,[tha_transitivity])).
% 0.07/0.26 tff(f23,definition,(
% 0.07/0.26 ( ! [X0 : $int,X1 : $int] : ($less(X1,$sum(X0,1)) | $less(X0,X1)) )),
% 0.07/0.26 introduced(theory,[tha_order_plus_one_dichotomy])).
% 0.07/0.26 tff(f26,plain,(
% 0.07/0.26 ~ ! [X0 : heap,X1 : $int] : (~ ! [X2 : heap] : (lsls(X2,X0) => $less(length(X2),length(X0))) | ! [X3 : heap] : (lsls(X3,app(X0,X1)) => $less(length(X3),length(app(X0,X1)))))),
% 0.07/0.26 inference(rectify,[],[f13])).
% 0.07/0.26 tff(f29,plain,(
% 0.07/0.26 ? [X0 : heap,X1 : $int] : (! [X2 : heap] : ($less(length(X2),length(X0)) | ~lsls(X2,X0)) & ? [X3 : heap] : (~$less(length(X3),length(app(X0,X1))) & lsls(X3,app(X0,X1))))),
% 0.07/0.26 inference(ennf_transformation,[],[f26])).
% 0.07/0.26 tff(f32,plain,(
% 0.07/0.26 ! [X0 : $int,X1 : heap,X2 : heap] : ((lsls(X1,app(X2,X0)) | (X1 != X2 & ~lsls(X1,X2))) & ((X1 = X2 | lsls(X1,X2)) | ~lsls(X1,app(X2,X0))))),
% 0.07/0.26 inference(nnf_transformation,[],[f11])).
% 0.07/0.26 tff(f33,plain,(
% 0.07/0.26 ! [X0 : $int,X1 : heap,X2 : heap] : ((lsls(X1,app(X2,X0)) | (X1 != X2 & ~lsls(X1,X2))) & (X1 = X2 | lsls(X1,X2) | ~lsls(X1,app(X2,X0))))),
% 0.07/0.26 inference(flattening,[],[f32])).
% 0.07/0.26 tff(f34,plain,(
% 0.07/0.26 ! [X2 : heap] : ($less(length(X2),length(sK0)) | ~lsls(X2,sK0)) & (~$less(length(sK2),length(app(sK0,sK1))) & lsls(sK2,app(sK0,sK1)))),
% 0.07/0.26 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X3,sK2)],[f29])).
% 0.07/0.26 tff(f43,plain,(
% 0.07/0.26 ( ! [X0 : $int,X1 : heap] : (length(app(X1,X0)) = $sum(1,length(X1))) )),
% 0.07/0.26 inference(cnf_transformation,[],[f7])).
% 0.07/0.26 tff(f47,plain,(
% 0.07/0.26 ( ! [X2 : heap,X0 : $int,X1 : heap] : (~lsls(X1,app(X2,X0)) | lsls(X1,X2) | X1 = X2) )),
% 0.07/0.26 inference(cnf_transformation,[],[f33])).
% 0.07/0.26 tff(f50,plain,(
% 0.07/0.26 lsls(sK2,app(sK0,sK1))),
% 0.07/0.26 inference(cnf_transformation,[],[f34])).
% 0.07/0.26 tff(f51,plain,(
% 0.07/0.26 ~$less(length(sK2),length(app(sK0,sK1)))),
% 0.07/0.26 inference(cnf_transformation,[],[f34])).
% 0.07/0.26 tff(f52,plain,(
% 0.07/0.26 ( ! [X2 : heap] : (~lsls(X2,sK0) | $less(length(X2),length(sK0))) )),
% 0.07/0.26 inference(cnf_transformation,[],[f34])).
% 0.07/0.26 tff(f68,plain,(
% 0.07/0.26 ( ! [X0 : $int] : ($less(X0,$sum(X0,1))) )),
% 0.07/0.26 inference(resolution,[],[f23,f19])).
% 0.07/0.26 tff(f69,plain,(
% 0.07/0.26 ( ! [X0 : $int,X1 : $int] : ($less(X1,$sum(1,X0)) | $less(X0,X1)) )),
% 0.07/0.26 inference(superposition,[],[f23,f14])).
% 0.07/0.26 tff(f79,plain,(
% 0.07/0.26 ( ! [X0 : $int] : ($less(X0,$sum(1,X0))) )),
% 0.07/0.26 inference(superposition,[],[f68,f14])).
% 0.07/0.26 tff(f97,plain,(
% 0.07/0.26 ~$less(length(sK2),$sum(1,length(sK0)))),
% 0.07/0.26 inference(superposition,[],[f51,f43])).
% 0.07/0.26 tff(f185,plain,(
% 0.07/0.26 lsls(sK2,sK0) | sK0 = sK2),
% 0.07/0.26 inference(resolution,[],[f47,f50])).
% 0.07/0.26 tff(f193,definition,(
% 0.07/0.26 spl3_1 <=> sK0 = sK2),
% 0.07/0.26 introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition])).
% 0.07/0.26 tff(f195,plain,(
% 0.07/0.26 sK0 = sK2 | ~spl3_1),
% 0.07/0.26 inference(avatar_component_clause,[],[f193])).
% 0.07/0.26 tff(f197,definition,(
% 0.07/0.26 spl3_2 <=> lsls(sK2,sK0)),
% 0.07/0.26 introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition])).
% 0.07/0.26 tff(f199,plain,(
% 0.07/0.26 lsls(sK2,sK0) | ~spl3_2),
% 0.07/0.26 inference(avatar_component_clause,[],[f197])).
% 0.07/0.26 tff(f200,plain,(
% 0.07/0.26 spl3_1 | spl3_2),
% 0.07/0.26 inference(avatar_split_clause,[],[f185,f197,f193])).
% 0.07/0.26 tff(f201,plain,(
% 0.07/0.26 $less(length(sK2),length(sK0)) | ~spl3_2),
% 0.07/0.26 inference(resolution,[],[f199,f52])).
% 0.07/0.26 tff(f217,plain,(
% 0.07/0.26 ( ! [X0 : $int] : (~$less(X0,length(sK2)) | $less(X0,length(sK0))) ) | ~spl3_2),
% 0.07/0.26 inference(resolution,[],[f201,f20])).
% 0.07/0.26 tff(f218,plain,(
% 0.07/0.26 $less(length(sK0),length(sK2))),
% 0.07/0.26 inference(resolution,[],[f69,f97])).
% 0.07/0.26 tff(f250,plain,(
% 0.07/0.26 $less(length(sK0),length(sK0)) | ~spl3_2),
% 0.07/0.26 inference(resolution,[],[f217,f218])).
% 0.07/0.26 tff(f251,plain,(
% 0.07/0.26 $false | ~spl3_2),
% 0.07/0.26 inference(forward_subsumption_resolution,[],[f250,f19])).
% 0.07/0.26 tff(f252,plain,(
% 0.07/0.26 ~spl3_2),
% 0.07/0.26 inference(avatar_contradiction_clause,[],[f251])).
% 0.07/0.26 tff(f254,plain,(
% 0.07/0.26 ~$less(length(sK0),length(app(sK0,sK1))) | ~spl3_1),
% 0.07/0.26 inference(superposition,[],[f51,f195])).
% 0.07/0.26 tff(f264,plain,(
% 0.07/0.26 ~$less(length(sK0),$sum(1,length(sK0))) | ~spl3_1),
% 0.07/0.26 inference(forward_demodulation,[],[f254,f43])).
% 0.07/0.26 tff(f265,plain,(
% 0.07/0.26 $false | ~spl3_1),
% 0.07/0.26 inference(forward_subsumption_resolution,[],[f264,f79])).
% 0.07/0.26 tff(f266,plain,(
% 0.07/0.26 ~spl3_1),
% 0.07/0.26 inference(avatar_contradiction_clause,[],[f265])).
% 0.07/0.26 cnf(s1, plain, spl3_1 | spl3_2, inference(sat_conversion,[],[f200])).
% 0.07/0.26 cnf(s3, plain, ~spl3_2, inference(sat_conversion,[],[f252])).
% 0.07/0.26 cnf(s6, plain, ~spl3_1, inference(sat_conversion,[],[f266])).
% 0.07/0.26 cnf(s7, plain, $false, inference(rat,[],[s1,s3,s6])).
% 0.07/0.26 tff(f267,plain,(
% 0.07/0.26 $false),
% 0.07/0.26 inference(avatar_sat_refutation,[],[s7])).
% 0.07/0.26 % SZS output end Proof for theBenchmark
% 0.07/0.26 % (915534)------------------------------
% 0.07/0.26 % (915534)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.26 % (915534)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.26 % (915534)CaDiCaL version: 2.1.3
% 0.07/0.26 % (915534)Termination reason: Refutation
% 0.07/0.26 % (915534)Time elapsed: 0.005 s
% 0.07/0.26 % (915534)Peak memory usage: 12 MB
% 0.07/0.26 % (915534)Instructions burned: 11 (million)
% 0.07/0.26 % (915526)Success in time 0.038 s
% 0.07/0.26 % Vampire exiting
%------------------------------------------------------------------------------