%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT032_1 : TPTP v9.3.1. Released v5.0.0.
% 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 09:47:59 AM UTC 2026
% Result : Theorem 0.51s 0.31s
% Output : Refutation 0.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT032_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.19 % Computer : n004.cluster.edu
% 0.11/0.19 % Model : x86_64 x86_64
% 0.11/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.19 % Memory : 8046.5625MB
% 0.11/0.19 % OS : Linux 6.8.0-71-generic
% 0.11/0.19 % CPULimit : 300
% 0.11/0.19 % WCLimit : 300
% 0.11/0.19 % DateTime : Tue Sep 29 00:05:52 UTC 2026
% 0.11/0.19 % CPUTime :
% 0.11/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.21 Running first-order model finding
% 0.11/0.21 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
% 0.51/0.31 % (912935)Will run a generic schedule for satisfiability detection.
% 0.51/0.31 % (912941)% WARNING: option uhcvi not known.
% 0.51/0.31 % (912941)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=640168027:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.51/0.31 % (912943)dis+10_1_sil=32000:sp=arity:random_seed=1321300015:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.51/0.31 % (912940)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2267631758_2999 on theBenchmark for (2999ds/0Mi)
% 0.51/0.31 % (912945)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=257727244:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.51/0.31 % (912942)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=242052196:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.51/0.31 % (912944)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=17189126:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.51/0.31 % (912946)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3620475179:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.51/0.31 % (912940)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.51/0.31 % (912940)Terminated due to inappropriate strategy.
% 0.51/0.31 % (912940)------------------------------
% 0.51/0.31 % (912940)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.31 % (912940)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.31 % (912940)CaDiCaL version: 2.1.3
% 0.51/0.31 % (912940)Termination reason: Inappropriate
% 0.51/0.31 % (912940)Time elapsed: 0.001 s
% 0.51/0.31 % (912940)Peak memory usage: 10 MB
% 0.51/0.31 % (912940)Instructions burned: 1 (million)
% 0.51/0.31 % (912940)------------------------------
% 0.51/0.31 % (912940)------------------------------
% 0.51/0.31 % (912954)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3981050408:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.51/0.31 % (912954)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.51/0.31 % (912954)Terminated due to inappropriate strategy.
% 0.51/0.31 % (912954)------------------------------
% 0.51/0.31 % (912954)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.31 % (912954)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.31 % (912954)CaDiCaL version: 2.1.3
% 0.51/0.31 % (912954)Termination reason: Inappropriate
% 0.51/0.31 % (912954)Time elapsed: 0.001 s
% 0.51/0.31 % (912954)Peak memory usage: 10 MB
% 0.51/0.31 % (912954)Instructions burned: 1 (million)
% 0.51/0.31 % (912954)------------------------------
% 0.51/0.31 % (912954)------------------------------
% 0.51/0.31 % (912941) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-912935-912941"...
% 0.51/0.31 % (912941)...printing done.
% 0.51/0.31 % (912941)Refutation found. Thanks to Tanya!
% 0.51/0.31 % SZS status Theorem for theBenchmark
% 0.51/0.31 % SZS output start Proof for theBenchmark
% 0.51/0.31 tff(type_def_5, type, collection: $tType).
% 0.51/0.31 tff(func_def_0, type, empty: collection).
% 0.51/0.31 tff(func_def_1, type, add: ($int * collection) > collection).
% 0.51/0.31 tff(func_def_2, type, remove: ($int * collection) > collection).
% 0.51/0.31 tff(func_def_3, type, count: collection > $int).
% 0.51/0.31 tff(func_def_13, type, sK0: collection).
% 0.51/0.31 tff(pred_def_1, type, in: ($int * collection) > $o).
% 0.51/0.31 tff(f10,axiom,(
% 0.51/0.31 ! [X0 : $int,X1 : collection] : (in(X0,X1) <=> count(remove(X0,X1)) = $difference(count(X1),1))),
% 0.51/0.31 file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax',ax5)).
% 0.51/0.31 tff(f11,axiom,(
% 0.51/0.31 ! [X0 : $int,X1 : collection] : (~in(X0,X1) <=> count(remove(X0,X1)) = count(X1))),
% 0.51/0.31 file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax',ax6)).
% 0.51/0.31 tff(f13,conjecture,(
% 0.51/0.31 ! [X0 : collection] : ($greatereq(count(remove(5,X0)),7) => $greatereq(count(remove(4,X0)),6))),
% 0.51/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1)).
% 0.51/0.31 tff(f14,negated_conjecture,(
% 0.51/0.31 ~ ! [X0 : collection] : ($greatereq(count(remove(5,X0)),7) => $greatereq(count(remove(4,X0)),6))),
% 0.51/0.31 inference(negated_conjecture,[status(cth)],[f13])).
% 0.51/0.31 tff(f16,plain,(
% 0.51/0.31 ! [X0 : $int,X1 : collection] : (in(X0,X1) <=> count(remove(X0,X1)) = $sum(count(X1),$uminus(1)))),
% 0.51/0.31 inference(theory_normalization,[],[f10])).
% 0.51/0.31 tff(f17,plain,(
% 0.51/0.31 ~ ! [X0 : collection] : (~$less(count(remove(5,X0)),7) => ~$less(count(remove(4,X0)),6))),
% 0.51/0.31 inference(theory_normalization,[],[f14])).
% 0.51/0.31 tff(f18,definition,(
% 0.51/0.31 ( ! [X0 : $int,X1 : $int] : ($sum(X0,X1) = $sum(X1,X0)) )),
% 0.51/0.31 introduced(theory,[tha_commutativity])).
% 0.51/0.31 tff(f19,definition,(
% 0.51/0.31 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2)) )),
% 0.51/0.31 introduced(theory,[tha_associativity])).
% 0.51/0.31 tff(f22,definition,(
% 0.51/0.31 ( ! [X0 : $int] : (0 = $sum(X0,$uminus(X0))) )),
% 0.51/0.31 introduced(theory,[tha_inverse_op_unit])).
% 0.51/0.31 tff(f24,definition,(
% 0.51/0.31 ( ! [X2 : $int,X0 : $int,X1 : $int] : (~$less(X1,X2) | ~$less(X0,X1) | $less(X0,X2)) )),
% 0.51/0.31 introduced(theory,[tha_transitivity])).
% 0.51/0.31 tff(f25,definition,(
% 0.51/0.31 ( ! [X0 : $int,X1 : $int] : ($less(X0,X1) | $less(X1,X0) | X0 = X1) )),
% 0.51/0.31 introduced(theory,[tha_order_totality])).
% 0.51/0.31 tff(f26,definition,(
% 0.51/0.31 ( ! [X2 : $int,X0 : $int,X1 : $int] : (~$less(X0,X1) | $less($sum(X0,X2),$sum(X1,X2))) )),
% 0.51/0.31 introduced(theory,[tha_order_monotonicity])).
% 0.51/0.31 tff(f27,definition,(
% 0.51/0.31 ( ! [X0 : $int,X1 : $int] : ($less(X1,$sum(X0,1)) | $less(X0,X1)) )),
% 0.51/0.31 introduced(theory,[tha_order_plus_one_dichotomy])).
% 0.51/0.31 tff(f28,definition,(
% 0.51/0.31 ( ! [X0 : $int] : ($uminus($uminus(X0)) = X0) )),
% 0.51/0.31 introduced(theory,[tha_minus_minus_x])).
% 0.51/0.31 tff(f29,definition,(
% 0.51/0.31 ( ! [X0 : $int,X1 : $int] : (~$less(X1,$sum(X0,1)) | ~$less(X0,X1)) )),
% 0.51/0.31 introduced(theory,[tha_extra_integer_ordering])).
% 0.51/0.31 tff(f31,plain,(
% 0.51/0.31 ? [X0 : collection] : ($less(count(remove(4,X0)),6) & ~$less(count(remove(5,X0)),7))),
% 0.51/0.31 inference(ennf_transformation,[],[f17])).
% 0.51/0.31 tff(f49,plain,(
% 0.51/0.31 ( ! [X0 : $int,X1 : collection] : (count(remove(X0,X1)) = $sum(count(X1),$uminus(1)) | ~in(X0,X1)) )),
% 0.51/0.31 inference(cnf_transformation,[],[f16])).
% 0.51/0.31 tff(f51,plain,(
% 0.51/0.31 ( ! [X0 : $int,X1 : collection] : (in(X0,X1) | count(X1) = count(remove(X0,X1))) )),
% 0.51/0.31 inference(cnf_transformation,[],[f11])).
% 0.51/0.31 tff(f53,plain,(
% 0.51/0.31 ~$less(count(remove(5,sK0)),7)),
% 0.51/0.31 inference(cnf_transformation,[],[f31])).
% 0.51/0.31 tff(f54,plain,(
% 0.51/0.31 $less(count(remove(4,sK0)),6)),
% 0.51/0.31 inference(cnf_transformation,[],[f31])).
% 0.51/0.31 tff(f59,plain,(
% 0.51/0.31 ( ! [X0 : $int,X1 : collection] : (count(remove(X0,X1)) = $sum(count(X1),-1) | ~in(X0,X1)) )),
% 0.51/0.31 inference(evaluation,[],[f49])).
% 0.51/0.31 tff(f61,plain,(
% 0.51/0.31 ( ! [X0 : $int] : (0 = $sum($uminus(X0),X0)) )),
% 0.51/0.31 inference(superposition,[],[f22,f28])).
% 0.51/0.31 tff(f67,plain,(
% 0.51/0.31 ( ! [X0 : $int,X1 : $int] : ($less(X1,$sum(1,X0)) | $less(X0,X1)) )),
% 0.51/0.31 inference(superposition,[],[f27,f18])).
% 0.51/0.31 tff(f80,plain,(
% 0.51/0.31 ( ! [X0 : $int] : (~$less(X0,count(remove(4,sK0))) | $less(X0,6)) )),
% 0.51/0.31 inference(resolution,[],[f24,f54])).
% 0.51/0.31 tff(f87,plain,(
% 0.51/0.31 ( ! [X2 : $int,X0 : $int,X1 : $int] : (~$less(X2,X0) | X0 = X1 | $less(X1,X0) | $less(X2,X1)) )),
% 0.51/0.31 inference(resolution,[],[f25,f24])).
% 0.51/0.31 tff(f115,plain,(
% 0.51/0.31 ( ! [X0 : $int] : ($less($sum(count(remove(4,sK0)),X0),$sum(6,X0))) )),
% 0.51/0.31 inference(resolution,[],[f26,f54])).
% 0.51/0.31 tff(f129,plain,(
% 0.51/0.31 ~$less(6,$sum(count(remove(4,sK0)),1))),
% 0.51/0.31 inference(resolution,[],[f115,f29])).
% 0.51/0.31 tff(f144,plain,(
% 0.51/0.31 ~$less(6,$sum(1,count(remove(4,sK0))))),
% 0.51/0.31 inference(forward_demodulation,[],[f129,f18])).
% 0.51/0.31 tff(f154,plain,(
% 0.51/0.31 ( ! [X0 : $int,X1 : $int] : ($sum(0,X1) = $sum(X0,$sum($uminus(X0),X1))) )),
% 0.51/0.31 inference(superposition,[],[f19,f22])).
% 0.51/0.31 tff(f170,plain,(
% 0.51/0.31 ( ! [X0 : $int,X1 : $int] : ($sum(X0,$sum($uminus(X0),X1)) = X1) )),
% 0.51/0.31 inference(evaluation,[],[f154])).
% 0.51/0.31 tff(f182,plain,(
% 0.51/0.31 ( ! [X0 : $int,X1 : collection] : (~in(X0,X1) | count(remove(X0,X1)) = $sum(-1,count(X1))) )),
% 0.51/0.31 inference(forward_demodulation,[],[f59,f18])).
% 0.51/0.31 tff(f199,plain,(
% 0.51/0.31 ( ! [X0 : $int,X1 : collection] : (count(remove(X0,X1)) = $sum(-1,count(X1)) | count(X1) = count(remove(X0,X1))) )),
% 0.51/0.31 inference(resolution,[],[f182,f51])).
% 0.51/0.31 tff(f210,plain,(
% 0.51/0.31 ( ! [X0 : $int,X1 : $int] : ($sum(0,X1) = $sum($uminus(X0),$sum(X0,X1))) )),
% 0.51/0.31 inference(superposition,[],[f19,f61])).
% 0.51/0.31 tff(f219,plain,(
% 0.51/0.31 ( ! [X0 : $int,X1 : $int] : ($sum($uminus(X0),$sum(X0,X1)) = X1) )),
% 0.51/0.31 inference(evaluation,[],[f210])).
% 0.51/0.31 tff(f295,plain,(
% 0.51/0.31 ( ! [X0 : $int,X1 : $int] : ($sum(X1,$sum(X0,$uminus(X1))) = X0) )),
% 0.51/0.31 inference(superposition,[],[f170,f18])).
% 0.51/0.31 tff(f305,plain,(
% 0.51/0.31 ( ! [X0 : $int,X1 : $int] : ($less(X1,X0) | $less($sum($uminus(1),X0),X1)) )),
% 0.51/0.31 inference(superposition,[],[f67,f170])).
% 0.51/0.31 tff(f313,plain,(
% 0.51/0.31 ( ! [X0 : $int,X1 : $int] : ($less($sum(-1,X0),X1) | $less(X1,X0)) )),
% 0.51/0.31 inference(evaluation,[],[f305])).
% 0.51/0.31 tff(f469,definition,(
% 0.51/0.31 spl1_6 <=> 8 = count(sK0)),
% 0.51/0.31 introduced(definition,[new_symbols(definition,[spl1_6])],[avatar_definition])).
% 0.51/0.31 tff(f470,plain,(
% 0.51/0.31 8 = count(sK0) | ~spl1_6),
% 0.51/0.31 inference(avatar_component_clause,[],[f469])).
% 0.51/0.31 tff(f471,plain,(
% 0.51/0.31 8 != count(sK0) | spl1_6),
% 0.51/0.31 inference(avatar_component_clause,[],[f469])).
% 0.51/0.31 tff(f689,plain,(
% 0.51/0.31 ( ! [X0 : $int] : (6 = X0 | $less(X0,6) | $less(count(remove(4,sK0)),X0)) )),
% 0.51/0.31 inference(resolution,[],[f87,f54])).
% 0.51/0.31 tff(f1298,plain,(
% 0.51/0.31 ~$less($sum(-1,count(sK0)),7) | count(remove(5,sK0)) = count(sK0)),
% 0.51/0.31 inference(superposition,[],[f53,f199])).
% 0.51/0.31 tff(f1300,plain,(
% 0.51/0.31 ~$less(6,$sum(1,$sum(-1,count(sK0)))) | count(remove(4,sK0)) = count(sK0)),
% 0.51/0.31 inference(superposition,[],[f144,f199])).
% 0.51/0.31 tff(f1302,plain,(
% 0.51/0.31 ( ! [X0 : $int] : ($less($sum($sum(-1,count(sK0)),X0),$sum(6,X0)) | count(remove(4,sK0)) = count(sK0)) )),
% 0.51/0.31 inference(superposition,[],[f115,f199])).
% 0.51/0.31 tff(f1303,plain,(
% 0.51/0.31 ( ! [X0 : $int] : (~$less(X0,$sum(-1,count(sK0))) | $less(X0,6) | count(remove(4,sK0)) = count(sK0)) )),
% 0.51/0.31 inference(superposition,[],[f80,f199])).
% 0.51/0.31 tff(f1314,plain,(
% 0.51/0.31 ( ! [X0 : $int] : ($less($sum(-1,$sum(count(sK0),X0)),$sum(6,X0)) | count(remove(4,sK0)) = count(sK0)) )),
% 0.51/0.31 inference(forward_demodulation,[],[f1302,f19])).
% 0.51/0.31 tff(f1316,plain,(
% 0.51/0.31 ~$less(6,$sum(1,$sum(-1,8))) | count(remove(4,sK0)) = count(sK0) | ~spl1_6),
% 0.51/0.31 inference(forward_demodulation,[],[f1300,f470])).
% 0.51/0.31 tff(f1317,plain,(
% 0.51/0.31 count(remove(4,sK0)) = count(sK0) | ~spl1_6),
% 0.51/0.31 inference(evaluation,[],[f1316])).
% 0.51/0.31 tff(f1335,plain,(
% 0.51/0.31 count(remove(4,sK0)) = 8 | ~spl1_6),
% 0.51/0.31 inference(forward_demodulation,[],[f1317,f470])).
% 0.51/0.31 tff(f1346,definition,(
% 0.51/0.31 spl1_9 <=> count(remove(4,sK0)) = 8),
% 0.51/0.31 introduced(definition,[new_symbols(definition,[spl1_9])],[avatar_definition])).
% 0.51/0.31 tff(f1348,plain,(
% 0.51/0.31 count(remove(4,sK0)) = 8 | ~spl1_9),
% 0.51/0.31 inference(avatar_component_clause,[],[f1346])).
% 0.51/0.31 tff(f1353,plain,(
% 0.51/0.31 spl1_9 | ~spl1_6),
% 0.51/0.31 inference(avatar_split_clause,[],[f1335,f469,f1346])).
% 0.51/0.31 tff(f1385,plain,(
% 0.51/0.31 $less(8,6) | ~spl1_9),
% 0.51/0.31 inference(superposition,[],[f54,f1348])).
% 0.51/0.31 tff(f1403,plain,(
% 0.51/0.31 $false | ~spl1_9),
% 0.51/0.31 inference(evaluation,[],[f1385])).
% 0.51/0.31 tff(f1404,plain,(
% 0.51/0.31 ~spl1_9),
% 0.51/0.31 inference(avatar_contradiction_clause,[],[f1403])).
% 0.51/0.31 tff(f1411,definition,(
% 0.51/0.31 spl1_11 <=> count(remove(4,sK0)) = count(sK0)),
% 0.51/0.31 introduced(definition,[new_symbols(definition,[spl1_11])],[avatar_definition])).
% 0.51/0.31 tff(f1413,plain,(
% 0.51/0.31 count(remove(4,sK0)) = count(sK0) | ~spl1_11),
% 0.51/0.31 inference(avatar_component_clause,[],[f1411])).
% 0.51/0.31 tff(f1420,definition,(
% 0.51/0.31 spl1_13 <=> ! [X0 : $int] : (~$less(X0,$sum(-1,count(sK0))) | $less(X0,6))),
% 0.51/0.31 introduced(definition,[new_symbols(definition,[spl1_13])],[avatar_definition])).
% 0.51/0.31 tff(f1421,plain,(
% 0.51/0.31 ( ! [X0 : $int] : (~$less(X0,$sum(-1,count(sK0))) | $less(X0,6)) ) | ~spl1_13),
% 0.51/0.31 inference(avatar_component_clause,[],[f1420])).
% 0.51/0.31 tff(f1422,plain,(
% 0.51/0.31 spl1_11 | spl1_13),
% 0.51/0.31 inference(avatar_split_clause,[],[f1303,f1420,f1411])).
% 0.51/0.31 tff(f1434,definition,(
% 0.51/0.31 spl1_16 <=> count(remove(5,sK0)) = count(sK0)),
% 0.51/0.31 introduced(definition,[new_symbols(definition,[spl1_16])],[avatar_definition])).
% 0.51/0.31 tff(f1436,plain,(
% 0.51/0.31 count(remove(5,sK0)) = count(sK0) | ~spl1_16),
% 0.51/0.31 inference(avatar_component_clause,[],[f1434])).
% 0.51/0.31 tff(f1438,definition,(
% 0.51/0.31 spl1_17 <=> $less($sum(-1,count(sK0)),7)),
% 0.51/0.31 introduced(definition,[new_symbols(definition,[spl1_17])],[avatar_definition])).
% 0.51/0.31 tff(f1440,plain,(
% 0.51/0.31 ~$less($sum(-1,count(sK0)),7) | spl1_17),
% 0.51/0.31 inference(avatar_component_clause,[],[f1438])).
% 0.51/0.31 tff(f1441,plain,(
% 0.51/0.31 spl1_16 | ~spl1_17),
% 0.51/0.31 inference(avatar_split_clause,[],[f1298,f1438,f1434])).
% 0.51/0.31 tff(f1443,definition,(
% 0.51/0.31 spl1_18 <=> $less(7,$sum(-1,count(sK0)))),
% 0.51/0.31 introduced(definition,[new_symbols(definition,[spl1_18])],[avatar_definition])).
% 0.51/0.31 tff(f1444,plain,(
% 0.51/0.31 ~$less(7,$sum(-1,count(sK0))) | spl1_18),
% 0.51/0.31 inference(avatar_component_clause,[],[f1443])).
% 0.51/0.31 tff(f1445,plain,(
% 0.51/0.31 $less(7,$sum(-1,count(sK0))) | ~spl1_18),
% 0.51/0.31 inference(avatar_component_clause,[],[f1443])).
% 0.51/0.31 tff(f1453,definition,(
% 0.51/0.31 spl1_20 <=> ! [X0 : $int] : $less($sum(-1,$sum(count(sK0),X0)),$sum(6,X0))),
% 0.51/0.31 introduced(definition,[new_symbols(definition,[spl1_20])],[avatar_definition])).
% 0.51/0.31 tff(f1454,plain,(
% 0.51/0.31 ( ! [X0 : $int] : ($less($sum(-1,$sum(count(sK0),X0)),$sum(6,X0))) ) | ~spl1_20),
% 0.51/0.31 inference(avatar_component_clause,[],[f1453])).
% 0.51/0.31 tff(f1455,plain,(
% 0.51/0.31 spl1_11 | spl1_20),
% 0.51/0.31 inference(avatar_split_clause,[],[f1314,f1453,f1411])).
% 0.51/0.31 tff(f1488,definition,(
% 0.51/0.31 spl1_24 <=> 7 = $sum(-1,count(sK0))),
% 0.51/0.31 introduced(definition,[new_symbols(definition,[spl1_24])],[avatar_definition])).
% 0.51/0.31 tff(f1490,plain,(
% 0.51/0.31 7 = $sum(-1,count(sK0)) | ~spl1_24),
% 0.51/0.31 inference(avatar_component_clause,[],[f1488])).
% 0.51/0.31 tff(f1518,plain,(
% 0.51/0.31 $less(7,$sum(-1,count(sK0))) | 7 = $sum(-1,count(sK0)) | spl1_17),
% 0.51/0.31 inference(resolution,[],[f1440,f25])).
% 0.51/0.31 tff(f1573,plain,(
% 0.51/0.31 ( ! [X0 : $int] : (~$less(X0,count(sK0)) | $less(X0,6)) ) | ~spl1_11),
% 0.51/0.31 inference(superposition,[],[f80,f1413])).
% 0.51/0.31 tff(f1608,plain,(
% 0.51/0.31 ~$less(count(sK0),7) | ~spl1_16),
% 0.51/0.31 inference(superposition,[],[f53,f1436])).
% 0.51/0.31 tff(f1873,plain,(
% 0.51/0.31 ( ! [X0 : $int] : ($less(count(sK0),X0) | 6 = X0 | $less(X0,6)) ) | ~spl1_11),
% 0.51/0.31 inference(forward_demodulation,[],[f689,f1413])).
% 0.51/0.31 tff(f1874,plain,(
% 0.51/0.31 7 = 6 | $less(7,6) | (~spl1_11 | ~spl1_16)),
% 0.51/0.31 inference(resolution,[],[f1873,f1608])).
% 0.51/0.31 tff(f1890,plain,(
% 0.51/0.31 $false | (~spl1_11 | ~spl1_16)),
% 0.51/0.31 inference(evaluation,[],[f1874])).
% 0.51/0.31 tff(f1891,plain,(
% 0.51/0.31 ~spl1_11 | ~spl1_16),
% 0.51/0.31 inference(avatar_contradiction_clause,[],[f1890])).
% 0.51/0.31 tff(f2975,plain,(
% 0.51/0.31 $less(7,count(sK0)) | spl1_17),
% 0.51/0.31 inference(resolution,[],[f313,f1440])).
% 0.51/0.31 tff(f3049,plain,(
% 0.51/0.31 $less(7,6) | (~spl1_11 | spl1_17)),
% 0.51/0.31 inference(resolution,[],[f2975,f1573])).
% 0.51/0.31 tff(f3054,plain,(
% 0.51/0.31 $false | (~spl1_11 | spl1_17)),
% 0.51/0.31 inference(evaluation,[],[f3049])).
% 0.51/0.31 tff(f3055,plain,(
% 0.51/0.31 ~spl1_11 | spl1_17),
% 0.51/0.31 inference(avatar_contradiction_clause,[],[f3054])).
% 0.51/0.31 tff(f3086,plain,(
% 0.51/0.31 $less(7,6) | (~spl1_13 | ~spl1_18)),
% 0.51/0.31 inference(resolution,[],[f1421,f1445])).
% 0.51/0.31 tff(f3090,plain,(
% 0.51/0.31 $false | (~spl1_13 | ~spl1_18)),
% 0.51/0.31 inference(evaluation,[],[f3086])).
% 0.51/0.31 tff(f3091,plain,(
% 0.51/0.31 ~spl1_13 | ~spl1_18),
% 0.51/0.31 inference(avatar_contradiction_clause,[],[f3090])).
% 0.51/0.31 tff(f3299,plain,(
% 0.51/0.31 $less(count(sK0),$sum(6,$uminus(-1))) | ~spl1_20),
% 0.51/0.31 inference(superposition,[],[f1454,f295])).
% 0.51/0.31 tff(f3314,plain,(
% 0.51/0.31 $less(count(sK0),7) | ~spl1_20),
% 0.51/0.31 inference(evaluation,[],[f3299])).
% 0.51/0.31 tff(f3321,plain,(
% 0.51/0.31 $false | (~spl1_16 | ~spl1_20)),
% 0.51/0.31 inference(forward_subsumption_resolution,[],[f3314,f1608])).
% 0.51/0.31 tff(f3322,plain,(
% 0.51/0.31 ~spl1_16 | ~spl1_20),
% 0.51/0.31 inference(avatar_contradiction_clause,[],[f3321])).
% 0.51/0.31 tff(f3340,plain,(
% 0.51/0.31 7 = $sum(-1,count(sK0)) | (spl1_17 | spl1_18)),
% 0.51/0.31 inference(forward_subsumption_resolution,[],[f1518,f1444])).
% 0.51/0.31 tff(f3345,plain,(
% 0.51/0.31 spl1_24 | spl1_17 | spl1_18),
% 0.51/0.31 inference(avatar_split_clause,[],[f3340,f1443,f1438,f1488])).
% 0.51/0.31 tff(f3380,plain,(
% 0.51/0.31 count(sK0) = $sum($uminus(-1),7) | ~spl1_24),
% 0.51/0.31 inference(superposition,[],[f219,f1490])).
% 0.51/0.31 tff(f3382,plain,(
% 0.51/0.31 8 = count(sK0) | ~spl1_24),
% 0.51/0.31 inference(evaluation,[],[f3380])).
% 0.51/0.31 tff(f3386,plain,(
% 0.51/0.31 $false | (spl1_6 | ~spl1_24)),
% 0.51/0.31 inference(forward_subsumption_resolution,[],[f3382,f471])).
% 0.51/0.31 tff(f3387,plain,(
% 0.51/0.31 spl1_6 | ~spl1_24),
% 0.51/0.31 inference(avatar_contradiction_clause,[],[f3386])).
% 0.51/0.31 cnf(s13, plain, ~spl1_6 | spl1_9, inference(sat_conversion,[],[f1353])).
% 0.51/0.31 cnf(s21, plain, ~spl1_9, inference(sat_conversion,[],[f1404])).
% 0.51/0.31 cnf(s23, plain, spl1_11 | spl1_13, inference(sat_conversion,[],[f1422])).
% 0.51/0.31 cnf(s26, plain, spl1_16 | ~spl1_17, inference(sat_conversion,[],[f1441])).
% 0.51/0.31 cnf(s29, plain, spl1_11 | spl1_20, inference(sat_conversion,[],[f1455])).
% 0.51/0.31 cnf(s60, plain, ~spl1_11 | ~spl1_16, inference(sat_conversion,[],[f1891])).
% 0.51/0.31 cnf(s98, plain, ~spl1_11 | spl1_17, inference(sat_conversion,[],[f3055])).
% 0.51/0.31 cnf(s104, plain, ~spl1_13 | ~spl1_18, inference(sat_conversion,[],[f3091])).
% 0.51/0.31 cnf(s116, plain, ~spl1_16 | ~spl1_20, inference(sat_conversion,[],[f3322])).
% 0.51/0.31 cnf(s130, plain, spl1_17 | spl1_18 | spl1_24, inference(sat_conversion,[],[f3345])).
% 0.51/0.31 cnf(s140, plain, spl1_6 | ~spl1_24, inference(sat_conversion,[],[f3387])).
% 0.51/0.31 cnf(s143, plain, ~spl1_6, inference(rat,[],[s13,s21])).
% 0.51/0.31 cnf(s144, plain, ~spl1_24, inference(rat,[],[s140,s143])).
% 0.51/0.31 cnf(s146, plain, ~spl1_16, inference(rat,[],[s29,s60,s116])).
% 0.51/0.31 cnf(s149, plain, ~spl1_17, inference(rat,[],[s26,s146])).
% 0.51/0.31 cnf(s150, plain, ~spl1_11, inference(rat,[],[s98,s149])).
% 0.51/0.31 cnf(s157, plain, spl1_13, inference(rat,[],[s23,s150])).
% 0.51/0.31 cnf(s158, plain, spl1_18, inference(rat,[],[s130,s144,s149])).
% 0.51/0.31 cnf(s161, plain, $false, inference(rat,[],[s104,s158,s157])).
% 0.51/0.31 tff(f3390,plain,(
% 0.51/0.31 $false),
% 0.51/0.31 inference(avatar_sat_refutation,[],[s161])).
% 0.51/0.31 % SZS output end Proof for theBenchmark
% 0.51/0.31 % (912941)------------------------------
% 0.51/0.31 % (912941)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.31 % (912941)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.31 % (912941)CaDiCaL version: 2.1.3
% 0.51/0.31 % (912941)Termination reason: Refutation
% 0.51/0.31 % (912941)Time elapsed: 0.050 s
% 0.51/0.31 % (912941)Peak memory usage: 14 MB
% 0.51/0.31 % (912941)Instructions burned: 145 (million)
% 0.51/0.31 % (912935)Success in time 0.085 s
% 0.51/0.31 % Vampire exiting
%------------------------------------------------------------------------------