%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT046_1 : TPTP v9.3.1. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n013.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 09:48:01 AM UTC 2026
% Result : Theorem 0.19s 0.30s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT046_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.19 % Computer : n013.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 00:06:37 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
% 0.19/0.30 % (1711012)Will run a generic schedule for satisfiability detection.
% 0.19/0.30 % (1711019)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2848458012:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.30 % (1711018)% WARNING: option uhcvi not known.
% 0.19/0.30 % (1711017)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=579865647_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.30 % (1711018)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1582401285:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.30 % (1711020)dis+10_1_sil=32000:sp=arity:random_seed=1142756119:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.30 % (1711021)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=145180158:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.30 % (1711022)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3048863121:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.30 % (1711023)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1903814065:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.30 % (1711017)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.19/0.30 % (1711017)Terminated due to inappropriate strategy.
% 0.19/0.30 % (1711017)------------------------------
% 0.19/0.30 % (1711017)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.30 % (1711017)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.30 % (1711017)CaDiCaL version: 2.1.3
% 0.19/0.30 % (1711017)Termination reason: Inappropriate
% 0.19/0.30 % (1711017)Time elapsed: 0.001 s
% 0.19/0.30 % (1711017)Peak memory usage: 10 MB
% 0.19/0.30 % (1711017)Instructions burned: 1 (million)
% 0.19/0.30 % (1711017)------------------------------
% 0.19/0.30 % (1711017)------------------------------
% 0.19/0.30 % (1711031)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3227699220:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.19/0.30 % (1711031)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.19/0.30 % (1711031)Terminated due to inappropriate strategy.
% 0.19/0.30 % (1711031)------------------------------
% 0.19/0.30 % (1711031)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.30 % (1711031)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.30 % (1711031)CaDiCaL version: 2.1.3
% 0.19/0.30 % (1711031)Termination reason: Inappropriate
% 0.19/0.30 % (1711031)Time elapsed: 0.001 s
% 0.19/0.30 % (1711031)Peak memory usage: 10 MB
% 0.19/0.30 % (1711031)Instructions burned: 1 (million)
% 0.19/0.30 % (1711031)------------------------------
% 0.19/0.30 % (1711031)------------------------------
% 0.19/0.30 % (1711018) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1711012-1711018"...
% 0.19/0.30 % (1711018)...printing done.
% 0.19/0.30 % (1711018)Refutation found. Thanks to Tanya!
% 0.19/0.30 % SZS status Theorem for theBenchmark
% 0.19/0.30 % SZS output start Proof for theBenchmark
% 0.19/0.30 tff(type_def_5, type, collection: $tType).
% 0.19/0.30 tff(func_def_0, type, empty: collection).
% 0.19/0.30 tff(func_def_1, type, add: ($int * collection) > collection).
% 0.19/0.30 tff(func_def_2, type, remove: ($int * collection) > collection).
% 0.19/0.30 tff(func_def_3, type, count: collection > $int).
% 0.19/0.30 tff(pred_def_1, type, in: ($int * collection) > $o).
% 0.19/0.30 tff(f1,axiom,(
% 0.19/0.30 ! [X0 : $int] : ~in(X0,empty)),
% 0.19/0.30 file('/export/starexec/sandbox2/benchmark/Axioms/DAT002_0.ax',ax1)).
% 0.19/0.30 tff(f4,axiom,(
% 0.19/0.30 ! [X0 : $int,X1 : collection,X2 : $int] : ((in(X0,X1) | X0 = X2) <=> in(X0,add(X2,X1)))),
% 0.19/0.30 file('/export/starexec/sandbox2/benchmark/Axioms/DAT002_0.ax',ax4)).
% 0.19/0.30 tff(f7,axiom,(
% 0.19/0.30 ! [X0 : collection] : (X0 = empty <=> count(X0) = 0)),
% 0.19/0.30 file('/export/starexec/sandbox2/benchmark/Axioms/DAT002=1.ax',ax2)).
% 0.19/0.30 tff(f8,axiom,(
% 0.19/0.30 ! [X0 : $int,X1 : collection] : (~in(X0,X1) <=> count(add(X0,X1)) = $sum(count(X1),1))),
% 0.19/0.30 file('/export/starexec/sandbox2/benchmark/Axioms/DAT002=1.ax',ax3)).
% 0.19/0.30 tff(f9,axiom,(
% 0.19/0.30 ! [X0 : $int,X1 : collection] : (in(X0,X1) <=> count(add(X0,X1)) = count(X1))),
% 0.19/0.30 file('/export/starexec/sandbox2/benchmark/Axioms/DAT002=1.ax',ax4)).
% 0.19/0.30 tff(f13,conjecture,(
% 0.19/0.30 count(add(1,add(3,empty))) = 2),
% 0.19/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1)).
% 0.19/0.30 tff(f14,negated_conjecture,(
% 0.19/0.30 ~ count(add(1,add(3,empty))) = 2),
% 0.19/0.30 inference(negated_conjecture,[status(cth)],[f13])).
% 0.19/0.30 tff(f17,definition,(
% 0.19/0.30 ( ! [X0 : $int,X1 : $int] : ($sum(X0,X1) = $sum(X1,X0)) )),
% 0.19/0.30 introduced(theory,[tha_commutativity])).
% 0.19/0.30 tff(f29,plain,(
% 0.19/0.30 count(add(1,add(3,empty))) != 2),
% 0.19/0.30 inference(flattening,[],[f14])).
% 0.19/0.30 tff(f31,plain,(
% 0.19/0.30 ( ! [X0 : $int] : (~in(X0,empty)) )),
% 0.19/0.30 inference(cnf_transformation,[],[f1])).
% 0.19/0.30 tff(f36,plain,(
% 0.19/0.30 ( ! [X2 : $int,X0 : $int,X1 : collection] : (~in(X0,add(X2,X1)) | X0 = X2 | in(X0,X1)) )),
% 0.19/0.30 inference(cnf_transformation,[],[f4])).
% 0.19/0.30 tff(f42,plain,(
% 0.19/0.30 ( ! [X0 : collection] : (count(X0) = 0 | empty != X0) )),
% 0.19/0.30 inference(cnf_transformation,[],[f7])).
% 0.19/0.30 tff(f44,plain,(
% 0.19/0.30 ( ! [X0 : $int,X1 : collection] : (count(add(X0,X1)) = $sum(count(X1),1) | in(X0,X1)) )),
% 0.19/0.30 inference(cnf_transformation,[],[f8])).
% 0.19/0.30 tff(f45,plain,(
% 0.19/0.30 ( ! [X0 : $int,X1 : collection] : (count(add(X0,X1)) != count(X1) | in(X0,X1)) )),
% 0.19/0.30 inference(cnf_transformation,[],[f9])).
% 0.19/0.30 tff(f46,plain,(
% 0.19/0.30 ( ! [X0 : $int,X1 : collection] : (count(add(X0,X1)) = count(X1) | ~in(X0,X1)) )),
% 0.19/0.30 inference(cnf_transformation,[],[f9])).
% 0.19/0.30 tff(f52,plain,(
% 0.19/0.30 count(add(1,add(3,empty))) != 2),
% 0.19/0.30 inference(cnf_transformation,[],[f29])).
% 0.19/0.30 tff(f55,plain,(
% 0.19/0.30 0 = count(empty)),
% 0.19/0.30 inference(equality_resolution,[],[f42])).
% 0.19/0.30 tff(f56,plain,(
% 0.19/0.30 ( ! [X0 : $int] : (in(X0,empty)) )),
% 0.19/0.30 inference(consistent_polarity_flipping,[],[f31])).
% 0.19/0.30 tff(f59,plain,(
% 0.19/0.30 ( ! [X2 : $int,X0 : $int,X1 : collection] : (in(X0,add(X2,X1)) | X0 = X2 | ~in(X0,X1)) )),
% 0.19/0.30 inference(consistent_polarity_flipping,[],[f36])).
% 0.19/0.30 tff(f65,plain,(
% 0.19/0.30 ( ! [X0 : $int,X1 : collection] : (count(add(X0,X1)) = $sum(count(X1),1) | ~in(X0,X1)) )),
% 0.19/0.30 inference(consistent_polarity_flipping,[],[f44])).
% 0.19/0.30 tff(f67,plain,(
% 0.19/0.30 ( ! [X0 : $int,X1 : collection] : (in(X0,X1) | count(add(X0,X1)) = count(X1)) )),
% 0.19/0.30 inference(consistent_polarity_flipping,[],[f46])).
% 0.19/0.30 tff(f68,plain,(
% 0.19/0.30 ( ! [X0 : $int,X1 : collection] : (count(add(X0,X1)) != count(X1) | ~in(X0,X1)) )),
% 0.19/0.30 inference(consistent_polarity_flipping,[],[f45])).
% 0.19/0.30 tff(f203,plain,(
% 0.19/0.30 ( ! [X0 : $int,X1 : collection] : (~in(X0,X1) | count(add(X0,X1)) = $sum(1,count(X1))) )),
% 0.19/0.30 inference(forward_demodulation,[],[f65,f17])).
% 0.19/0.30 tff(f227,plain,(
% 0.19/0.30 ( ! [X0 : $int,X1 : collection] : (count(add(X0,X1)) = $sum(1,count(X1)) | count(add(X0,X1)) = count(X1)) )),
% 0.19/0.30 inference(resolution,[],[f203,f67])).
% 0.19/0.30 tff(f228,plain,(
% 0.19/0.30 ( ! [X0 : $int] : (count(add(X0,empty)) = $sum(1,count(empty))) )),
% 0.19/0.30 inference(resolution,[],[f203,f56])).
% 0.19/0.30 tff(f232,plain,(
% 0.19/0.30 ( ! [X0 : $int] : ($sum(1,0) = count(add(X0,empty))) )),
% 0.19/0.30 inference(forward_demodulation,[],[f228,f55])).
% 0.19/0.30 tff(f233,plain,(
% 0.19/0.30 ( ! [X0 : $int] : (1 = count(add(X0,empty))) )),
% 0.19/0.30 inference(evaluation,[],[f232])).
% 0.19/0.30 tff(f1141,plain,(
% 0.19/0.30 2 != $sum(1,count(add(3,empty))) | count(add(1,add(3,empty))) = count(add(3,empty))),
% 0.19/0.30 inference(superposition,[],[f52,f227])).
% 0.19/0.30 tff(f1157,plain,(
% 0.19/0.30 2 != $sum(1,1) | count(add(1,add(3,empty))) = count(add(3,empty))),
% 0.19/0.30 inference(forward_demodulation,[],[f1141,f233])).
% 0.19/0.30 tff(f1158,plain,(
% 0.19/0.30 count(add(1,add(3,empty))) = count(add(3,empty))),
% 0.19/0.30 inference(evaluation,[],[f1157])).
% 0.19/0.30 tff(f1161,plain,(
% 0.19/0.30 1 = count(add(1,add(3,empty)))),
% 0.19/0.30 inference(forward_demodulation,[],[f1158,f233])).
% 0.19/0.30 tff(f1214,plain,(
% 0.19/0.30 1 != count(add(3,empty)) | ~in(1,add(3,empty))),
% 0.19/0.30 inference(superposition,[],[f68,f1161])).
% 0.19/0.30 tff(f1221,plain,(
% 0.19/0.30 ~in(1,add(3,empty))),
% 0.19/0.30 inference(forward_subsumption_resolution,[],[f1214,f233])).
% 0.19/0.30 tff(f1242,plain,(
% 0.19/0.30 1 = 3 | ~in(1,empty)),
% 0.19/0.30 inference(resolution,[],[f1221,f59])).
% 0.19/0.30 tff(f1251,plain,(
% 0.19/0.30 ~in(1,empty)),
% 0.19/0.30 inference(evaluation,[],[f1242])).
% 0.19/0.30 tff(f1255,plain,(
% 0.19/0.30 $false),
% 0.19/0.30 inference(forward_subsumption_resolution,[],[f1251,f56])).
% 0.19/0.30 % SZS output end Proof for theBenchmark
% 0.19/0.30 % (1711018)------------------------------
% 0.19/0.30 % (1711018)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.30 % (1711018)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.30 % (1711018)CaDiCaL version: 2.1.3
% 0.19/0.30 % (1711018)Termination reason: Refutation
% 0.19/0.30 % (1711018)Time elapsed: 0.034 s
% 0.19/0.30 % (1711018)Peak memory usage: 12 MB
% 0.19/0.30 % (1711018)Instructions burned: 53 (million)
% 0.19/0.30 % (1711012)Success in time 0.071 s
% 0.19/0.30 % Vampire exiting
%------------------------------------------------------------------------------