%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT040_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 : n014.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 09:48:00 AM UTC 2026
% Result : Theorem 2.86s 0.62s
% Output : Refutation 2.86s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : DAT040_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.16 % Computer : n014.cluster.edu
% 0.11/0.16 % Model : x86_64 x86_64
% 0.11/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.16 % Memory : 8046.5625MB
% 0.11/0.16 % OS : Linux 6.8.0-71-generic
% 0.11/0.16 % CPULimit : 300
% 0.11/0.16 % WCLimit : 300
% 0.11/0.16 % DateTime : Tue Sep 29 00:06:01 UTC 2026
% 0.11/0.17 % CPUTime :
% 0.11/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.19 Running first-order model finding
% 0.11/0.19 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
% 2.86/0.62 % (2302366)Will run a generic schedule for satisfiability detection.
% 2.86/0.62 % (2302373)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1275846193:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 2.86/0.62 % (2302372)% WARNING: option uhcvi not known.
% 2.86/0.62 % (2302371)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2393377059_2999 on theBenchmark for (2999ds/0Mi)
% 2.86/0.62 % (2302372)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3023981321:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 2.86/0.62 % (2302374)dis+10_1_sil=32000:sp=arity:random_seed=45003256:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 2.86/0.62 % (2302377)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=64051755:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 2.86/0.62 % (2302375)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2079068536:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 2.86/0.62 % (2302376)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1984687307:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 2.86/0.62 % (2302371)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 2.86/0.62 % (2302371)Terminated due to inappropriate strategy.
% 2.86/0.62 % (2302371)------------------------------
% 2.86/0.62 % (2302371)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.86/0.62 % (2302371)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.86/0.62 % (2302371)CaDiCaL version: 2.1.3
% 2.86/0.62 % (2302371)Termination reason: Inappropriate
% 2.86/0.62 % (2302371)Time elapsed: 0.001 s
% 2.86/0.62 % (2302371)Peak memory usage: 10 MB
% 2.86/0.62 % (2302371)Instructions burned: 1 (million)
% 2.86/0.62 % (2302371)------------------------------
% 2.86/0.62 % (2302371)------------------------------
% 2.86/0.62 % (2302385)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3073743499:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 2.86/0.62 % (2302385)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 2.86/0.62 % (2302385)Terminated due to inappropriate strategy.
% 2.86/0.62 % (2302385)------------------------------
% 2.86/0.62 % (2302385)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.86/0.62 % (2302385)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.86/0.62 % (2302385)CaDiCaL version: 2.1.3
% 2.86/0.62 % (2302385)Termination reason: Inappropriate
% 2.86/0.62 % (2302385)Time elapsed: 0.001 s
% 2.86/0.62 % (2302385)Peak memory usage: 10 MB
% 2.86/0.62 % (2302385)Instructions burned: 1 (million)
% 2.86/0.62 % (2302385)------------------------------
% 2.86/0.62 % (2302385)------------------------------
% 2.86/0.62 % (2302387)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=910298394:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 2.86/0.62 % (2302374)Instruction limit reached!
% 2.86/0.62 % (2302374)------------------------------
% 2.86/0.62 % (2302374)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.86/0.62 % (2302374)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.86/0.62 % (2302374)CaDiCaL version: 2.1.3
% 2.86/0.62 % (2302374)Termination reason: Instruction limit
% 2.86/0.62 % (2302374)Termination phase: Saturation
% 2.86/0.62 % (2302374)Time elapsed: 0.064 s
% 2.86/0.62 % (2302374)Peak memory usage: 12 MB
% 2.86/0.62 % (2302374)Instructions burned: 103 (million)
% 2.86/0.62 % (2302375)Instruction limit reached!
% 2.86/0.62 % (2302375)------------------------------
% 2.86/0.62 % (2302375)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.86/0.62 % (2302375)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.86/0.62 % (2302375)CaDiCaL version: 2.1.3
% 2.86/0.62 % (2302375)Termination reason: Instruction limit
% 2.86/0.62 % (2302375)Termination phase: Saturation
% 2.86/0.62 % (2302375)Time elapsed: 0.070 s
% 2.86/0.62 % (2302375)Peak memory usage: 12 MB
% 2.86/0.62 % (2302375)Instructions burned: 116 (million)
% 2.86/0.62 % (2302389)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=1505178181:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 2.86/0.62 % (2302376)Instruction limit reached!
% 2.86/0.62 % (2302376)------------------------------
% 2.86/0.62 % (2302376)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.86/0.62 % (2302376)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.86/0.62 % (2302376)CaDiCaL version: 2.1.3
% 2.86/0.62 % (2302376)Termination reason: Instruction limit
% 2.86/0.62 % (2302376)Termination phase: Saturation
% 2.86/0.62 % (2302376)Time elapsed: 0.086 s
% 2.86/0.62 % (2302376)Peak memory usage: 13 MB
% 2.86/0.62 % (2302376)Instructions burned: 132 (million)
% 2.86/0.62 % (2302390)ott-21_1_sil=16000:fs=off:random_seed=2083377532:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 2.86/0.62 % (2302392)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1699849853:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 2.86/0.62 % (2302377)Instruction limit reached!
% 2.86/0.62 % (2302377)------------------------------
% 2.86/0.62 % (2302377)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.86/0.62 % (2302377)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.86/0.62 % (2302377)CaDiCaL version: 2.1.3
% 2.86/0.62 % (2302377)Termination reason: Instruction limit
% 2.86/0.62 % (2302377)Termination phase: Saturation
% 2.86/0.62 % (2302377)Time elapsed: 0.110 s
% 2.86/0.62 % (2302377)Peak memory usage: 13 MB
% 2.86/0.62 % (2302377)Instructions burned: 160 (million)
% 2.86/0.62 % (2302395)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=4238864259:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 2.86/0.62 % (2302387)Instruction limit reached!
% 2.86/0.62 % (2302387)------------------------------
% 2.86/0.62 % (2302387)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.86/0.62 % (2302387)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.86/0.62 % (2302387)CaDiCaL version: 2.1.3
% 2.86/0.62 % (2302387)Termination reason: Instruction limit
% 2.86/0.62 % (2302387)Termination phase: Saturation
% 2.86/0.62 % (2302387)Time elapsed: 0.088 s
% 2.86/0.62 % (2302387)Peak memory usage: 13 MB
% 2.86/0.62 % (2302387)Instructions burned: 132 (million)
% 2.86/0.62 % (2302395)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 2.86/0.62 % (2302395)Terminated due to inappropriate strategy.
% 2.86/0.62 % (2302395)------------------------------
% 2.86/0.62 % (2302395)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.86/0.62 % (2302395)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.86/0.62 % (2302395)CaDiCaL version: 2.1.3
% 2.86/0.62 % (2302395)Termination reason: Inappropriate
% 2.86/0.62 % (2302395)Time elapsed: 0.001 s
% 2.86/0.62 % (2302395)Peak memory usage: 10 MB
% 2.86/0.62 % (2302395)------------------------------
% 2.86/0.62 % (2302395)------------------------------
% 2.86/0.62 % (2302397)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=141076699:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 2.86/0.62 % (2302398)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=2380718137:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 2.86/0.62 % (2302398)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 2.86/0.62 % (2302398)Terminated due to inappropriate strategy.
% 2.86/0.62 % (2302398)------------------------------
% 2.86/0.62 % (2302398)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.86/0.62 % (2302398)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.86/0.62 % (2302398)CaDiCaL version: 2.1.3
% 2.86/0.62 % (2302398)Termination reason: Inappropriate
% 2.86/0.62 % (2302398)Time elapsed: 0.001 s
% 2.86/0.62 % (2302398)Peak memory usage: 10 MB
% 2.86/0.62 % (2302398)Instructions burned: 1 (million)
% 2.86/0.62 % (2302398)------------------------------
% 2.86/0.62 % (2302398)------------------------------
% 2.86/0.62 % (2302401)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=2108512803:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2998 on theBenchmark for (2998ds/692Mi)
% 2.86/0.62 % (2302390)Instruction limit reached!
% 2.86/0.62 % (2302390)------------------------------
% 2.86/0.62 % (2302390)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.86/0.62 % (2302390)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.86/0.62 % (2302390)CaDiCaL version: 2.1.3
% 2.86/0.62 % (2302390)Termination reason: Instruction limit
% 2.86/0.62 % (2302390)Termination phase: Saturation
% 2.86/0.62 % (2302390)Time elapsed: 0.084 s
% 2.86/0.62 % (2302390)Peak memory usage: 12 MB
% 2.86/0.62 % (2302390)Instructions burned: 180 (million)
% 2.86/0.62 % (2302403)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=1346819200:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 2.86/0.62 % (2302392) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2302366-2302392"...
% 2.86/0.62 % (2302392)...printing done.
% 2.86/0.62 % (2302392)Refutation found. Thanks to Tanya!
% 2.86/0.62 % SZS status Theorem for theBenchmark
% 2.86/0.62 % SZS output start Proof for theBenchmark
% 2.86/0.62 tff(type_def_5, type, collection: $tType).
% 2.86/0.62 tff(func_def_0, type, empty: collection).
% 2.86/0.62 tff(func_def_1, type, add: ($int * collection) > collection).
% 2.86/0.62 tff(func_def_2, type, remove: ($int * collection) > collection).
% 2.86/0.62 tff(func_def_3, type, count: collection > $int).
% 2.86/0.62 tff(func_def_13, type, sK0: collection).
% 2.86/0.62 tff(func_def_14, type, sK1: $int).
% 2.86/0.62 tff(func_def_15, type, sK2: $int).
% 2.86/0.62 tff(pred_def_1, type, in: ($int * collection) > $o).
% 2.86/0.62 tff(f1,axiom,(
% 2.86/0.62 ! [X0 : $int] : ~in(X0,empty)),
% 2.86/0.62 file('/export/starexec/sandbox/benchmark/Axioms/DAT002_0.ax',ax1)).
% 2.86/0.62 tff(f4,axiom,(
% 2.86/0.62 ! [X0 : $int,X1 : collection,X2 : $int] : ((in(X0,X1) | X0 = X2) <=> in(X0,add(X2,X1)))),
% 2.86/0.62 file('/export/starexec/sandbox/benchmark/Axioms/DAT002_0.ax',ax4)).
% 2.86/0.62 tff(f5,axiom,(
% 2.86/0.62 ! [X0 : $int,X1 : collection,X2 : $int] : ((in(X0,X1) & X0 != X2) <=> in(X0,remove(X2,X1)))),
% 2.86/0.62 file('/export/starexec/sandbox/benchmark/Axioms/DAT002_0.ax',ax5)).
% 2.86/0.62 tff(f7,axiom,(
% 2.86/0.62 ! [X0 : collection] : (X0 = empty <=> count(X0) = 0)),
% 2.86/0.62 file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax',ax2)).
% 2.86/0.62 tff(f9,axiom,(
% 2.86/0.62 ! [X0 : $int,X1 : collection] : (in(X0,X1) <=> count(add(X0,X1)) = count(X1))),
% 2.86/0.62 file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax',ax4)).
% 2.86/0.62 tff(f10,axiom,(
% 2.86/0.62 ! [X0 : $int,X1 : collection] : (in(X0,X1) <=> count(remove(X0,X1)) = $difference(count(X1),1))),
% 2.86/0.62 file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax',ax5)).
% 2.86/0.62 tff(f12,axiom,(
% 2.86/0.62 ! [X0 : $int,X1 : collection] : (in(X0,X1) => X1 = add(X0,remove(X0,X1)))),
% 2.86/0.62 file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax',ax7)).
% 2.86/0.62 tff(f13,conjecture,(
% 2.86/0.62 ! [X0 : collection,X1 : $int,X2 : $int] : (($less(X1,3) & $less(6,X2) & in(X1,X0) & in(X2,X0) & count(X0) = 2) => ~in(5,X0))),
% 2.86/0.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1)).
% 2.86/0.62 tff(f14,negated_conjecture,(
% 2.86/0.62 ~ ! [X0 : collection,X1 : $int,X2 : $int] : (($less(X1,3) & $less(6,X2) & in(X1,X0) & in(X2,X0) & count(X0) = 2) => ~in(5,X0))),
% 2.86/0.62 inference(negated_conjecture,[status(cth)],[f13])).
% 2.86/0.62 tff(f16,plain,(
% 2.86/0.62 ! [X0 : $int,X1 : collection] : (in(X0,X1) <=> count(remove(X0,X1)) = $sum(count(X1),$uminus(1)))),
% 2.86/0.62 inference(theory_normalization,[],[f10])).
% 2.86/0.62 tff(f17,definition,(
% 2.86/0.62 ( ! [X0 : $int,X1 : $int] : ($sum(X0,X1) = $sum(X1,X0)) )),
% 2.86/0.62 introduced(theory,[tha_commutativity])).
% 2.86/0.62 tff(f22,definition,(
% 2.86/0.62 ( ! [X0 : $int] : (~$less(X0,X0)) )),
% 2.86/0.62 introduced(theory,[tha_non-reflexivity])).
% 2.86/0.62 tff(f23,definition,(
% 2.86/0.62 ( ! [X2 : $int,X0 : $int,X1 : $int] : (~$less(X1,X2) | ~$less(X0,X1) | $less(X0,X2)) )),
% 2.86/0.62 introduced(theory,[tha_transitivity])).
% 2.86/0.62 tff(f24,definition,(
% 2.86/0.62 ( ! [X0 : $int,X1 : $int] : ($less(X1,X0) | $less(X0,X1) | X0 = X1) )),
% 2.86/0.62 introduced(theory,[tha_order_totality])).
% 2.86/0.62 tff(f29,plain,(
% 2.86/0.62 ! [X0 : $int,X1 : collection] : (X1 = add(X0,remove(X0,X1)) | ~in(X0,X1))),
% 2.86/0.62 inference(ennf_transformation,[],[f12])).
% 2.86/0.62 tff(f30,plain,(
% 2.86/0.62 ? [X0 : collection,X1 : $int,X2 : $int] : (in(5,X0) & ($less(X1,3) & $less(6,X2) & in(X1,X0) & in(X2,X0) & count(X0) = 2))),
% 2.86/0.62 inference(ennf_transformation,[],[f14])).
% 2.86/0.62 tff(f31,plain,(
% 2.86/0.62 ? [X0 : collection,X1 : $int,X2 : $int] : (in(5,X0) & $less(X1,3) & $less(6,X2) & in(X1,X0) & in(X2,X0) & count(X0) = 2)),
% 2.86/0.62 inference(flattening,[],[f30])).
% 2.86/0.62 tff(f32,plain,(
% 2.86/0.62 ! [X0 : $int,X1 : collection,X2 : $int] : (((in(X0,X1) | X0 = X2) | ~in(X0,add(X2,X1))) & (in(X0,add(X2,X1)) | (~in(X0,X1) & X0 != X2)))),
% 2.86/0.62 inference(nnf_transformation,[],[f4])).
% 2.86/0.62 tff(f33,plain,(
% 2.86/0.62 ! [X0 : $int,X1 : collection,X2 : $int] : ((in(X0,X1) | X0 = X2 | ~in(X0,add(X2,X1))) & (in(X0,add(X2,X1)) | (~in(X0,X1) & X0 != X2)))),
% 2.86/0.62 inference(flattening,[],[f32])).
% 2.86/0.62 tff(f34,plain,(
% 2.86/0.62 ! [X0 : $int,X1 : collection,X2 : $int] : (((in(X0,X1) & X0 != X2) | ~in(X0,remove(X2,X1))) & (in(X0,remove(X2,X1)) | (~in(X0,X1) | X0 = X2)))),
% 2.86/0.62 inference(nnf_transformation,[],[f5])).
% 2.86/0.62 tff(f35,plain,(
% 2.86/0.62 ! [X0 : $int,X1 : collection,X2 : $int] : (((in(X0,X1) & X0 != X2) | ~in(X0,remove(X2,X1))) & (in(X0,remove(X2,X1)) | ~in(X0,X1) | X0 = X2))),
% 2.86/0.62 inference(flattening,[],[f34])).
% 2.86/0.62 tff(f36,plain,(
% 2.86/0.62 ! [X0 : collection] : ((X0 = empty | count(X0) != 0) & (count(X0) = 0 | empty != X0))),
% 2.86/0.62 inference(nnf_transformation,[],[f7])).
% 2.86/0.62 tff(f38,plain,(
% 2.86/0.62 ! [X0 : $int,X1 : collection] : ((in(X0,X1) | count(add(X0,X1)) != count(X1)) & (count(add(X0,X1)) = count(X1) | ~in(X0,X1)))),
% 2.86/0.62 inference(nnf_transformation,[],[f9])).
% 2.86/0.62 tff(f39,plain,(
% 2.86/0.62 ! [X0 : $int,X1 : collection] : ((in(X0,X1) | count(remove(X0,X1)) != $sum(count(X1),$uminus(1))) & (count(remove(X0,X1)) = $sum(count(X1),$uminus(1)) | ~in(X0,X1)))),
% 2.86/0.62 inference(nnf_transformation,[],[f16])).
% 2.86/0.62 tff(f41,plain,(
% 2.86/0.62 in(5,sK0) & $less(sK1,3) & $less(6,sK2) & in(sK1,sK0) & in(sK2,sK0) & 2 = count(sK0)),
% 2.86/0.62 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f31])).
% 2.86/0.62 tff(f42,plain,(
% 2.86/0.62 ( ! [X0 : $int] : (~in(X0,empty)) )),
% 2.86/0.62 inference(cnf_transformation,[],[f1])).
% 2.86/0.62 tff(f47,plain,(
% 2.86/0.62 ( ! [X2 : $int,X0 : $int,X1 : collection] : (~in(X0,add(X2,X1)) | X0 = X2 | in(X0,X1)) )),
% 2.86/0.62 inference(cnf_transformation,[],[f33])).
% 2.86/0.62 tff(f48,plain,(
% 2.86/0.62 ( ! [X2 : $int,X0 : $int,X1 : collection] : (in(X0,remove(X2,X1)) | ~in(X0,X1) | X0 = X2) )),
% 2.86/0.62 inference(cnf_transformation,[],[f35])).
% 2.86/0.62 tff(f53,plain,(
% 2.86/0.62 ( ! [X0 : collection] : (count(X0) != 0 | empty = X0) )),
% 2.86/0.62 inference(cnf_transformation,[],[f36])).
% 2.86/0.62 tff(f56,plain,(
% 2.86/0.62 ( ! [X0 : $int,X1 : collection] : (~in(X0,X1) | count(add(X0,X1)) = count(X1)) )),
% 2.86/0.62 inference(cnf_transformation,[],[f38])).
% 2.86/0.62 tff(f57,plain,(
% 2.86/0.62 ( ! [X0 : $int,X1 : collection] : (count(add(X0,X1)) != count(X1) | in(X0,X1)) )),
% 2.86/0.62 inference(cnf_transformation,[],[f38])).
% 2.86/0.62 tff(f58,plain,(
% 2.86/0.62 ( ! [X0 : $int,X1 : collection] : (count(remove(X0,X1)) = $sum(count(X1),$uminus(1)) | ~in(X0,X1)) )),
% 2.86/0.62 inference(cnf_transformation,[],[f39])).
% 2.86/0.62 tff(f62,plain,(
% 2.86/0.62 ( ! [X0 : $int,X1 : collection] : (~in(X0,X1) | add(X0,remove(X0,X1)) = X1) )),
% 2.86/0.62 inference(cnf_transformation,[],[f29])).
% 2.86/0.62 tff(f63,plain,(
% 2.86/0.62 2 = count(sK0)),
% 2.86/0.62 inference(cnf_transformation,[],[f41])).
% 2.86/0.62 tff(f64,plain,(
% 2.86/0.62 in(sK2,sK0)),
% 2.86/0.62 inference(cnf_transformation,[],[f41])).
% 2.86/0.62 tff(f65,plain,(
% 2.86/0.62 in(sK1,sK0)),
% 2.86/0.62 inference(cnf_transformation,[],[f41])).
% 2.86/0.62 tff(f66,plain,(
% 2.86/0.62 $less(6,sK2)),
% 2.86/0.62 inference(cnf_transformation,[],[f41])).
% 2.86/0.62 tff(f67,plain,(
% 2.86/0.62 $less(sK1,3)),
% 2.86/0.62 inference(cnf_transformation,[],[f41])).
% 2.86/0.62 tff(f68,plain,(
% 2.86/0.62 in(5,sK0)),
% 2.86/0.62 inference(cnf_transformation,[],[f41])).
% 2.86/0.62 tff(f72,plain,(
% 2.86/0.62 ( ! [X0 : $int,X1 : collection] : (count(remove(X0,X1)) = $sum(count(X1),-1) | ~in(X0,X1)) )),
% 2.86/0.62 inference(evaluation,[],[f58])).
% 2.86/0.62 tff(f212,plain,(
% 2.86/0.62 ( ! [X0 : $int] : (~$less(X0,6) | $less(X0,sK2)) )),
% 2.86/0.62 inference(resolution,[],[f23,f66])).
% 2.86/0.62 tff(f213,plain,(
% 2.86/0.62 ( ! [X0 : $int] : (~$less(X0,sK1) | $less(X0,3)) )),
% 2.86/0.62 inference(resolution,[],[f23,f67])).
% 2.86/0.62 tff(f239,plain,(
% 2.86/0.62 ( ! [X0 : $int] : ($less(sK1,X0) | $less(X0,3) | sK1 = X0) )),
% 2.86/0.62 inference(resolution,[],[f24,f213])).
% 2.86/0.62 tff(f463,plain,(
% 2.86/0.62 $less(6,3) | 6 = sK1 | $less(sK1,sK2)),
% 2.86/0.62 inference(resolution,[],[f239,f212])).
% 2.86/0.62 tff(f467,plain,(
% 2.86/0.62 6 = sK1 | $less(sK1,sK2)),
% 2.86/0.62 inference(evaluation,[],[f463])).
% 2.86/0.62 tff(f469,definition,(
% 2.86/0.62 spl3_20 <=> $less(sK1,sK2)),
% 2.86/0.62 introduced(definition,[new_symbols(definition,[spl3_20])],[avatar_definition])).
% 2.86/0.62 tff(f471,plain,(
% 2.86/0.62 $less(sK1,sK2) | ~spl3_20),
% 2.86/0.62 inference(avatar_component_clause,[],[f469])).
% 2.86/0.62 tff(f473,definition,(
% 2.86/0.62 spl3_21 <=> 6 = sK1),
% 2.86/0.62 introduced(definition,[new_symbols(definition,[spl3_21])],[avatar_definition])).
% 2.86/0.62 tff(f475,plain,(
% 2.86/0.62 6 = sK1 | ~spl3_21),
% 2.86/0.62 inference(avatar_component_clause,[],[f473])).
% 2.86/0.62 tff(f476,plain,(
% 2.86/0.62 spl3_20 | spl3_21),
% 2.86/0.62 inference(avatar_split_clause,[],[f467,f473,f469])).
% 2.86/0.62 tff(f516,plain,(
% 2.86/0.62 $less(6,3) | ~spl3_21),
% 2.86/0.62 inference(backward_demodulation,[],[f67,f475])).
% 2.86/0.62 tff(f522,plain,(
% 2.86/0.62 $false | ~spl3_21),
% 2.86/0.62 inference(evaluation,[],[f516])).
% 2.86/0.62 tff(f523,plain,(
% 2.86/0.62 ~spl3_21),
% 2.86/0.62 inference(avatar_contradiction_clause,[],[f522])).
% 2.86/0.62 tff(f2974,plain,(
% 2.86/0.62 sK0 = add(5,remove(5,sK0))),
% 2.86/0.62 inference(resolution,[],[f62,f68])).
% 2.86/0.62 tff(f3121,plain,(
% 2.86/0.62 ( ! [X0 : $int,X1 : collection] : (~in(X0,X1) | count(remove(X0,X1)) = $sum(-1,count(X1))) )),
% 2.86/0.62 inference(forward_demodulation,[],[f72,f17])).
% 2.86/0.62 tff(f3850,plain,(
% 2.86/0.62 count(remove(5,sK0)) = $sum(-1,count(sK0))),
% 2.86/0.62 inference(resolution,[],[f3121,f68])).
% 2.86/0.62 tff(f3862,plain,(
% 2.86/0.62 count(remove(5,sK0)) = $sum(-1,2)),
% 2.86/0.62 inference(forward_demodulation,[],[f3850,f63])).
% 2.86/0.62 tff(f3863,plain,(
% 2.86/0.62 1 = count(remove(5,sK0))),
% 2.86/0.62 inference(evaluation,[],[f3862])).
% 2.86/0.62 tff(f5748,plain,(
% 2.86/0.62 ( ! [X0 : $int] : (in(X0,remove(5,sK0)) | 5 = X0 | ~in(X0,sK0)) )),
% 2.86/0.62 inference(superposition,[],[f47,f2974])).
% 2.86/0.62 tff(f5994,plain,(
% 2.86/0.62 ( ! [X0 : $int] : (5 = X0 | ~in(X0,sK0) | count(remove(5,sK0)) = count(add(X0,remove(5,sK0)))) )),
% 2.86/0.62 inference(resolution,[],[f5748,f56])).
% 2.86/0.62 tff(f5996,plain,(
% 2.86/0.62 ( ! [X0 : $int] : (~in(X0,sK0) | 5 = X0 | 1 = count(add(X0,remove(5,sK0)))) )),
% 2.86/0.62 inference(forward_demodulation,[],[f5994,f3863])).
% 2.86/0.62 tff(f10005,plain,(
% 2.86/0.62 5 = sK2 | 1 = count(add(sK2,remove(5,sK0)))),
% 2.86/0.62 inference(resolution,[],[f5996,f64])).
% 2.86/0.62 tff(f10060,definition,(
% 2.86/0.62 spl3_104 <=> 5 = sK2),
% 2.86/0.62 introduced(definition,[new_symbols(definition,[spl3_104])],[avatar_definition])).
% 2.86/0.62 tff(f10062,plain,(
% 2.86/0.62 5 = sK2 | ~spl3_104),
% 2.86/0.62 inference(avatar_component_clause,[],[f10060])).
% 2.86/0.62 tff(f10189,definition,(
% 2.86/0.62 spl3_106 <=> 1 = count(add(sK2,remove(5,sK0)))),
% 2.86/0.62 introduced(definition,[new_symbols(definition,[spl3_106])],[avatar_definition])).
% 2.86/0.62 tff(f10191,plain,(
% 2.86/0.62 1 = count(add(sK2,remove(5,sK0))) | ~spl3_106),
% 2.86/0.62 inference(avatar_component_clause,[],[f10189])).
% 2.86/0.62 tff(f10192,plain,(
% 2.86/0.62 spl3_106 | spl3_104),
% 2.86/0.62 inference(avatar_split_clause,[],[f10005,f10060,f10189])).
% 2.86/0.62 tff(f10250,plain,(
% 2.86/0.62 $less(6,5) | ~spl3_104),
% 2.86/0.62 inference(backward_demodulation,[],[f66,f10062])).
% 2.86/0.62 tff(f10277,plain,(
% 2.86/0.62 $false | ~spl3_104),
% 2.86/0.62 inference(evaluation,[],[f10250])).
% 2.86/0.62 tff(f10278,plain,(
% 2.86/0.62 ~spl3_104),
% 2.86/0.62 inference(avatar_contradiction_clause,[],[f10277])).
% 2.86/0.62 tff(f10359,plain,(
% 2.86/0.62 1 != count(remove(5,sK0)) | in(sK2,remove(5,sK0)) | ~spl3_106),
% 2.86/0.62 inference(superposition,[],[f57,f10191])).
% 2.86/0.62 tff(f10362,plain,(
% 2.86/0.62 in(sK2,remove(5,sK0)) | ~spl3_106),
% 2.86/0.62 inference(forward_subsumption_resolution,[],[f10359,f3863])).
% 2.86/0.62 tff(f10365,plain,(
% 2.86/0.62 $sum(-1,count(remove(5,sK0))) = count(remove(sK2,remove(5,sK0))) | ~spl3_106),
% 2.86/0.62 inference(resolution,[],[f10362,f3121])).
% 2.86/0.62 tff(f10369,plain,(
% 2.86/0.62 $sum(-1,1) = count(remove(sK2,remove(5,sK0))) | ~spl3_106),
% 2.86/0.62 inference(forward_demodulation,[],[f10365,f3863])).
% 2.86/0.62 tff(f10370,plain,(
% 2.86/0.62 0 = count(remove(sK2,remove(5,sK0))) | ~spl3_106),
% 2.86/0.62 inference(evaluation,[],[f10369])).
% 2.86/0.62 tff(f10374,plain,(
% 2.86/0.62 0 != 0 | empty = remove(sK2,remove(5,sK0)) | ~spl3_106),
% 2.86/0.62 inference(superposition,[],[f53,f10370])).
% 2.86/0.62 tff(f10375,plain,(
% 2.86/0.62 empty = remove(sK2,remove(5,sK0)) | ~spl3_106),
% 2.86/0.62 inference(trivial_inequality_removal,[],[f10374])).
% 2.86/0.62 tff(f10381,plain,(
% 2.86/0.62 ( ! [X0 : $int] : (in(X0,empty) | ~in(X0,remove(5,sK0)) | sK2 = X0) ) | ~spl3_106),
% 2.86/0.62 inference(superposition,[],[f48,f10375])).
% 2.86/0.62 tff(f10384,plain,(
% 2.86/0.62 ( ! [X0 : $int] : (~in(X0,remove(5,sK0)) | sK2 = X0) ) | ~spl3_106),
% 2.86/0.62 inference(forward_subsumption_resolution,[],[f10381,f42])).
% 2.86/0.62 tff(f10388,plain,(
% 2.86/0.62 ( ! [X0 : $int] : (~in(X0,sK0) | sK2 = X0 | 5 = X0) ) | ~spl3_106),
% 2.86/0.62 inference(resolution,[],[f10384,f48])).
% 2.86/0.62 tff(f10443,plain,(
% 2.86/0.62 sK1 = sK2 | 5 = sK1 | ~spl3_106),
% 2.86/0.62 inference(resolution,[],[f10388,f65])).
% 2.86/0.62 tff(f10451,definition,(
% 2.86/0.62 spl3_107 <=> 5 = sK1),
% 2.86/0.62 introduced(definition,[new_symbols(definition,[spl3_107])],[avatar_definition])).
% 2.86/0.62 tff(f10453,plain,(
% 2.86/0.62 5 = sK1 | ~spl3_107),
% 2.86/0.62 inference(avatar_component_clause,[],[f10451])).
% 2.86/0.62 tff(f10455,definition,(
% 2.86/0.62 spl3_108 <=> sK1 = sK2),
% 2.86/0.62 introduced(definition,[new_symbols(definition,[spl3_108])],[avatar_definition])).
% 2.86/0.62 tff(f10457,plain,(
% 2.86/0.62 sK1 = sK2 | ~spl3_108),
% 2.86/0.62 inference(avatar_component_clause,[],[f10455])).
% 2.86/0.62 tff(f10458,plain,(
% 2.86/0.62 spl3_107 | spl3_108 | ~spl3_106),
% 2.86/0.62 inference(avatar_split_clause,[],[f10443,f10189,f10455,f10451])).
% 2.86/0.62 tff(f10638,plain,(
% 2.86/0.62 $less(sK1,sK1) | (~spl3_20 | ~spl3_108)),
% 2.86/0.62 inference(backward_demodulation,[],[f471,f10457])).
% 2.86/0.62 tff(f10643,plain,(
% 2.86/0.62 $false | (~spl3_20 | ~spl3_108)),
% 2.86/0.62 inference(forward_subsumption_resolution,[],[f10638,f22])).
% 2.86/0.62 tff(f10644,plain,(
% 2.86/0.62 ~spl3_20 | ~spl3_108),
% 2.86/0.62 inference(avatar_contradiction_clause,[],[f10643])).
% 2.86/0.62 tff(f10660,plain,(
% 2.86/0.62 $less(5,3) | ~spl3_107),
% 2.86/0.62 inference(backward_demodulation,[],[f67,f10453])).
% 2.86/0.62 tff(f10666,plain,(
% 2.86/0.62 $false | ~spl3_107),
% 2.86/0.62 inference(evaluation,[],[f10660])).
% 2.86/0.62 tff(f10667,plain,(
% 2.86/0.62 ~spl3_107),
% 2.86/0.62 inference(avatar_contradiction_clause,[],[f10666])).
% 2.86/0.62 cnf(s45, plain, spl3_20 | spl3_21, inference(sat_conversion,[],[f476])).
% 2.86/0.62 cnf(s47, plain, ~spl3_21, inference(sat_conversion,[],[f523])).
% 2.86/0.62 cnf(s280, plain, spl3_104 | spl3_106, inference(sat_conversion,[],[f10192])).
% 2.86/0.62 cnf(s281, plain, ~spl3_104, inference(sat_conversion,[],[f10278])).
% 2.86/0.62 cnf(s282, plain, ~spl3_106 | spl3_107 | spl3_108, inference(sat_conversion,[],[f10458])).
% 2.86/0.62 cnf(s289, plain, ~spl3_20 | ~spl3_108, inference(sat_conversion,[],[f10644])).
% 2.86/0.62 cnf(s290, plain, ~spl3_107, inference(sat_conversion,[],[f10667])).
% 2.86/0.62 cnf(s291, plain, ~spl3_106 | spl3_108, inference(rat,[],[s282,s290])).
% 2.86/0.62 cnf(s292, plain, spl3_106, inference(rat,[],[s280,s281])).
% 2.86/0.62 cnf(s293, plain, spl3_108, inference(rat,[],[s291,s292])).
% 2.86/0.62 cnf(s294, plain, ~spl3_20, inference(rat,[],[s289,s293])).
% 2.86/0.62 cnf(s314, plain, $false, inference(rat,[],[s45,s47,s294])).
% 2.86/0.62 tff(f10668,plain,(
% 2.86/0.62 $false),
% 2.86/0.62 inference(avatar_sat_refutation,[],[s314])).
% 2.86/0.62 % SZS output end Proof for theBenchmark
% 2.86/0.62 % (2302392)------------------------------
% 2.86/0.62 % (2302392)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.86/0.62 % (2302392)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.86/0.62 % (2302392)CaDiCaL version: 2.1.3
% 2.86/0.62 % (2302392)Termination reason: Refutation
% 2.86/0.62 % (2302392)Time elapsed: 0.283 s
% 2.86/0.62 % (2302392)Peak memory usage: 14 MB
% 2.86/0.62 % (2302392)Instructions burned: 453 (million)
% 2.86/0.62 % (2302366)Success in time 0.42 s
% 2.86/0.62 % Vampire exiting
%------------------------------------------------------------------------------