%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT049_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 : n015.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 1.18s 0.53s
% Output : Refutation 1.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT049_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 % Computer : n015.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Sep 29 00:10:34 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 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
% 1.18/0.53 % (3166281)Will run a generic schedule for satisfiability detection.
% 1.18/0.53 % (3166294)% WARNING: option uhcvi not known.
% 1.18/0.53 % (3166294)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3861555816:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.18/0.53 % (3166296)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2549952492:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.18/0.53 % (3166300)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=323038432:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.18/0.53 % (3166292)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4142501192_2999 on theBenchmark for (2999ds/0Mi)
% 1.18/0.53 % (3166302)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3958890815:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.18/0.53 % (3166304)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1410574984:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.18/0.53 % (3166298)dis+10_1_sil=32000:sp=arity:random_seed=323632269:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.18/0.53 % (3166292)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 1.18/0.53 % (3166292)Terminated due to inappropriate strategy.
% 1.18/0.53 % (3166292)------------------------------
% 1.18/0.53 % (3166292)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.18/0.53 % (3166292)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.18/0.53 % (3166292)CaDiCaL version: 2.1.3
% 1.18/0.53 % (3166292)Termination reason: Inappropriate
% 1.18/0.53 % (3166292)Time elapsed: 0.002 s
% 1.18/0.53 % (3166292)Peak memory usage: 10 MB
% 1.18/0.53 % (3166292)Instructions burned: 1 (million)
% 1.18/0.53 % (3166292)------------------------------
% 1.18/0.53 % (3166292)------------------------------
% 1.18/0.53 % (3166315)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=462250633:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.18/0.53 % (3166315)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 1.18/0.53 % (3166315)Terminated due to inappropriate strategy.
% 1.18/0.53 % (3166315)------------------------------
% 1.18/0.53 % (3166315)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.18/0.53 % (3166315)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.18/0.53 % (3166315)CaDiCaL version: 2.1.3
% 1.18/0.53 % (3166315)Termination reason: Inappropriate
% 1.18/0.53 % (3166315)Time elapsed: 0.001 s
% 1.18/0.53 % (3166315)Peak memory usage: 10 MB
% 1.18/0.53 % (3166315)Instructions burned: 1 (million)
% 1.18/0.53 % (3166315)------------------------------
% 1.18/0.53 % (3166315)------------------------------
% 1.18/0.53 % (3166300)Instruction limit reached!
% 1.18/0.53 % (3166300)------------------------------
% 1.18/0.53 % (3166300)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.18/0.53 % (3166300)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.18/0.53 % (3166300)CaDiCaL version: 2.1.3
% 1.18/0.53 % (3166300)Termination reason: Instruction limit
% 1.18/0.53 % (3166300)Termination phase: Saturation
% 1.18/0.53 % (3166300)Time elapsed: 0.062 s
% 1.18/0.53 % (3166300)Peak memory usage: 12 MB
% 1.18/0.53 % (3166300)Instructions burned: 118 (million)
% 1.18/0.53 % (3166324)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=1750047676:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 1.18/0.53 % (3166322)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=548056792:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 1.18/0.53 % (3166298)Instruction limit reached!
% 1.18/0.53 % (3166298)------------------------------
% 1.18/0.53 % (3166298)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.18/0.53 % (3166298)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.18/0.53 % (3166298)CaDiCaL version: 2.1.3
% 1.18/0.53 % (3166298)Termination reason: Instruction limit
% 1.18/0.53 % (3166298)Termination phase: Saturation
% 1.18/0.53 % (3166298)Time elapsed: 0.106 s
% 1.18/0.53 % (3166298)Peak memory usage: 13 MB
% 1.18/0.53 % (3166298)Instructions burned: 104 (million)
% 1.18/0.53 % (3166302)Instruction limit reached!
% 1.18/0.53 % (3166302)------------------------------
% 1.18/0.53 % (3166302)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.18/0.53 % (3166302)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.18/0.53 % (3166302)CaDiCaL version: 2.1.3
% 1.18/0.53 % (3166302)Termination reason: Instruction limit
% 1.18/0.53 % (3166302)Termination phase: Saturation
% 1.18/0.53 % (3166302)Time elapsed: 0.135 s
% 1.18/0.53 % (3166302)Peak memory usage: 13 MB
% 1.18/0.53 % (3166302)Instructions burned: 131 (million)
% 1.18/0.53 % (3166329)ott-21_1_sil=16000:fs=off:random_seed=2089158818:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.18/0.53 % (3166331)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3014418573:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 1.18/0.53 % (3166304)Instruction limit reached!
% 1.18/0.53 % (3166304)------------------------------
% 1.18/0.53 % (3166304)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.18/0.53 % (3166304)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.18/0.53 % (3166304)CaDiCaL version: 2.1.3
% 1.18/0.53 % (3166304)Termination reason: Instruction limit
% 1.18/0.53 % (3166304)Termination phase: Saturation
% 1.18/0.53 % (3166304)Time elapsed: 0.163 s
% 1.18/0.53 % (3166304)Peak memory usage: 13 MB
% 1.18/0.53 % (3166304)Instructions burned: 160 (million)
% 1.18/0.53 % (3166337)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=62216000:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 1.18/0.53 % (3166337)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 1.18/0.53 % (3166337)Terminated due to inappropriate strategy.
% 1.18/0.53 % (3166337)------------------------------
% 1.18/0.53 % (3166337)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.18/0.53 % (3166337)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.18/0.53 % (3166337)CaDiCaL version: 2.1.3
% 1.18/0.53 % (3166337)Termination reason: Inappropriate
% 1.18/0.53 % (3166337)Time elapsed: 0.001 s
% 1.18/0.53 % (3166337)Peak memory usage: 10 MB
% 1.18/0.53 % (3166337)------------------------------
% 1.18/0.53 % (3166337)------------------------------
% 1.18/0.53 % (3166340)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=4142970511:i=1179_2997 on theBenchmark for (2997ds/1179Mi)
% 1.18/0.53 % (3166322)Instruction limit reached!
% 1.18/0.53 % (3166322)------------------------------
% 1.18/0.53 % (3166322)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.18/0.53 % (3166322)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.18/0.53 % (3166322)CaDiCaL version: 2.1.3
% 1.18/0.53 % (3166322)Termination reason: Instruction limit
% 1.18/0.53 % (3166322)Termination phase: Saturation
% 1.18/0.53 % (3166322)Time elapsed: 0.140 s
% 1.18/0.53 % (3166322)Peak memory usage: 13 MB
% 1.18/0.53 % (3166322)Instructions burned: 131 (million)
% 1.18/0.53 % (3166324) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3166281-3166324"...
% 1.18/0.53 % (3166324)...printing done.
% 1.18/0.53 % (3166324)Refutation found. Thanks to Tanya!
% 1.18/0.53 % SZS status Theorem for theBenchmark
% 1.18/0.53 % SZS output start Proof for theBenchmark
% 1.18/0.53 tff(type_def_5, type, collection: $tType).
% 1.18/0.53 tff(func_def_0, type, empty: collection).
% 1.18/0.53 tff(func_def_1, type, add: ($int * collection) > collection).
% 1.18/0.53 tff(func_def_2, type, remove: ($int * collection) > collection).
% 1.18/0.53 tff(func_def_3, type, count: collection > $int).
% 1.18/0.53 tff(func_def_9, type, sK0: collection).
% 1.18/0.53 tff(func_def_10, type, sK1: $int).
% 1.18/0.53 tff(pred_def_1, type, in: ($int * collection) > $o).
% 1.18/0.53 tff(f2,axiom,(
% 1.18/0.53 ! [X0 : $int,X1 : collection] : in(X0,add(X0,X1))),
% 1.18/0.53 file('/export/starexec/sandbox/benchmark/Axioms/DAT002_0.ax',ax2)).
% 1.18/0.53 tff(f3,axiom,(
% 1.18/0.53 ! [X0 : $int,X1 : collection] : ~in(X0,remove(X0,X1))),
% 1.18/0.53 file('/export/starexec/sandbox/benchmark/Axioms/DAT002_0.ax',ax3)).
% 1.18/0.53 tff(f8,axiom,(
% 1.18/0.53 ! [X0 : $int,X1 : collection] : (~in(X0,X1) <=> count(add(X0,X1)) = $sum(count(X1),1))),
% 1.18/0.53 file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax',ax3)).
% 1.18/0.53 tff(f9,axiom,(
% 1.18/0.53 ! [X0 : $int,X1 : collection] : (in(X0,X1) <=> count(add(X0,X1)) = count(X1))),
% 1.18/0.53 file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax',ax4)).
% 1.18/0.53 tff(f10,axiom,(
% 1.18/0.53 ! [X0 : $int,X1 : collection] : (in(X0,X1) <=> count(remove(X0,X1)) = $difference(count(X1),1))),
% 1.18/0.53 file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax',ax5)).
% 1.18/0.53 tff(f11,axiom,(
% 1.18/0.53 ! [X0 : $int,X1 : collection] : (~in(X0,X1) <=> count(remove(X0,X1)) = count(X1))),
% 1.18/0.53 file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax',ax6)).
% 1.18/0.53 tff(f12,axiom,(
% 1.18/0.53 ! [X0 : $int,X1 : collection] : (in(X0,X1) => X1 = add(X0,remove(X0,X1)))),
% 1.18/0.53 file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax',ax7)).
% 1.18/0.53 tff(f13,conjecture,(
% 1.18/0.53 ! [X0 : collection,X1 : $int] : count(remove(X1,add(X1,X0))) = count(remove(X1,X0))),
% 1.18/0.53 file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1)).
% 1.18/0.53 tff(f14,negated_conjecture,(
% 1.18/0.53 ~ ! [X0 : collection,X1 : $int] : count(remove(X1,add(X1,X0))) = count(remove(X1,X0))),
% 1.18/0.53 inference(negated_conjecture,[status(cth)],[f13])).
% 1.18/0.53 tff(f16,plain,(
% 1.18/0.53 ! [X0 : $int,X1 : collection] : (in(X0,X1) <=> count(remove(X0,X1)) = $sum(count(X1),$uminus(1)))),
% 1.18/0.53 inference(theory_normalization,[],[f10])).
% 1.18/0.53 tff(f17,definition,(
% 1.18/0.53 ( ! [X0 : $int,X1 : $int] : ($sum(X0,X1) = $sum(X1,X0)) )),
% 1.18/0.53 introduced(theory,[tha_commutativity])).
% 1.18/0.53 tff(f18,definition,(
% 1.18/0.53 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2)) )),
% 1.18/0.53 introduced(theory,[tha_associativity])).
% 1.18/0.53 tff(f21,definition,(
% 1.18/0.53 ( ! [X0 : $int] : (0 = $sum(X0,$uminus(X0))) )),
% 1.18/0.53 introduced(theory,[tha_inverse_op_unit])).
% 1.18/0.53 tff(f22,definition,(
% 1.18/0.53 ( ! [X0 : $int] : (~$less(X0,X0)) )),
% 1.18/0.53 introduced(theory,[tha_non-reflexivity])).
% 1.18/0.53 tff(f24,definition,(
% 1.18/0.53 ( ! [X0 : $int,X1 : $int] : ($less(X1,X0) | $less(X0,X1) | X0 = X1) )),
% 1.18/0.53 introduced(theory,[tha_order_totality])).
% 1.18/0.53 tff(f26,definition,(
% 1.18/0.53 ( ! [X0 : $int,X1 : $int] : ($less(X1,$sum(X0,1)) | $less(X0,X1)) )),
% 1.18/0.53 introduced(theory,[tha_order_plus_one_dichotomy])).
% 1.18/0.53 tff(f28,definition,(
% 1.18/0.53 ( ! [X0 : $int,X1 : $int] : (~$less(X1,$sum(X0,1)) | ~$less(X0,X1)) )),
% 1.18/0.53 introduced(theory,[tha_extra_integer_ordering])).
% 1.18/0.53 tff(f29,plain,(
% 1.18/0.53 ! [X0 : $int,X1 : collection] : (X1 = add(X0,remove(X0,X1)) | ~in(X0,X1))),
% 1.18/0.53 inference(ennf_transformation,[],[f12])).
% 1.18/0.53 tff(f30,plain,(
% 1.18/0.53 ? [X0 : collection,X1 : $int] : count(remove(X1,add(X1,X0))) != count(remove(X1,X0))),
% 1.18/0.53 inference(ennf_transformation,[],[f14])).
% 1.18/0.53 tff(f32,plain,(
% 1.18/0.53 ( ! [X0 : $int,X1 : collection] : (in(X0,add(X0,X1))) )),
% 1.18/0.53 inference(cnf_transformation,[],[f2])).
% 1.18/0.53 tff(f33,plain,(
% 1.18/0.53 ( ! [X0 : $int,X1 : collection] : (~in(X0,remove(X0,X1))) )),
% 1.18/0.53 inference(cnf_transformation,[],[f3])).
% 1.18/0.53 tff(f44,plain,(
% 1.18/0.53 ( ! [X0 : $int,X1 : collection] : (count(add(X0,X1)) = $sum(count(X1),1) | in(X0,X1)) )),
% 1.18/0.53 inference(cnf_transformation,[],[f8])).
% 1.18/0.53 tff(f45,plain,(
% 1.18/0.53 ( ! [X0 : $int,X1 : collection] : (count(add(X0,X1)) != count(X1) | in(X0,X1)) )),
% 1.18/0.53 inference(cnf_transformation,[],[f9])).
% 1.18/0.53 tff(f46,plain,(
% 1.18/0.53 ( ! [X0 : $int,X1 : collection] : (~in(X0,X1) | count(add(X0,X1)) = count(X1)) )),
% 1.18/0.53 inference(cnf_transformation,[],[f9])).
% 1.18/0.53 tff(f48,plain,(
% 1.18/0.53 ( ! [X0 : $int,X1 : collection] : (count(remove(X0,X1)) = $sum(count(X1),$uminus(1)) | ~in(X0,X1)) )),
% 1.18/0.53 inference(cnf_transformation,[],[f16])).
% 1.18/0.53 tff(f50,plain,(
% 1.18/0.53 ( ! [X0 : $int,X1 : collection] : (in(X0,X1) | count(X1) = count(remove(X0,X1))) )),
% 1.18/0.53 inference(cnf_transformation,[],[f11])).
% 1.18/0.53 tff(f51,plain,(
% 1.18/0.53 ( ! [X0 : $int,X1 : collection] : (~in(X0,X1) | add(X0,remove(X0,X1)) = X1) )),
% 1.18/0.53 inference(cnf_transformation,[],[f29])).
% 1.18/0.53 tff(f52,plain,(
% 1.18/0.53 count(remove(sK1,add(sK1,sK0))) != count(remove(sK1,sK0))),
% 1.18/0.53 inference(cnf_transformation,[],[f30])).
% 1.18/0.53 tff(f57,plain,(
% 1.18/0.53 ( ! [X0 : $int,X1 : collection] : (count(remove(X0,X1)) = $sum(count(X1),-1) | ~in(X0,X1)) )),
% 1.18/0.53 inference(evaluation,[],[f48])).
% 1.18/0.53 tff(f71,plain,(
% 1.18/0.53 ( ! [X0 : $int] : ($less(X0,$sum(X0,1))) )),
% 1.18/0.53 inference(resolution,[],[f26,f22])).
% 1.18/0.53 tff(f76,plain,(
% 1.18/0.53 ( ! [X0 : $int] : ($less(X0,$sum(1,X0))) )),
% 1.18/0.53 inference(superposition,[],[f71,f17])).
% 1.18/0.53 tff(f88,plain,(
% 1.18/0.53 ( ! [X0 : collection,X1 : $int] : (count(X0) = count(add(X1,X0)) | count(X0) = count(remove(X1,X0))) )),
% 1.18/0.53 inference(resolution,[],[f50,f46])).
% 1.18/0.53 tff(f108,plain,(
% 1.18/0.53 ( ! [X0 : $int,X1 : $int] : (~$less(X1,$sum(1,X0)) | ~$less(X0,X1)) )),
% 1.18/0.53 inference(superposition,[],[f28,f17])).
% 1.18/0.53 tff(f112,plain,(
% 1.18/0.53 ( ! [X0 : $int,X1 : collection] : (add(X0,X1) = add(X0,remove(X0,add(X0,X1)))) )),
% 1.18/0.53 inference(resolution,[],[f51,f32])).
% 1.18/0.53 tff(f156,plain,(
% 1.18/0.53 ( ! [X0 : $int,X1 : collection] : (count(add(X0,X1)) != count(remove(X0,add(X0,X1))) | in(X0,remove(X0,add(X0,X1)))) )),
% 1.18/0.53 inference(superposition,[],[f45,f112])).
% 1.18/0.53 tff(f159,plain,(
% 1.18/0.53 ( ! [X0 : $int,X1 : collection] : (count(add(X0,X1)) != count(remove(X0,add(X0,X1)))) )),
% 1.18/0.53 inference(forward_subsumption_resolution,[],[f156,f33])).
% 1.18/0.53 tff(f162,plain,(
% 1.18/0.53 ( ! [X0 : $int,X1 : collection] : (in(X0,X1) | count(add(X0,X1)) = $sum(1,count(X1))) )),
% 1.18/0.53 inference(forward_demodulation,[],[f44,f17])).
% 1.18/0.53 tff(f182,plain,(
% 1.18/0.53 ( ! [X0 : $int,X1 : collection] : (~in(X0,X1) | count(remove(X0,X1)) = $sum(-1,count(X1))) )),
% 1.18/0.53 inference(forward_demodulation,[],[f57,f17])).
% 1.18/0.53 tff(f189,plain,(
% 1.18/0.53 ( ! [X0 : $int,X1 : collection] : (count(add(X0,X1)) = $sum(1,count(X1)) | count(add(X0,X1)) = count(X1)) )),
% 1.18/0.53 inference(resolution,[],[f162,f46])).
% 1.18/0.53 tff(f300,plain,(
% 1.18/0.53 ( ! [X0 : $int,X1 : collection] : (count(remove(X0,add(X0,X1))) = $sum(-1,count(add(X0,X1)))) )),
% 1.18/0.53 inference(resolution,[],[f182,f32])).
% 1.18/0.53 tff(f303,plain,(
% 1.18/0.53 ( ! [X0 : $int,X1 : collection] : (count(remove(X0,X1)) = $sum(-1,count(X1)) | count(X1) = count(remove(X0,X1))) )),
% 1.18/0.53 inference(resolution,[],[f182,f50])).
% 1.18/0.53 tff(f627,plain,(
% 1.18/0.53 count(remove(sK1,sK0)) != $sum(-1,count(add(sK1,sK0)))),
% 1.18/0.53 inference(superposition,[],[f52,f300])).
% 1.18/0.53 tff(f1223,plain,(
% 1.18/0.53 ( ! [X0 : $int,X1 : $int] : ($sum(0,X1) = $sum(X0,$sum($uminus(X0),X1))) )),
% 1.18/0.53 inference(superposition,[],[f18,f21])).
% 1.18/0.53 tff(f1264,plain,(
% 1.18/0.53 ( ! [X0 : $int,X1 : $int] : ($sum(X0,$sum($uminus(X0),X1)) = X1) )),
% 1.18/0.53 inference(evaluation,[],[f1223])).
% 1.18/0.53 tff(f1283,plain,(
% 1.18/0.53 ( ! [X0 : $int,X1 : $int] : ($sum(X1,$sum(X0,$uminus(X1))) = X0) )),
% 1.18/0.53 inference(superposition,[],[f1264,f17])).
% 1.18/0.53 tff(f1298,plain,(
% 1.18/0.53 ( ! [X0 : $int] : ($less($sum($uminus(1),X0),X0)) )),
% 1.18/0.53 inference(superposition,[],[f76,f1264])).
% 1.18/0.53 tff(f1336,plain,(
% 1.18/0.53 ( ! [X0 : $int] : ($less($sum(-1,X0),X0)) )),
% 1.18/0.53 inference(evaluation,[],[f1298])).
% 1.18/0.53 tff(f1371,plain,(
% 1.18/0.53 ( ! [X0 : $int] : (~$less(X0,$sum(-1,$sum(1,X0)))) )),
% 1.18/0.53 inference(resolution,[],[f1336,f108])).
% 1.18/0.53 tff(f3281,plain,(
% 1.18/0.53 ( ! [X0 : $int] : (~$less($sum(X0,$uminus(1)),$sum(-1,X0))) )),
% 1.18/0.53 inference(superposition,[],[f1371,f1283])).
% 1.18/0.53 tff(f3309,plain,(
% 1.18/0.53 ( ! [X0 : $int] : (~$less($sum(X0,-1),$sum(-1,X0))) )),
% 1.18/0.53 inference(evaluation,[],[f3281])).
% 1.18/0.53 tff(f3358,plain,(
% 1.18/0.53 ( ! [X0 : $int] : (~$less($sum($sum($uminus(-1),X0),-1),X0)) )),
% 1.18/0.53 inference(superposition,[],[f3309,f1264])).
% 1.18/0.53 tff(f3362,plain,(
% 1.18/0.53 ( ! [X0 : $int] : (~$less($sum($sum(1,X0),-1),X0)) )),
% 1.18/0.53 inference(evaluation,[],[f3358])).
% 1.18/0.53 tff(f3364,plain,(
% 1.18/0.53 ( ! [X0 : $int] : (~$less($sum(-1,$sum(1,X0)),X0)) )),
% 1.18/0.53 inference(forward_demodulation,[],[f3362,f17])).
% 1.18/0.53 tff(f3460,plain,(
% 1.18/0.53 ( ! [X0 : $int] : ($less(X0,$sum(-1,$sum(1,X0))) | $sum(-1,$sum(1,X0)) = X0) )),
% 1.18/0.53 inference(resolution,[],[f3364,f24])).
% 1.18/0.53 tff(f3479,plain,(
% 1.18/0.53 ( ! [X0 : $int] : ($sum(-1,$sum(1,X0)) = X0) )),
% 1.18/0.53 inference(forward_subsumption_resolution,[],[f3460,f1371])).
% 1.18/0.53 tff(f5109,plain,(
% 1.18/0.53 count(remove(sK1,sK0)) != $sum(-1,$sum(1,count(sK0))) | count(add(sK1,sK0)) = count(sK0)),
% 1.18/0.53 inference(superposition,[],[f627,f189])).
% 1.18/0.53 tff(f5174,plain,(
% 1.18/0.53 count(remove(sK1,sK0)) != count(sK0) | count(add(sK1,sK0)) = count(sK0)),
% 1.18/0.53 inference(forward_demodulation,[],[f5109,f3479])).
% 1.18/0.53 tff(f5392,plain,(
% 1.18/0.53 count(add(sK1,sK0)) = count(sK0)),
% 1.18/0.53 inference(forward_subsumption_resolution,[],[f5174,f88])).
% 1.18/0.53 tff(f6888,plain,(
% 1.18/0.53 count(remove(sK1,sK0)) != $sum(-1,count(sK0))),
% 1.18/0.53 inference(superposition,[],[f627,f5392])).
% 1.18/0.53 tff(f6889,plain,(
% 1.18/0.53 count(sK0) != count(sK0) | in(sK1,sK0)),
% 1.18/0.53 inference(superposition,[],[f45,f5392])).
% 1.18/0.53 tff(f6965,plain,(
% 1.18/0.53 in(sK1,sK0)),
% 1.18/0.53 inference(trivial_inequality_removal,[],[f6889])).
% 1.18/0.53 tff(f7199,plain,(
% 1.18/0.53 sK0 = add(sK1,remove(sK1,sK0))),
% 1.18/0.53 inference(resolution,[],[f6965,f51])).
% 1.18/0.53 tff(f7272,plain,(
% 1.18/0.53 count(remove(sK1,sK0)) != count(sK0)),
% 1.18/0.53 inference(superposition,[],[f159,f7199])).
% 1.18/0.53 tff(f9670,plain,(
% 1.18/0.53 $sum(-1,count(sK0)) != $sum(-1,count(sK0)) | count(remove(sK1,sK0)) = count(sK0)),
% 1.18/0.53 inference(superposition,[],[f6888,f303])).
% 1.18/0.53 tff(f9671,plain,(
% 1.18/0.53 count(remove(sK1,sK0)) = count(sK0)),
% 1.18/0.53 inference(trivial_inequality_removal,[],[f9670])).
% 1.18/0.53 tff(f9672,plain,(
% 1.18/0.53 $false),
% 1.18/0.53 inference(forward_subsumption_resolution,[],[f9671,f7272])).
% 1.18/0.53 % SZS output end Proof for theBenchmark
% 1.18/0.53 % (3166324)------------------------------
% 1.18/0.53 % (3166324)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.18/0.53 % (3166324)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.18/0.53 % (3166324)CaDiCaL version: 2.1.3
% 1.18/0.53 % (3166324)Termination reason: Refutation
% 1.18/0.53 % (3166324)Time elapsed: 0.155 s
% 1.18/0.53 % (3166324)Peak memory usage: 15 MB
% 1.18/0.53 % (3166324)Instructions burned: 285 (million)
% 1.18/0.53 % (3166281)Success in time 0.282 s
% 1.18/0.53 % Vampire exiting
%------------------------------------------------------------------------------