%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT038_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 : n017.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 1.71s 0.47s
% Output : Refutation 1.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : DAT038_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.17 % Computer : n017.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 00:01:37 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.20 Running first-order model finding
% 0.07/0.20 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
% 1.71/0.47 % (4147159)Will run a generic schedule for satisfiability detection.
% 1.71/0.47 % (4147165)% WARNING: option uhcvi not known.
% 1.71/0.47 % (4147165)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1475476296:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.71/0.47 % (4147169)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2461980903:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.71/0.47 % (4147167)dis+10_1_sil=32000:sp=arity:random_seed=4283157967:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.71/0.47 % (4147166)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=978517770:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.71/0.47 % (4147168)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3360305732:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.71/0.47 % (4147170)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1124811874:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.71/0.47 % (4147164)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3127924539_2999 on theBenchmark for (2999ds/0Mi)
% 1.71/0.47 % (4147164)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 1.71/0.47 % (4147164)Terminated due to inappropriate strategy.
% 1.71/0.47 % (4147164)------------------------------
% 1.71/0.47 % (4147164)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.71/0.47 % (4147164)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.71/0.47 % (4147164)CaDiCaL version: 2.1.3
% 1.71/0.47 % (4147164)Termination reason: Inappropriate
% 1.71/0.47 % (4147164)Time elapsed: 0.005 s
% 1.71/0.47 % (4147164)Peak memory usage: 10 MB
% 1.71/0.47 % (4147164)Instructions burned: 1 (million)
% 1.71/0.47 % (4147164)------------------------------
% 1.71/0.47 % (4147164)------------------------------
% 1.71/0.47 % (4147178)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3663102813:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.71/0.47 % (4147178)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 1.71/0.47 % (4147178)Terminated due to inappropriate strategy.
% 1.71/0.47 % (4147178)------------------------------
% 1.71/0.47 % (4147178)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.71/0.47 % (4147178)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.71/0.47 % (4147178)CaDiCaL version: 2.1.3
% 1.71/0.47 % (4147178)Termination reason: Inappropriate
% 1.71/0.47 % (4147178)Time elapsed: 0.001 s
% 1.71/0.47 % (4147178)Peak memory usage: 10 MB
% 1.71/0.47 % (4147178)Instructions burned: 1 (million)
% 1.71/0.47 % (4147178)------------------------------
% 1.71/0.47 % (4147178)------------------------------
% 1.71/0.47 % (4147167)Instruction limit reached!
% 1.71/0.47 % (4147167)------------------------------
% 1.71/0.47 % (4147167)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.71/0.47 % (4147167)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.71/0.47 % (4147167)CaDiCaL version: 2.1.3
% 1.71/0.47 % (4147167)Termination reason: Instruction limit
% 1.71/0.47 % (4147167)Termination phase: Saturation
% 1.71/0.47 % (4147167)Time elapsed: 0.067 s
% 1.71/0.47 % (4147167)Peak memory usage: 12 MB
% 1.71/0.47 % (4147167)Instructions burned: 104 (million)
% 1.71/0.47 % (4147180)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=408060438:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 1.71/0.47 % (4147168)Instruction limit reached!
% 1.71/0.47 % (4147168)------------------------------
% 1.71/0.47 % (4147168)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.71/0.47 % (4147168)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.71/0.47 % (4147168)CaDiCaL version: 2.1.3
% 1.71/0.47 % (4147168)Termination reason: Instruction limit
% 1.71/0.47 % (4147168)Termination phase: Saturation
% 1.71/0.47 % (4147168)Time elapsed: 0.074 s
% 1.71/0.47 % (4147168)Peak memory usage: 12 MB
% 1.71/0.47 % (4147168)Instructions burned: 117 (million)
% 1.71/0.47 % (4147169)Instruction limit reached!
% 1.71/0.47 % (4147169)------------------------------
% 1.71/0.47 % (4147169)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.71/0.47 % (4147169)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.71/0.47 % (4147169)CaDiCaL version: 2.1.3
% 1.71/0.47 % (4147169)Termination reason: Instruction limit
% 1.71/0.47 % (4147169)Termination phase: Saturation
% 1.71/0.47 % (4147169)Time elapsed: 0.086 s
% 1.71/0.47 % (4147169)Peak memory usage: 12 MB
% 1.71/0.47 % (4147169)Instructions burned: 131 (million)
% 1.71/0.47 % (4147181)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=3661321052:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 1.71/0.47 % (4147183)ott-21_1_sil=16000:fs=off:random_seed=1629341829:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.71/0.47 % (4147170)Instruction limit reached!
% 1.71/0.47 % (4147170)------------------------------
% 1.71/0.47 % (4147170)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.71/0.47 % (4147170)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.71/0.47 % (4147170)CaDiCaL version: 2.1.3
% 1.71/0.47 % (4147170)Termination reason: Instruction limit
% 1.71/0.47 % (4147170)Termination phase: Saturation
% 1.71/0.47 % (4147170)Time elapsed: 0.103 s
% 1.71/0.47 % (4147170)Peak memory usage: 12 MB
% 1.71/0.47 % (4147170)Instructions burned: 159 (million)
% 1.71/0.47 % (4147184)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3187718713:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 1.71/0.47 % (4147188)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1557490982:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 1.71/0.47 % (4147188)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 1.71/0.47 % (4147188)Terminated due to inappropriate strategy.
% 1.71/0.47 % (4147188)------------------------------
% 1.71/0.47 % (4147188)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.71/0.47 % (4147188)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.71/0.47 % (4147188)CaDiCaL version: 2.1.3
% 1.71/0.47 % (4147188)Termination reason: Inappropriate
% 1.71/0.47 % (4147188)Time elapsed: 0.001 s
% 1.71/0.47 % (4147188)Peak memory usage: 10 MB
% 1.71/0.47 % (4147188)------------------------------
% 1.71/0.47 % (4147188)------------------------------
% 1.71/0.47 % (4147190)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=2601578389:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 1.71/0.47 % (4147180)Instruction limit reached!
% 1.71/0.47 % (4147180)------------------------------
% 1.71/0.47 % (4147180)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.71/0.47 % (4147180)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.71/0.47 % (4147180)CaDiCaL version: 2.1.3
% 1.71/0.47 % (4147180)Termination reason: Instruction limit
% 1.71/0.47 % (4147180)Termination phase: Saturation
% 1.71/0.47 % (4147180)Time elapsed: 0.085 s
% 1.71/0.47 % (4147180)Peak memory usage: 13 MB
% 1.71/0.47 % (4147180)Instructions burned: 131 (million)
% 1.71/0.47 % (4147183)Instruction limit reached!
% 1.71/0.47 % (4147183)------------------------------
% 1.71/0.47 % (4147183)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.71/0.47 % (4147183)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.71/0.47 % (4147183)CaDiCaL version: 2.1.3
% 1.71/0.47 % (4147183)Termination reason: Instruction limit
% 1.71/0.47 % (4147183)Termination phase: Saturation
% 1.71/0.47 % (4147183)Time elapsed: 0.083 s
% 1.71/0.47 % (4147183)Peak memory usage: 12 MB
% 1.71/0.47 % (4147183)Instructions burned: 180 (million)
% 1.71/0.47 % (4147192)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=2083577756:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 1.71/0.47 % (4147192)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 1.71/0.47 % (4147192)Terminated due to inappropriate strategy.
% 1.71/0.47 % (4147192)------------------------------
% 1.71/0.47 % (4147192)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.71/0.47 % (4147192)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.71/0.47 % (4147192)CaDiCaL version: 2.1.3
% 1.71/0.47 % (4147192)Termination reason: Inappropriate
% 1.71/0.47 % (4147192)Time elapsed: 0.001 s
% 1.71/0.47 % (4147192)Peak memory usage: 10 MB
% 1.71/0.47 % (4147192)Instructions burned: 1 (million)
% 1.71/0.47 % (4147192)------------------------------
% 1.71/0.47 % (4147192)------------------------------
% 1.71/0.47 % (4147194)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=1144721473:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2997 on theBenchmark for (2997ds/692Mi)
% 1.71/0.47 % (4147195)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=4174298529:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 1.71/0.47 % (4147184) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4147159-4147184"...
% 1.71/0.47 % (4147184)...printing done.
% 1.71/0.47 % (4147184)Refutation found. Thanks to Tanya!
% 1.71/0.47 % SZS status Theorem for theBenchmark
% 1.71/0.47 % SZS output start Proof for theBenchmark
% 1.71/0.47 tff(type_def_5, type, collection: $tType).
% 1.71/0.47 tff(func_def_0, type, empty: collection).
% 1.71/0.47 tff(func_def_1, type, add: ($int * collection) > collection).
% 1.71/0.47 tff(func_def_2, type, remove: ($int * collection) > collection).
% 1.71/0.47 tff(func_def_3, type, count: collection > $int).
% 1.71/0.47 tff(func_def_12, type, sK0: collection).
% 1.71/0.47 tff(pred_def_1, type, in: ($int * collection) > $o).
% 1.71/0.47 tff(f1,axiom,(
% 1.71/0.47 ! [X0 : $int] : ~in(X0,empty)),
% 1.71/0.47 file('/export/starexec/sandbox/benchmark/Axioms/DAT002_0.ax',ax1)).
% 1.71/0.47 tff(f4,axiom,(
% 1.71/0.47 ! [X0 : $int,X1 : collection,X2 : $int] : ((in(X0,X1) | X0 = X2) <=> in(X0,add(X2,X1)))),
% 1.71/0.47 file('/export/starexec/sandbox/benchmark/Axioms/DAT002_0.ax',ax4)).
% 1.71/0.47 tff(f7,axiom,(
% 1.71/0.47 ! [X0 : collection] : (X0 = empty <=> count(X0) = 0)),
% 1.71/0.47 file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax',ax2)).
% 1.71/0.47 tff(f9,axiom,(
% 1.71/0.47 ! [X0 : $int,X1 : collection] : (in(X0,X1) <=> count(add(X0,X1)) = count(X1))),
% 1.71/0.47 file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax',ax4)).
% 1.71/0.47 tff(f10,axiom,(
% 1.71/0.47 ! [X0 : $int,X1 : collection] : (in(X0,X1) <=> count(remove(X0,X1)) = $difference(count(X1),1))),
% 1.71/0.47 file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax',ax5)).
% 1.71/0.47 tff(f12,axiom,(
% 1.71/0.47 ! [X0 : $int,X1 : collection] : (in(X0,X1) => X1 = add(X0,remove(X0,X1)))),
% 1.71/0.47 file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax',ax7)).
% 1.71/0.47 tff(f13,conjecture,(
% 1.71/0.47 ! [X0 : collection] : ((in(2,X0) & in(3,X0) & count(X0) = 2) => ~in(5,X0))),
% 1.71/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1)).
% 1.71/0.47 tff(f14,negated_conjecture,(
% 1.71/0.47 ~ ! [X0 : collection] : ((in(2,X0) & in(3,X0) & count(X0) = 2) => ~in(5,X0))),
% 1.71/0.48 inference(negated_conjecture,[status(cth)],[f13])).
% 1.71/0.48 tff(f16,plain,(
% 1.71/0.48 ! [X0 : $int,X1 : collection] : (in(X0,X1) <=> count(remove(X0,X1)) = $sum(count(X1),$uminus(1)))),
% 1.71/0.48 inference(theory_normalization,[],[f10])).
% 1.71/0.48 tff(f17,definition,(
% 1.71/0.48 ( ! [X0 : $int,X1 : $int] : ($sum(X0,X1) = $sum(X1,X0)) )),
% 1.71/0.48 introduced(theory,[tha_commutativity])).
% 1.71/0.48 tff(f29,plain,(
% 1.71/0.48 ! [X0 : $int,X1 : collection] : (X1 = add(X0,remove(X0,X1)) | ~in(X0,X1))),
% 1.71/0.48 inference(ennf_transformation,[],[f12])).
% 1.71/0.48 tff(f30,plain,(
% 1.71/0.48 ? [X0 : collection] : (in(5,X0) & (in(2,X0) & in(3,X0) & count(X0) = 2))),
% 1.71/0.48 inference(ennf_transformation,[],[f14])).
% 1.71/0.48 tff(f31,plain,(
% 1.71/0.48 ? [X0 : collection] : (in(5,X0) & in(2,X0) & in(3,X0) & count(X0) = 2)),
% 1.71/0.48 inference(flattening,[],[f30])).
% 1.71/0.48 tff(f32,plain,(
% 1.71/0.48 ! [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)))),
% 1.71/0.48 inference(nnf_transformation,[],[f4])).
% 1.71/0.48 tff(f33,plain,(
% 1.71/0.48 ! [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)))),
% 1.71/0.48 inference(flattening,[],[f32])).
% 1.71/0.48 tff(f36,plain,(
% 1.71/0.48 ! [X0 : collection] : ((X0 = empty | count(X0) != 0) & (count(X0) = 0 | empty != X0))),
% 1.71/0.48 inference(nnf_transformation,[],[f7])).
% 1.71/0.48 tff(f38,plain,(
% 1.71/0.48 ! [X0 : $int,X1 : collection] : ((in(X0,X1) | count(add(X0,X1)) != count(X1)) & (count(add(X0,X1)) = count(X1) | ~in(X0,X1)))),
% 1.71/0.48 inference(nnf_transformation,[],[f9])).
% 1.71/0.48 tff(f39,plain,(
% 1.71/0.48 ! [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)))),
% 1.71/0.48 inference(nnf_transformation,[],[f16])).
% 1.71/0.48 tff(f41,plain,(
% 1.71/0.48 in(5,sK0) & in(2,sK0) & in(3,sK0) & 2 = count(sK0)),
% 1.71/0.48 inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f31])).
% 1.71/0.48 tff(f42,plain,(
% 1.71/0.48 ( ! [X0 : $int] : (~in(X0,empty)) )),
% 1.71/0.48 inference(cnf_transformation,[],[f1])).
% 1.71/0.48 tff(f47,plain,(
% 1.71/0.48 ( ! [X2 : $int,X0 : $int,X1 : collection] : (~in(X0,add(X2,X1)) | X0 = X2 | in(X0,X1)) )),
% 1.71/0.48 inference(cnf_transformation,[],[f33])).
% 1.71/0.48 tff(f53,plain,(
% 1.71/0.48 ( ! [X0 : collection] : (count(X0) != 0 | empty = X0) )),
% 1.71/0.48 inference(cnf_transformation,[],[f36])).
% 1.71/0.48 tff(f56,plain,(
% 1.71/0.48 ( ! [X0 : $int,X1 : collection] : (~in(X0,X1) | count(add(X0,X1)) = count(X1)) )),
% 1.71/0.48 inference(cnf_transformation,[],[f38])).
% 1.71/0.48 tff(f57,plain,(
% 1.71/0.48 ( ! [X0 : $int,X1 : collection] : (count(add(X0,X1)) != count(X1) | in(X0,X1)) )),
% 1.71/0.48 inference(cnf_transformation,[],[f38])).
% 1.71/0.48 tff(f58,plain,(
% 1.71/0.48 ( ! [X0 : $int,X1 : collection] : (count(remove(X0,X1)) = $sum(count(X1),$uminus(1)) | ~in(X0,X1)) )),
% 1.71/0.48 inference(cnf_transformation,[],[f39])).
% 1.71/0.48 tff(f62,plain,(
% 1.71/0.48 ( ! [X0 : $int,X1 : collection] : (~in(X0,X1) | add(X0,remove(X0,X1)) = X1) )),
% 1.71/0.48 inference(cnf_transformation,[],[f29])).
% 1.71/0.48 tff(f63,plain,(
% 1.71/0.48 2 = count(sK0)),
% 1.71/0.48 inference(cnf_transformation,[],[f41])).
% 1.71/0.48 tff(f64,plain,(
% 1.71/0.48 in(3,sK0)),
% 1.71/0.48 inference(cnf_transformation,[],[f41])).
% 1.71/0.48 tff(f65,plain,(
% 1.71/0.48 in(2,sK0)),
% 1.71/0.48 inference(cnf_transformation,[],[f41])).
% 1.71/0.48 tff(f66,plain,(
% 1.71/0.48 in(5,sK0)),
% 1.71/0.48 inference(cnf_transformation,[],[f41])).
% 1.71/0.48 tff(f70,plain,(
% 1.71/0.48 ( ! [X0 : $int,X1 : collection] : (count(remove(X0,X1)) = $sum(count(X1),-1) | ~in(X0,X1)) )),
% 1.71/0.48 inference(evaluation,[],[f58])).
% 1.71/0.48 tff(f1988,plain,(
% 1.71/0.48 sK0 = add(3,remove(3,sK0))),
% 1.71/0.48 inference(resolution,[],[f62,f64])).
% 1.71/0.48 tff(f2846,plain,(
% 1.71/0.48 ( ! [X0 : $int,X1 : collection] : (~in(X0,X1) | count(remove(X0,X1)) = $sum(-1,count(X1))) )),
% 1.71/0.48 inference(forward_demodulation,[],[f70,f17])).
% 1.71/0.48 tff(f3682,plain,(
% 1.71/0.48 $sum(-1,count(sK0)) = count(remove(3,sK0))),
% 1.71/0.48 inference(resolution,[],[f2846,f64])).
% 1.71/0.48 tff(f3689,plain,(
% 1.71/0.48 count(remove(3,sK0)) = $sum(-1,2)),
% 1.71/0.48 inference(forward_demodulation,[],[f3682,f63])).
% 1.71/0.48 tff(f3690,plain,(
% 1.71/0.48 1 = count(remove(3,sK0))),
% 1.71/0.48 inference(evaluation,[],[f3689])).
% 1.71/0.48 tff(f5035,plain,(
% 1.71/0.48 ( ! [X0 : $int] : (in(X0,remove(3,sK0)) | 3 = X0 | ~in(X0,sK0)) )),
% 1.71/0.48 inference(superposition,[],[f47,f1988])).
% 1.71/0.48 tff(f5656,plain,(
% 1.71/0.48 ( ! [X0 : $int] : (count(remove(3,sK0)) = count(add(X0,remove(3,sK0))) | 3 = X0 | ~in(X0,sK0)) )),
% 1.71/0.48 inference(resolution,[],[f56,f5035])).
% 1.71/0.48 tff(f5659,plain,(
% 1.71/0.48 ( ! [X0 : $int] : (~in(X0,sK0) | 3 = X0 | 1 = count(add(X0,remove(3,sK0)))) )),
% 1.71/0.48 inference(forward_demodulation,[],[f5656,f3690])).
% 1.71/0.48 tff(f6752,plain,(
% 1.71/0.48 2 = 3 | 1 = count(add(2,remove(3,sK0)))),
% 1.71/0.48 inference(resolution,[],[f5659,f65])).
% 1.71/0.48 tff(f6754,plain,(
% 1.71/0.48 3 = 5 | 1 = count(add(5,remove(3,sK0)))),
% 1.71/0.48 inference(resolution,[],[f5659,f66])).
% 1.71/0.48 tff(f6755,plain,(
% 1.71/0.48 1 = count(add(5,remove(3,sK0)))),
% 1.71/0.48 inference(evaluation,[],[f6754])).
% 1.71/0.48 tff(f6756,plain,(
% 1.71/0.48 1 = count(add(2,remove(3,sK0)))),
% 1.71/0.48 inference(evaluation,[],[f6752])).
% 1.71/0.48 tff(f6820,plain,(
% 1.71/0.48 1 != count(remove(3,sK0)) | in(5,remove(3,sK0))),
% 1.71/0.48 inference(superposition,[],[f57,f6755])).
% 1.71/0.48 tff(f6821,plain,(
% 1.71/0.48 1 != count(remove(3,sK0)) | in(2,remove(3,sK0))),
% 1.71/0.48 inference(superposition,[],[f57,f6756])).
% 1.71/0.48 tff(f6824,plain,(
% 1.71/0.48 in(2,remove(3,sK0))),
% 1.71/0.48 inference(forward_subsumption_resolution,[],[f6821,f3690])).
% 1.71/0.48 tff(f6825,plain,(
% 1.71/0.48 in(5,remove(3,sK0))),
% 1.71/0.48 inference(forward_subsumption_resolution,[],[f6820,f3690])).
% 1.71/0.48 tff(f6850,plain,(
% 1.71/0.48 remove(3,sK0) = add(5,remove(5,remove(3,sK0)))),
% 1.71/0.48 inference(resolution,[],[f6825,f62])).
% 1.71/0.48 tff(f7071,plain,(
% 1.71/0.48 $sum(-1,count(remove(3,sK0))) = count(remove(5,remove(3,sK0)))),
% 1.71/0.48 inference(resolution,[],[f2846,f6825])).
% 1.71/0.48 tff(f7085,plain,(
% 1.71/0.48 $sum(-1,1) = count(remove(5,remove(3,sK0)))),
% 1.71/0.48 inference(forward_demodulation,[],[f7071,f3690])).
% 1.71/0.48 tff(f7086,plain,(
% 1.71/0.48 0 = count(remove(5,remove(3,sK0)))),
% 1.71/0.48 inference(evaluation,[],[f7085])).
% 1.71/0.48 tff(f7106,plain,(
% 1.71/0.48 0 != 0 | empty = remove(5,remove(3,sK0))),
% 1.71/0.48 inference(superposition,[],[f53,f7086])).
% 1.71/0.48 tff(f7108,plain,(
% 1.71/0.48 empty = remove(5,remove(3,sK0))),
% 1.71/0.48 inference(trivial_inequality_removal,[],[f7106])).
% 1.71/0.48 tff(f7112,plain,(
% 1.71/0.48 remove(3,sK0) = add(5,empty)),
% 1.71/0.48 inference(backward_demodulation,[],[f6850,f7108])).
% 1.71/0.48 tff(f7127,plain,(
% 1.71/0.48 in(2,add(5,empty))),
% 1.71/0.48 inference(backward_demodulation,[],[f6824,f7112])).
% 1.71/0.48 tff(f7139,plain,(
% 1.71/0.48 2 = 5 | in(2,empty)),
% 1.71/0.48 inference(resolution,[],[f7127,f47])).
% 1.71/0.48 tff(f7143,plain,(
% 1.71/0.48 in(2,empty)),
% 1.71/0.48 inference(evaluation,[],[f7139])).
% 1.71/0.48 tff(f7144,plain,(
% 1.71/0.48 $false),
% 1.71/0.48 inference(forward_subsumption_resolution,[],[f7143,f42])).
% 1.71/0.48 % SZS output end Proof for theBenchmark
% 1.71/0.48 % (4147184)------------------------------
% 1.71/0.48 % (4147184)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.71/0.48 % (4147184)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.71/0.48 % (4147184)CaDiCaL version: 2.1.3
% 1.71/0.48 % (4147184)Termination reason: Refutation
% 1.71/0.48 % (4147184)Time elapsed: 0.122 s
% 1.71/0.48 % (4147184)Peak memory usage: 13 MB
% 1.71/0.48 % (4147184)Instructions burned: 293 (million)
% 1.71/0.48 % (4147159)Success in time 0.263 s
% 1.71/0.48 % Vampire exiting
%------------------------------------------------------------------------------