0.04/0.11	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.04/0.11	% Command    : run_vampire %s %d THM
0.11/0.32	% Computer : n016.cluster.edu
0.11/0.32	% Model    : x86_64 x86_64
0.11/0.32	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.11/0.32	% Memory   : 8042.1875MB
0.11/0.32	% OS       : Linux 3.10.0-693.el7.x86_64
0.11/0.32	% CPULimit   : 960
0.11/0.32	% WCLimit    : 120
0.11/0.32	% DateTime   : Wed Jul 30 05:43:49 EDT 2025
0.17/0.32	% CPUTime    : 
0.17/0.34	This is a TFF_ problem
0.17/0.34	Running first-order theorem proving
0.17/0.34	Running /export/starexec/sandbox2/solver/bin/vampire --mode casc -m 16384 --cores 7 -t 120 /export/starexec/sandbox2/benchmark/theBenchmark.p
0.19/0.41	% (30845)Running in auto input_syntax mode. Trying TPTP
0.19/0.41	% (30856)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=32:si=on:rawr=on:rtra=on_0 on theBenchmark for (1200ds/32Mi)
0.19/0.41	% (30845)Running in auto input_syntax mode. Trying TPTP
0.19/0.41	% (30852)dis+1011_1:64_drc=off:flr=on:nwc=2.0:sac=on:urr=ec_only:i=8:si=on:rawr=on:rtra=on_0 on theBenchmark for (1200ds/8Mi)
0.19/0.41	% (30845)Running in auto input_syntax mode. Trying TPTP
0.19/0.41	% (30850)dis+1010_1:4_aac=none:abs=on:atotf=0.5:avsq=on:avsqc=2:avsqr=215,247:awrs=converge:awrsf=128:bsd=on:erd=off:fde=none:gve=cautious:newcnf=on:nwc=5.0:rnwc=on:sac=on:sas=z3:sp=const_min:tgt=ground:thsq=on:thsqc=64:thsqr=1,4:i=59848:si=on:rawr=on:rtra=on_0 on theBenchmark for (1200ds/59848Mi)
0.19/0.41	% (30845)Running in auto input_syntax mode. Trying TPTP
0.19/0.41	% (30854)ott+1011_1:2_br=off:bs=unit_only:bsr=unit_only:nwc=5.0:s2a=on:s2agt=32:urr=on:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (1200ds/37Mi)
0.19/0.41	% (30845)Running in auto input_syntax mode. Trying TPTP
0.19/0.41	% (30851)lrs+1010_1:1_aac=none:bce=on:nicw=on:nm=0:plsq=on:plsql=on:sac=on:sos=on:sp=frequency:spb=units:to=lpo:i=34:si=on:rawr=on:rtra=on_0 on theBenchmark for (1200ds/34Mi)
0.19/0.41	% (30845)Running in auto input_syntax mode. Trying TPTP
0.19/0.41	% (30855)lrs+10_1:32_s2a=on:s2agt=10:sgt=8:ss=axioms:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (1200ds/15Mi)
0.19/0.42	% (30852)Instruction limit reached!
0.19/0.42	% (30852)------------------------------
0.19/0.42	% (30852)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
0.19/0.42	% (30852)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
0.19/0.42	% (30852)Termination reason: Time limit
0.19/0.42	% (30852)Termination phase: Saturation
0.19/0.42	
0.19/0.42	% (30852)Memory used [KB]: 905
0.19/0.42	% (30852)Time elapsed: 0.009 s
0.19/0.42	% (30852)Instructions burned: 8 (million)
0.19/0.42	% (30845)Running in auto input_syntax mode. Trying TPTP
0.19/0.42	% (30853)ott+21_1:1_erd=off:s2a=on:sac=on:sd=1:sgt=64:sos=on:ss=included:st=3.0:to=lpo:urr=on:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (1200ds/2Mi)
0.19/0.42	% (30853)Instruction limit reached!
0.19/0.42	% (30853)------------------------------
0.19/0.42	% (30853)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
0.19/0.42	% (30853)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
0.19/0.42	% (30853)Termination reason: Time limit
0.19/0.42	% (30853)Termination phase: Saturation
0.19/0.42	
0.19/0.42	% (30853)Memory used [KB]: 780
0.19/0.42	% (30853)Time elapsed: 0.004 s
0.19/0.42	% (30853)Instructions burned: 2 (million)
0.19/0.42	% (30851)First to succeed.
0.19/0.42	% (30855)Instruction limit reached!
0.19/0.42	% (30855)------------------------------
0.19/0.42	% (30855)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
0.19/0.42	% (30855)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
0.19/0.42	% (30855)Termination reason: Time limit
0.19/0.42	% (30855)Termination phase: Saturation
0.19/0.42	
0.19/0.42	% (30855)Memory used [KB]: 931
0.19/0.42	% (30855)Time elapsed: 0.014 s
0.19/0.42	% (30855)Instructions burned: 16 (million)
0.19/0.42	% (30851)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-30845"
0.19/0.42	% (30845)Running in auto input_syntax mode. Trying TPTP
0.19/0.42	% (30851)Refutation found. Thanks to Tanya!
0.19/0.42	% SZS status Theorem for theBenchmark
0.19/0.42	% SZS output start Proof for theBenchmark
0.19/0.42	tff(type_def_5, type, collection: $tType).
0.19/0.42	tff(func_def_0, type, empty: collection).
0.19/0.42	tff(func_def_1, type, add: ($int * collection) > collection).
0.19/0.42	tff(func_def_2, type, remove: ($int * collection) > collection).
0.19/0.42	tff(func_def_3, type, count: collection > $int).
0.19/0.42	tff(func_def_9, type, sK0: $int).
0.19/0.42	tff(func_def_10, type, sK1: collection).
0.19/0.42	tff(pred_def_1, type, in: ($int * collection) > $o).
0.19/0.42	tff(f270,plain,(
0.19/0.42	  $false),
0.19/0.42	  inference(avatar_sat_refutation,[],[f97,f111,f121,f126,f136,f155,f159,f164,f169,f178,f193,f200,f223,f226,f236,f269])).
0.19/0.42	tff(f269,plain,(
0.19/0.42	  ~spl2_6 | spl2_13),
0.19/0.42	  inference(avatar_contradiction_clause,[],[f268])).
0.19/0.42	tff(f268,plain,(
0.19/0.42	  $false | (~spl2_6 | spl2_13)),
0.19/0.42	  inference(subsumption_resolution,[],[f267,f127])).
0.19/0.42	tff(f127,plain,(
0.19/0.42	  in(sK0,sK1) | ~spl2_6),
0.19/0.42	  inference(avatar_component_clause,[],[f119])).
0.19/0.42	tff(f119,plain,(
0.19/0.42	  spl2_6 <=> in(sK0,sK1)),
0.19/0.42	  introduced(avatar_definition,[new_symbols(naming,[spl2_6])])).
0.19/0.42	tff(f267,plain,(
0.19/0.42	  ~in(sK0,sK1) | (~spl2_6 | spl2_13)),
0.19/0.42	  inference(trivial_inequality_removal,[],[f265])).
0.19/0.42	tff(f265,plain,(
0.19/0.42	  count(sK1) != count(sK1) | ~in(sK0,sK1) | (~spl2_6 | spl2_13)),
0.19/0.42	  inference(superposition,[],[f264,f75])).
0.19/0.42	tff(f75,plain,(
0.19/0.42	  ( ! [X0 : $int,X1 : collection] : (count(X1) = count(add(X0,X1)) | ~in(X0,X1)) )),
0.19/0.42	  inference(cnf_transformation,[],[f55])).
0.19/0.42	tff(f55,plain,(
0.19/0.42	  ! [X0 : $int,X1 : collection] : ((count(X1) = count(add(X0,X1)) | ~in(X0,X1)) & (in(X0,X1) | count(X1) != count(add(X0,X1))))),
0.19/0.42	  inference(rectify,[],[f54])).
0.19/0.42	tff(f54,plain,(
0.19/0.42	  ! [X1 : $int,X0 : collection] : ((count(add(X1,X0)) = count(X0) | ~in(X1,X0)) & (in(X1,X0) | count(add(X1,X0)) != count(X0)))),
0.19/0.42	  inference(nnf_transformation,[],[f30])).
0.19/0.42	tff(f30,plain,(
0.19/0.42	  ! [X1 : $int,X0 : collection] : (count(add(X1,X0)) = count(X0) <=> in(X1,X0))),
0.19/0.42	  inference(rectify,[],[f9])).
0.19/0.42	tff(f9,axiom,(
0.19/0.42	  ! [X17 : collection,X16 : $int] : (in(X16,X17) <=> count(add(X16,X17)) = count(X17))),
0.19/0.42	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown)).
0.19/0.42	tff(f264,plain,(
0.19/0.42	  count(add(sK0,sK1)) != count(sK1) | (~spl2_6 | spl2_13)),
0.19/0.42	  inference(subsumption_resolution,[],[f263,f127])).
0.19/0.42	tff(f263,plain,(
0.19/0.42	  count(add(sK0,sK1)) != count(sK1) | ~in(sK0,sK1) | spl2_13),
0.19/0.42	  inference(evaluation,[],[f261])).
0.19/0.42	tff(f261,plain,(
0.19/0.42	  ~in(sK0,sK1) | count(add(sK0,sK1)) != $sum(1,$sum(count(sK1),-1)) | spl2_13),
0.19/0.42	  inference(superposition,[],[f167,f86])).
0.19/0.42	tff(f86,plain,(
0.19/0.42	  ( ! [X0 : $int,X1 : collection] : (count(remove(X0,X1)) = $sum(count(X1),-1) | ~in(X0,X1)) )),
0.19/0.42	  inference(evaluation,[],[f80])).
0.19/0.42	tff(f80,plain,(
0.19/0.42	  ( ! [X0 : $int,X1 : collection] : (~in(X0,X1) | count(remove(X0,X1)) = $sum(count(X1),$uminus(1))) )),
0.19/0.42	  inference(cnf_transformation,[],[f59])).
0.19/0.42	tff(f59,plain,(
0.19/0.42	  ! [X0 : $int,X1 : collection] : ((count(remove(X0,X1)) = $sum(count(X1),$uminus(1)) | ~in(X0,X1)) & (in(X0,X1) | count(remove(X0,X1)) != $sum(count(X1),$uminus(1))))),
0.19/0.42	  inference(nnf_transformation,[],[f31])).
0.19/0.42	tff(f31,plain,(
0.19/0.42	  ! [X0 : $int,X1 : collection] : (count(remove(X0,X1)) = $sum(count(X1),$uminus(1)) <=> in(X0,X1))),
0.19/0.42	  inference(rectify,[],[f15])).
0.19/0.42	tff(f15,plain,(
0.19/0.42	  ! [X11 : $int,X12 : collection] : (count(remove(X11,X12)) = $sum(count(X12),$uminus(1)) <=> in(X11,X12))),
0.19/0.42	  inference(theory_normalization,[],[f6])).
0.19/0.42	tff(f6,axiom,(
0.19/0.42	  ! [X11 : $int,X12 : collection] : (count(remove(X11,X12)) = $difference(count(X12),1) <=> in(X11,X12))),
0.19/0.42	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown)).
0.19/0.42	tff(f167,plain,(
0.19/0.42	  count(add(sK0,sK1)) != $sum(1,count(remove(sK0,sK1))) | spl2_13),
0.19/0.42	  inference(avatar_component_clause,[],[f166])).
0.19/0.42	tff(f166,plain,(
0.19/0.42	  spl2_13 <=> count(add(sK0,sK1)) = $sum(1,count(remove(sK0,sK1)))),
0.19/0.42	  introduced(avatar_definition,[new_symbols(naming,[spl2_13])])).
0.19/0.42	tff(f236,plain,(
0.19/0.42	  ~spl2_4 | ~spl2_11),
0.19/0.42	  inference(avatar_contradiction_clause,[],[f235])).
0.19/0.42	tff(f235,plain,(
0.19/0.42	  $false | (~spl2_4 | ~spl2_11)),
0.19/0.42	  inference(subsumption_resolution,[],[f232,f62])).
0.19/0.42	tff(f62,plain,(
0.19/0.42	  ( ! [X0 : collection,X1 : $int] : (~in(X1,remove(X1,X0))) )),
0.19/0.42	  inference(cnf_transformation,[],[f43])).
0.19/0.42	tff(f43,plain,(
0.19/0.42	  ! [X0 : collection,X1 : $int] : ~in(X1,remove(X1,X0))),
0.19/0.42	  inference(rectify,[],[f37])).
0.19/0.42	tff(f37,plain,(
0.19/0.42	  ! [X1 : collection,X0 : $int] : ~in(X0,remove(X0,X1))),
0.19/0.42	  inference(rectify,[],[f5])).
0.19/0.42	tff(f5,axiom,(
0.19/0.42	  ! [X9 : $int,X10 : collection] : ~in(X9,remove(X9,X10))),
0.19/0.42	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown)).
0.19/0.42	tff(f232,plain,(
0.19/0.42	  in(0,remove(0,sK1)) | (~spl2_4 | ~spl2_11)),
0.19/0.42	  inference(backward_demodulation,[],[f168,f154])).
0.19/0.42	tff(f154,plain,(
0.19/0.42	  0 = sK0 | ~spl2_11),
0.19/0.42	  inference(avatar_component_clause,[],[f153])).
0.19/0.42	tff(f153,plain,(
0.19/0.42	  spl2_11 <=> 0 = sK0),
0.19/0.42	  introduced(avatar_definition,[new_symbols(naming,[spl2_11])])).
0.19/0.42	tff(f168,plain,(
0.19/0.42	  in(0,remove(sK0,sK1)) | ~spl2_4),
0.19/0.42	  inference(avatar_component_clause,[],[f109])).
0.19/0.42	tff(f109,plain,(
0.19/0.42	  spl2_4 <=> in(0,remove(sK0,sK1))),
0.19/0.42	  introduced(avatar_definition,[new_symbols(naming,[spl2_4])])).
0.19/0.42	tff(f226,plain,(
0.19/0.42	  ~spl2_4 | spl2_14),
0.19/0.42	  inference(avatar_contradiction_clause,[],[f225])).
0.19/0.42	tff(f225,plain,(
0.19/0.42	  $false | (~spl2_4 | spl2_14)),
0.19/0.42	  inference(subsumption_resolution,[],[f224,f206])).
0.19/0.42	tff(f206,plain,(
0.19/0.42	  in(0,sK1) | ~spl2_4),
0.19/0.42	  inference(resolution,[],[f168,f77])).
0.19/0.42	tff(f77,plain,(
0.19/0.42	  ( ! [X2 : collection,X0 : $int,X1 : $int] : (~in(X0,remove(X1,X2)) | in(X0,X2)) )),
0.19/0.42	  inference(cnf_transformation,[],[f58])).
0.19/0.42	tff(f58,plain,(
0.19/0.42	  ! [X0 : $int,X1 : $int,X2 : collection] : ((in(X0,remove(X1,X2)) | ~in(X0,X2) | X0 = X1) & ((in(X0,X2) & X0 != X1) | ~in(X0,remove(X1,X2))))),
0.19/0.42	  inference(rectify,[],[f57])).
0.19/0.42	tff(f57,plain,(
0.19/0.42	  ! [X2 : $int,X1 : $int,X0 : collection] : ((in(X2,remove(X1,X0)) | ~in(X2,X0) | X1 = X2) & ((in(X2,X0) & X1 != X2) | ~in(X2,remove(X1,X0))))),
0.19/0.42	  inference(flattening,[],[f56])).
0.19/0.42	tff(f56,plain,(
0.19/0.42	  ! [X2 : $int,X1 : $int,X0 : collection] : ((in(X2,remove(X1,X0)) | (~in(X2,X0) | X1 = X2)) & ((in(X2,X0) & X1 != X2) | ~in(X2,remove(X1,X0))))),
0.19/0.42	  inference(nnf_transformation,[],[f34])).
0.19/0.42	tff(f34,plain,(
0.19/0.42	  ! [X2 : $int,X1 : $int,X0 : collection] : (in(X2,remove(X1,X0)) <=> (in(X2,X0) & X1 != X2))),
0.19/0.42	  inference(rectify,[],[f3])).
0.19/0.42	tff(f3,axiom,(
0.19/0.42	  ! [X5 : collection,X6 : $int,X4 : $int] : (in(X4,remove(X6,X5)) <=> (X4 != X6 & in(X4,X5)))),
0.19/0.42	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown)).
0.19/0.42	tff(f224,plain,(
0.19/0.42	  ~in(0,sK1) | spl2_14),
0.19/0.42	  inference(resolution,[],[f222,f65])).
0.19/0.42	tff(f65,plain,(
0.19/0.42	  ( ! [X2 : $int,X0 : collection,X1 : $int] : (in(X1,add(X2,X0)) | ~in(X1,X0)) )),
0.19/0.42	  inference(cnf_transformation,[],[f48])).
0.19/0.42	tff(f48,plain,(
0.19/0.42	  ! [X0 : collection,X1 : $int,X2 : $int] : ((X1 = X2 | in(X1,X0) | ~in(X1,add(X2,X0))) & (in(X1,add(X2,X0)) | (X1 != X2 & ~in(X1,X0))))),
0.19/0.42	  inference(rectify,[],[f47])).
0.19/0.42	tff(f47,plain,(
0.19/0.42	  ! [X1 : collection,X2 : $int,X0 : $int] : ((X0 = X2 | in(X2,X1) | ~in(X2,add(X0,X1))) & (in(X2,add(X0,X1)) | (X0 != X2 & ~in(X2,X1))))),
0.19/0.42	  inference(flattening,[],[f46])).
0.19/0.42	tff(f46,plain,(
0.19/0.42	  ! [X1 : collection,X2 : $int,X0 : $int] : (((X0 = X2 | in(X2,X1)) | ~in(X2,add(X0,X1))) & (in(X2,add(X0,X1)) | (X0 != X2 & ~in(X2,X1))))),
0.19/0.42	  inference(nnf_transformation,[],[f36])).
0.19/0.42	tff(f36,plain,(
0.19/0.42	  ! [X1 : collection,X2 : $int,X0 : $int] : ((X0 = X2 | in(X2,X1)) <=> in(X2,add(X0,X1)))),
0.19/0.42	  inference(rectify,[],[f2])).
0.19/0.42	tff(f2,axiom,(
0.19/0.42	  ! [X3 : $int,X2 : collection,X1 : $int] : (in(X1,add(X3,X2)) <=> (X1 = X3 | in(X1,X2)))),
0.19/0.42	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown)).
0.19/0.42	tff(f222,plain,(
0.19/0.42	  ~in(0,add(sK0,sK1)) | spl2_14),
0.19/0.42	  inference(avatar_component_clause,[],[f221])).
0.19/0.42	tff(f221,plain,(
0.19/0.42	  spl2_14 <=> in(0,add(sK0,sK1))),
0.19/0.42	  introduced(avatar_definition,[new_symbols(naming,[spl2_14])])).
0.19/0.42	tff(f223,plain,(
0.19/0.42	  ~spl2_14 | spl2_11 | spl2_2),
0.19/0.42	  inference(avatar_split_clause,[],[f207,f95,f153,f221])).
0.19/0.42	tff(f95,plain,(
0.19/0.42	  spl2_2 <=> in(0,remove(sK0,add(sK0,sK1)))),
0.19/0.42	  introduced(avatar_definition,[new_symbols(naming,[spl2_2])])).
0.19/0.42	tff(f207,plain,(
0.19/0.42	  0 = sK0 | ~in(0,add(sK0,sK1)) | spl2_2),
0.19/0.42	  inference(resolution,[],[f96,f78])).
0.19/0.42	tff(f78,plain,(
0.19/0.42	  ( ! [X2 : collection,X0 : $int,X1 : $int] : (in(X0,remove(X1,X2)) | X0 = X1 | ~in(X0,X2)) )),
0.19/0.43	  inference(cnf_transformation,[],[f58])).
0.19/0.43	tff(f96,plain,(
0.19/0.43	  ~in(0,remove(sK0,add(sK0,sK1))) | spl2_2),
0.19/0.43	  inference(avatar_component_clause,[],[f95])).
0.19/0.43	tff(f200,plain,(
0.19/0.43	  ~spl2_2 | ~spl2_11),
0.19/0.43	  inference(avatar_contradiction_clause,[],[f199])).
0.19/0.43	tff(f199,plain,(
0.19/0.43	  $false | (~spl2_2 | ~spl2_11)),
0.19/0.43	  inference(subsumption_resolution,[],[f198,f62])).
0.19/0.43	tff(f198,plain,(
0.19/0.43	  in(0,remove(0,add(0,sK1))) | (~spl2_2 | ~spl2_11)),
0.19/0.43	  inference(forward_demodulation,[],[f135,f154])).
0.19/0.43	tff(f135,plain,(
0.19/0.43	  in(0,remove(sK0,add(sK0,sK1))) | ~spl2_2),
0.19/0.43	  inference(avatar_component_clause,[],[f95])).
0.19/0.43	tff(f193,plain,(
0.19/0.43	  ~spl2_2 | spl2_10),
0.19/0.43	  inference(avatar_contradiction_clause,[],[f192])).
0.19/0.43	tff(f192,plain,(
0.19/0.43	  $false | (~spl2_2 | spl2_10)),
0.19/0.43	  inference(subsumption_resolution,[],[f188,f62])).
0.19/0.43	tff(f188,plain,(
0.19/0.43	  in(0,remove(0,add(0,sK1))) | (~spl2_2 | spl2_10)),
0.19/0.43	  inference(backward_demodulation,[],[f135,f181])).
0.19/0.43	tff(f181,plain,(
0.19/0.43	  0 = sK0 | (~spl2_2 | spl2_10)),
0.19/0.43	  inference(subsumption_resolution,[],[f180,f151])).
0.19/0.43	tff(f151,plain,(
0.19/0.43	  ~in(0,sK1) | spl2_10),
0.19/0.43	  inference(avatar_component_clause,[],[f150])).
0.19/0.43	tff(f150,plain,(
0.19/0.43	  spl2_10 <=> in(0,sK1)),
0.19/0.43	  introduced(avatar_definition,[new_symbols(naming,[spl2_10])])).
0.19/0.43	tff(f180,plain,(
0.19/0.43	  in(0,sK1) | 0 = sK0 | ~spl2_2),
0.19/0.43	  inference(resolution,[],[f179,f67])).
0.19/0.43	tff(f67,plain,(
0.19/0.43	  ( ! [X2 : $int,X0 : collection,X1 : $int] : (~in(X1,add(X2,X0)) | in(X1,X0) | X1 = X2) )),
0.19/0.43	  inference(cnf_transformation,[],[f48])).
0.19/0.43	tff(f179,plain,(
0.19/0.43	  in(0,add(sK0,sK1)) | ~spl2_2),
0.19/0.43	  inference(resolution,[],[f135,f77])).
0.19/0.43	tff(f178,plain,(
0.19/0.43	  spl2_6 | spl2_13),
0.19/0.43	  inference(avatar_contradiction_clause,[],[f177])).
0.19/0.43	tff(f177,plain,(
0.19/0.43	  $false | (spl2_6 | spl2_13)),
0.19/0.43	  inference(subsumption_resolution,[],[f176,f17])).
0.19/0.43	tff(f17,plain,(
0.19/0.43	  ( ! [X0 : $int,X1 : $int] : ($sum(X0,X1) = $sum(X1,X0)) )),
0.19/0.43	  introduced(theory_axiom_143,[])).
0.19/0.43	tff(f176,plain,(
0.19/0.43	  $sum(count(sK1),1) != $sum(1,count(sK1)) | (spl2_6 | spl2_13)),
0.19/0.43	  inference(subsumption_resolution,[],[f175,f120])).
0.19/0.43	tff(f120,plain,(
0.19/0.43	  ~in(sK0,sK1) | spl2_6),
0.19/0.43	  inference(avatar_component_clause,[],[f119])).
0.19/0.43	tff(f175,plain,(
0.19/0.43	  in(sK0,sK1) | $sum(count(sK1),1) != $sum(1,count(sK1)) | (spl2_6 | spl2_13)),
0.19/0.43	  inference(superposition,[],[f173,f63])).
0.19/0.43	tff(f63,plain,(
0.19/0.43	  ( ! [X0 : $int,X1 : collection] : (count(add(X0,X1)) = $sum(count(X1),1) | in(X0,X1)) )),
0.19/0.43	  inference(cnf_transformation,[],[f45])).
0.19/0.43	tff(f45,plain,(
0.19/0.43	  ! [X0 : $int,X1 : collection] : ((~in(X0,X1) | count(add(X0,X1)) != $sum(count(X1),1)) & (count(add(X0,X1)) = $sum(count(X1),1) | in(X0,X1)))),
0.19/0.43	  inference(rectify,[],[f44])).
0.19/0.43	tff(f44,plain,(
0.19/0.43	  ! [X1 : $int,X0 : collection] : ((~in(X1,X0) | count(add(X1,X0)) != $sum(count(X0),1)) & (count(add(X1,X0)) = $sum(count(X0),1) | in(X1,X0)))),
0.19/0.43	  inference(nnf_transformation,[],[f39])).
0.19/0.43	tff(f39,plain,(
0.19/0.43	  ! [X1 : $int,X0 : collection] : (~in(X1,X0) <=> count(add(X1,X0)) = $sum(count(X0),1))),
0.19/0.43	  inference(rectify,[],[f12])).
0.19/0.43	tff(f12,axiom,(
0.19/0.43	  ! [X22 : collection,X21 : $int] : (~in(X21,X22) <=> count(add(X21,X22)) = $sum(count(X22),1))),
0.19/0.43	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown)).
0.19/0.43	tff(f173,plain,(
0.19/0.43	  count(add(sK0,sK1)) != $sum(1,count(sK1)) | (spl2_6 | spl2_13)),
0.19/0.43	  inference(subsumption_resolution,[],[f171,f120])).
0.19/0.43	tff(f171,plain,(
0.19/0.43	  count(add(sK0,sK1)) != $sum(1,count(sK1)) | in(sK0,sK1) | spl2_13),
0.19/0.43	  inference(superposition,[],[f167,f70])).
0.19/0.43	tff(f70,plain,(
0.19/0.43	  ( ! [X0 : collection,X1 : $int] : (count(X0) = count(remove(X1,X0)) | in(X1,X0)) )),
0.19/0.43	  inference(cnf_transformation,[],[f50])).
0.19/0.43	tff(f50,plain,(
0.19/0.43	  ! [X0 : collection,X1 : $int] : ((count(X0) = count(remove(X1,X0)) | in(X1,X0)) & (~in(X1,X0) | count(X0) != count(remove(X1,X0))))),
0.19/0.43	  inference(rectify,[],[f49])).
0.19/0.43	tff(f49,plain,(
0.19/0.43	  ! [X1 : collection,X0 : $int] : ((count(remove(X0,X1)) = count(X1) | in(X0,X1)) & (~in(X0,X1) | count(remove(X0,X1)) != count(X1)))),
0.19/0.43	  inference(nnf_transformation,[],[f29])).
0.19/0.43	tff(f29,plain,(
0.19/0.43	  ! [X1 : collection,X0 : $int] : (count(remove(X0,X1)) = count(X1) <=> ~in(X0,X1))),
0.19/0.43	  inference(rectify,[],[f7])).
0.19/0.43	tff(f7,axiom,(
0.19/0.43	  ! [X13 : $int,X14 : collection] : (count(remove(X13,X14)) = count(X14) <=> ~in(X13,X14))),
0.19/0.43	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown)).
0.19/0.43	tff(f169,plain,(
0.19/0.43	  ~spl2_13 | spl2_4 | spl2_8),
0.19/0.43	  inference(avatar_split_clause,[],[f143,f133,f109,f166])).
0.19/0.43	tff(f133,plain,(
0.19/0.43	  spl2_8 <=> count(add(0,remove(sK0,sK1))) = $sum(1,count(remove(sK0,add(sK0,sK1))))),
0.19/0.43	  introduced(avatar_definition,[new_symbols(naming,[spl2_8])])).
0.19/0.43	tff(f143,plain,(
0.19/0.43	  in(0,remove(sK0,sK1)) | count(add(sK0,sK1)) != $sum(1,count(remove(sK0,sK1))) | spl2_8),
0.19/0.43	  inference(forward_demodulation,[],[f142,f17])).
0.19/0.43	tff(f142,plain,(
0.19/0.43	  in(0,remove(sK0,sK1)) | count(add(sK0,sK1)) != $sum(count(remove(sK0,sK1)),1) | spl2_8),
0.19/0.43	  inference(superposition,[],[f140,f63])).
0.19/0.43	tff(f140,plain,(
0.19/0.43	  count(add(0,remove(sK0,sK1))) != count(add(sK0,sK1)) | spl2_8),
0.19/0.43	  inference(subsumption_resolution,[],[f139,f73])).
0.19/0.43	tff(f73,plain,(
0.19/0.43	  ( ! [X0 : $int,X1 : collection] : (in(X0,add(X0,X1))) )),
0.19/0.43	  inference(cnf_transformation,[],[f53])).
0.19/0.43	tff(f53,plain,(
0.19/0.43	  ! [X0 : $int,X1 : collection] : in(X0,add(X0,X1))),
0.19/0.43	  inference(rectify,[],[f40])).
0.19/0.43	tff(f40,plain,(
0.19/0.43	  ! [X1 : $int,X0 : collection] : in(X1,add(X1,X0))),
0.19/0.43	  inference(rectify,[],[f4])).
0.19/0.43	tff(f4,axiom,(
0.19/0.43	  ! [X8 : collection,X7 : $int] : in(X7,add(X7,X8))),
0.19/0.43	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown)).
0.19/0.43	tff(f139,plain,(
0.19/0.43	  ~in(sK0,add(sK0,sK1)) | count(add(0,remove(sK0,sK1))) != count(add(sK0,sK1)) | spl2_8),
0.19/0.43	  inference(evaluation,[],[f137])).
0.19/0.43	tff(f137,plain,(
0.19/0.43	  count(add(0,remove(sK0,sK1))) != $sum(1,$sum(count(add(sK0,sK1)),-1)) | ~in(sK0,add(sK0,sK1)) | spl2_8),
0.19/0.43	  inference(superposition,[],[f134,f86])).
0.19/0.43	tff(f134,plain,(
0.19/0.43	  count(add(0,remove(sK0,sK1))) != $sum(1,count(remove(sK0,add(sK0,sK1)))) | spl2_8),
0.19/0.43	  inference(avatar_component_clause,[],[f133])).
0.19/0.43	tff(f164,plain,(
0.19/0.43	  spl2_6 | spl2_12),
0.19/0.43	  inference(avatar_contradiction_clause,[],[f163])).
0.19/0.43	tff(f163,plain,(
0.19/0.43	  $false | (spl2_6 | spl2_12)),
0.19/0.43	  inference(subsumption_resolution,[],[f162,f120])).
0.19/0.43	tff(f162,plain,(
0.19/0.43	  in(sK0,sK1) | spl2_12),
0.19/0.43	  inference(evaluation,[],[f161])).
0.19/0.43	tff(f161,plain,(
0.19/0.43	  count(sK1) != $sum(-1,$sum(count(sK1),1)) | in(sK0,sK1) | spl2_12),
0.19/0.43	  inference(superposition,[],[f158,f63])).
0.19/0.43	tff(f158,plain,(
0.19/0.43	  $sum(-1,count(add(sK0,sK1))) != count(sK1) | spl2_12),
0.19/0.43	  inference(avatar_component_clause,[],[f157])).
0.19/0.43	tff(f157,plain,(
0.19/0.43	  spl2_12 <=> $sum(-1,count(add(sK0,sK1))) = count(sK1)),
0.19/0.43	  introduced(avatar_definition,[new_symbols(naming,[spl2_12])])).
0.19/0.43	tff(f159,plain,(
0.19/0.43	  spl2_6 | ~spl2_12 | spl2_3),
0.19/0.43	  inference(avatar_split_clause,[],[f113,f106,f157,f119])).
0.19/0.43	tff(f106,plain,(
0.19/0.43	  spl2_3 <=> $sum(-1,count(add(sK0,sK1))) = count(remove(sK0,sK1))),
0.19/0.43	  introduced(avatar_definition,[new_symbols(naming,[spl2_3])])).
0.19/0.43	tff(f113,plain,(
0.19/0.43	  $sum(-1,count(add(sK0,sK1))) != count(sK1) | in(sK0,sK1) | spl2_3),
0.19/0.43	  inference(superposition,[],[f107,f70])).
0.19/0.43	tff(f107,plain,(
0.19/0.43	  $sum(-1,count(add(sK0,sK1))) != count(remove(sK0,sK1)) | spl2_3),
0.19/0.43	  inference(avatar_component_clause,[],[f106])).
0.19/0.43	tff(f155,plain,(
0.19/0.43	  ~spl2_10 | spl2_11 | spl2_4),
0.19/0.43	  inference(avatar_split_clause,[],[f148,f109,f153,f150])).
0.19/0.43	tff(f148,plain,(
0.19/0.43	  0 = sK0 | ~in(0,sK1) | spl2_4),
0.19/0.43	  inference(resolution,[],[f110,f78])).
0.19/0.43	tff(f110,plain,(
0.19/0.43	  ~in(0,remove(sK0,sK1)) | spl2_4),
0.19/0.43	  inference(avatar_component_clause,[],[f109])).
0.19/0.43	tff(f136,plain,(
0.19/0.43	  ~spl2_8 | spl2_2),
0.19/0.43	  inference(avatar_split_clause,[],[f90,f95,f133])).
0.19/0.43	tff(f90,plain,(
0.19/0.43	  in(0,remove(sK0,add(sK0,sK1))) | count(add(0,remove(sK0,sK1))) != $sum(1,count(remove(sK0,add(sK0,sK1))))),
0.19/0.43	  inference(forward_demodulation,[],[f89,f17])).
0.19/0.43	tff(f89,plain,(
0.19/0.43	  count(add(0,remove(sK0,sK1))) != $sum(count(remove(sK0,add(sK0,sK1))),1) | in(0,remove(sK0,add(sK0,sK1)))),
0.19/0.43	  inference(superposition,[],[f71,f63])).
0.19/0.43	tff(f71,plain,(
0.19/0.43	  count(add(0,remove(sK0,add(sK0,sK1)))) != count(add(0,remove(sK0,sK1)))),
0.19/0.43	  inference(cnf_transformation,[],[f52])).
0.19/0.43	tff(f52,plain,(
0.19/0.43	  count(add(0,remove(sK0,add(sK0,sK1)))) != count(add(0,remove(sK0,sK1)))),
0.19/0.43	  inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f42,f51])).
0.19/0.43	tff(f51,plain,(
0.19/0.43	  ? [X0 : $int,X1 : collection] : count(add(0,remove(X0,add(X0,X1)))) != count(add(0,remove(X0,X1))) => count(add(0,remove(sK0,add(sK0,sK1)))) != count(add(0,remove(sK0,sK1)))),
0.19/0.43	  introduced(choice_axiom,[])).
0.19/0.43	tff(f42,plain,(
0.19/0.43	  ? [X0 : $int,X1 : collection] : count(add(0,remove(X0,add(X0,X1)))) != count(add(0,remove(X0,X1)))),
0.19/0.43	  inference(ennf_transformation,[],[f33])).
0.19/0.43	tff(f33,plain,(
0.19/0.43	  ~! [X1 : collection,X0 : $int] : count(add(0,remove(X0,add(X0,X1)))) = count(add(0,remove(X0,X1)))),
0.19/0.43	  inference(rectify,[],[f14])).
0.19/0.43	tff(f14,negated_conjecture,(
0.19/0.43	  ~! [X7 : $int,X0 : collection] : count(add(0,remove(X7,add(X7,X0)))) = count(add(0,remove(X7,X0)))),
0.19/0.43	  inference(negated_conjecture,[],[f13])).
0.19/0.43	tff(f13,conjecture,(
0.19/0.43	  ! [X7 : $int,X0 : collection] : count(add(0,remove(X7,add(X7,X0)))) = count(add(0,remove(X7,X0)))),
0.19/0.43	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown)).
0.19/0.43	tff(f126,plain,(
0.19/0.43	  ~spl2_6 | spl2_5),
0.19/0.43	  inference(avatar_split_clause,[],[f124,f116,f119])).
0.19/0.43	tff(f116,plain,(
0.19/0.43	  spl2_5 <=> $sum(-1,count(add(sK0,sK1))) = $sum(-1,count(sK1))),
0.19/0.43	  introduced(avatar_definition,[new_symbols(naming,[spl2_5])])).
0.19/0.43	tff(f124,plain,(
0.19/0.43	  ~in(sK0,sK1) | spl2_5),
0.19/0.43	  inference(trivial_inequality_removal,[],[f122])).
0.19/0.43	tff(f122,plain,(
0.19/0.43	  ~in(sK0,sK1) | $sum(-1,count(sK1)) != $sum(-1,count(sK1)) | spl2_5),
0.19/0.43	  inference(superposition,[],[f117,f75])).
0.19/0.43	tff(f117,plain,(
0.19/0.43	  $sum(-1,count(add(sK0,sK1))) != $sum(-1,count(sK1)) | spl2_5),
0.19/0.43	  inference(avatar_component_clause,[],[f116])).
0.19/0.43	tff(f121,plain,(
0.19/0.43	  ~spl2_5 | ~spl2_6 | spl2_3),
0.19/0.43	  inference(avatar_split_clause,[],[f114,f106,f119,f116])).
0.19/0.43	tff(f114,plain,(
0.19/0.43	  $sum(-1,count(add(sK0,sK1))) != $sum(-1,count(sK1)) | ~in(sK0,sK1) | spl2_3),
0.19/0.43	  inference(forward_demodulation,[],[f112,f17])).
0.19/0.43	tff(f112,plain,(
0.19/0.43	  $sum(-1,count(add(sK0,sK1))) != $sum(count(sK1),-1) | ~in(sK0,sK1) | spl2_3),
0.19/0.43	  inference(superposition,[],[f107,f86])).
0.19/0.43	tff(f111,plain,(
0.19/0.43	  ~spl2_3 | ~spl2_4 | spl2_1),
0.19/0.43	  inference(avatar_split_clause,[],[f102,f92,f109,f106])).
0.19/0.43	tff(f92,plain,(
0.19/0.43	  spl2_1 <=> count(add(0,remove(sK0,sK1))) = count(remove(sK0,add(sK0,sK1)))),
0.19/0.43	  introduced(avatar_definition,[new_symbols(naming,[spl2_1])])).
0.19/0.43	tff(f102,plain,(
0.19/0.43	  ~in(0,remove(sK0,sK1)) | $sum(-1,count(add(sK0,sK1))) != count(remove(sK0,sK1)) | spl2_1),
0.19/0.43	  inference(superposition,[],[f101,f75])).
0.19/0.43	tff(f101,plain,(
0.19/0.43	  count(add(0,remove(sK0,sK1))) != $sum(-1,count(add(sK0,sK1))) | spl2_1),
0.19/0.43	  inference(forward_demodulation,[],[f100,f17])).
0.19/0.43	tff(f100,plain,(
0.19/0.43	  count(add(0,remove(sK0,sK1))) != $sum(count(add(sK0,sK1)),-1) | spl2_1),
0.19/0.43	  inference(subsumption_resolution,[],[f98,f73])).
0.19/0.43	tff(f98,plain,(
0.19/0.43	  ~in(sK0,add(sK0,sK1)) | count(add(0,remove(sK0,sK1))) != $sum(count(add(sK0,sK1)),-1) | spl2_1),
0.19/0.43	  inference(superposition,[],[f93,f86])).
0.19/0.43	tff(f93,plain,(
0.19/0.43	  count(add(0,remove(sK0,sK1))) != count(remove(sK0,add(sK0,sK1))) | spl2_1),
0.19/0.43	  inference(avatar_component_clause,[],[f92])).
0.19/0.43	tff(f97,plain,(
0.19/0.43	  ~spl2_1 | ~spl2_2),
0.19/0.43	  inference(avatar_split_clause,[],[f88,f95,f92])).
0.19/0.43	tff(f88,plain,(
0.19/0.43	  count(add(0,remove(sK0,sK1))) != count(remove(sK0,add(sK0,sK1))) | ~in(0,remove(sK0,add(sK0,sK1)))),
0.19/0.43	  inference(superposition,[],[f71,f75])).
0.19/0.43	% SZS output end Proof for theBenchmark
0.19/0.43	% (30851)------------------------------
0.19/0.43	% (30851)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
0.19/0.43	% (30851)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
0.19/0.43	% (30851)Termination reason: Refutation
0.19/0.43	
0.19/0.43	% (30851)Memory used [KB]: 905
0.19/0.43	% (30851)Time elapsed: 0.015 s
0.19/0.43	% (30851)Instructions burned: 18 (million)
0.19/0.43	% (30851)------------------------------
0.19/0.43	% (30851)------------------------------
0.19/0.43	% (30845)Success in time 0.073 s
0.19/0.43	EOF