0.07/0.13	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.07/0.13	% Command    : run_vampire %s %d THM
0.12/0.34	% Computer : n021.cluster.edu
0.12/0.34	% Model    : x86_64 x86_64
0.12/0.34	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.34	% Memory   : 8042.1875MB
0.12/0.34	% OS       : Linux 3.10.0-693.el7.x86_64
0.12/0.34	% CPULimit   : 1440
0.12/0.34	% WCLimit    : 180
0.12/0.34	% DateTime   : Thu Jul  4 05:57:39 EDT 2024
0.12/0.34	% CPUTime    : 
0.12/0.36	This is a TFF_ problem
0.12/0.36	Running first-order theorem proving
0.12/0.36	Running /export/starexec/sandbox/solver/bin/vampire --mode casc -m 16384 --cores 7 -t 180 /export/starexec/sandbox/benchmark/theBenchmark.p
0.22/0.43	% (31313)Running in auto input_syntax mode. Trying TPTP
0.22/0.43	% (31316)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 (1800ds/8Mi)
0.22/0.43	% (31313)Running in auto input_syntax mode. Trying TPTP
0.22/0.43	% (31318)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 (1800ds/37Mi)
0.22/0.43	% (31313)Running in auto input_syntax mode. Trying TPTP
0.22/0.43	% (31314)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 (1800ds/59848Mi)
0.22/0.43	% (31313)Running in auto input_syntax mode. Trying TPTP
0.22/0.43	% (31317)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 (1800ds/2Mi)
0.22/0.43	% (31313)Running in auto input_syntax mode. Trying TPTP
0.22/0.43	% (31315)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 (1800ds/34Mi)
0.22/0.43	% (31313)Running in auto input_syntax mode. Trying TPTP
0.22/0.43	% (31319)lrs+10_1:32_s2a=on:s2agt=10:sgt=8:ss=axioms:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (1800ds/15Mi)
0.22/0.43	% (31313)Running in auto input_syntax mode. Trying TPTP
0.22/0.43	% (31320)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 (1800ds/32Mi)
0.22/0.43	% (31317)Instruction limit reached!
0.22/0.43	% (31317)------------------------------
0.22/0.43	% (31317)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
0.22/0.43	% (31317)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
0.22/0.43	% (31317)Termination reason: Time limit
0.22/0.43	% (31317)Termination phase: Property scanning
0.22/0.43	
0.22/0.43	% (31317)Memory used [KB]: 766
0.22/0.43	% (31317)Time elapsed: 0.003 s
0.22/0.43	% (31317)Instructions burned: 2 (million)
0.22/0.43	% (31316)Instruction limit reached!
0.22/0.43	% (31316)------------------------------
0.22/0.43	% (31316)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
0.22/0.43	% (31316)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
0.22/0.43	% (31316)Termination reason: Time limit
0.22/0.43	% (31316)Termination phase: Saturation
0.22/0.43	
0.22/0.43	% (31316)Memory used [KB]: 910
0.22/0.43	% (31316)Time elapsed: 0.009 s
0.22/0.43	% (31316)Instructions burned: 8 (million)
0.22/0.44	% (31315)First to succeed.
0.22/0.44	% (31319)Instruction limit reached!
0.22/0.44	% (31319)------------------------------
0.22/0.44	% (31319)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
0.22/0.44	% (31319)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
0.22/0.44	% (31319)Termination reason: Time limit
0.22/0.44	% (31319)Termination phase: Saturation
0.22/0.44	
0.22/0.44	% (31319)Memory used [KB]: 930
0.22/0.44	% (31319)Time elapsed: 0.013 s
0.22/0.44	% (31319)Instructions burned: 15 (million)
0.22/0.44	% (31315)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-31313"
0.22/0.44	% (31313)Running in auto input_syntax mode. Trying TPTP
0.22/0.44	% (31315)Refutation found. Thanks to Tanya!
0.22/0.44	% SZS status Theorem for theBenchmark
0.22/0.44	% SZS output start Proof for theBenchmark
0.22/0.44	tff(type_def_5, type, collection: $tType).
0.22/0.44	tff(func_def_0, type, empty: collection).
0.22/0.44	tff(func_def_1, type, add: ($int * collection) > collection).
0.22/0.44	tff(func_def_2, type, remove: ($int * collection) > collection).
0.22/0.44	tff(func_def_3, type, count: collection > $int).
0.22/0.44	tff(func_def_9, type, sK0: $int).
0.22/0.44	tff(func_def_10, type, sK1: collection).
0.22/0.44	tff(pred_def_1, type, in: ($int * collection) > $o).
0.22/0.44	tff(f271,plain,(
0.22/0.44	  $false),
0.22/0.44	  inference(avatar_sat_refutation,[],[f97,f105,f111,f147,f156,f162,f174,f184,f187,f215,f219,f229,f240,f243,f248,f266,f268])).
0.22/0.44	tff(f268,plain,(
0.22/0.44	  spl2_7 | spl2_9 | ~spl2_12),
0.22/0.44	  inference(avatar_contradiction_clause,[],[f267])).
0.22/0.44	tff(f267,plain,(
0.22/0.44	  $false | (spl2_7 | spl2_9 | ~spl2_12)),
0.22/0.44	  inference(subsumption_resolution,[],[f258,f173])).
0.22/0.44	tff(f173,plain,(
0.22/0.44	  in(0,sK1) | ~spl2_12),
0.22/0.44	  inference(avatar_component_clause,[],[f172])).
0.22/0.44	tff(f172,plain,(
0.22/0.44	  spl2_12 <=> in(0,sK1)),
0.22/0.44	  introduced(avatar_definition,[new_symbols(naming,[spl2_12])])).
0.22/0.44	tff(f258,plain,(
0.22/0.44	  ~in(0,sK1) | (spl2_7 | spl2_9 | ~spl2_12)),
0.22/0.44	  inference(backward_demodulation,[],[f134,f251])).
0.22/0.44	tff(f251,plain,(
0.22/0.44	  0 = sK0 | (spl2_7 | ~spl2_12)),
0.22/0.44	  inference(subsumption_resolution,[],[f250,f173])).
0.22/0.44	tff(f250,plain,(
0.22/0.44	  0 = sK0 | ~in(0,sK1) | spl2_7),
0.22/0.44	  inference(resolution,[],[f124,f78])).
0.22/0.44	tff(f78,plain,(
0.22/0.44	  ( ! [X2 : collection,X0 : $int,X1 : $int] : (in(X0,remove(X1,X2)) | ~in(X0,X2) | X0 = X1) )),
0.22/0.44	  inference(cnf_transformation,[],[f58])).
0.22/0.44	tff(f58,plain,(
0.22/0.44	  ! [X0 : $int,X1 : $int,X2 : collection] : ((in(X0,remove(X1,X2)) | X0 = X1 | ~in(X0,X2)) & ((X0 != X1 & in(X0,X2)) | ~in(X0,remove(X1,X2))))),
0.22/0.44	  inference(rectify,[],[f57])).
0.22/0.44	tff(f57,plain,(
0.22/0.44	  ! [X2 : $int,X1 : $int,X0 : collection] : ((in(X2,remove(X1,X0)) | X1 = X2 | ~in(X2,X0)) & ((X1 != X2 & in(X2,X0)) | ~in(X2,remove(X1,X0))))),
0.22/0.44	  inference(flattening,[],[f56])).
0.22/0.44	tff(f56,plain,(
0.22/0.44	  ! [X2 : $int,X1 : $int,X0 : collection] : ((in(X2,remove(X1,X0)) | (X1 = X2 | ~in(X2,X0))) & ((X1 != X2 & in(X2,X0)) | ~in(X2,remove(X1,X0))))),
0.22/0.44	  inference(nnf_transformation,[],[f34])).
0.22/0.44	tff(f34,plain,(
0.22/0.44	  ! [X2 : $int,X1 : $int,X0 : collection] : (in(X2,remove(X1,X0)) <=> (X1 != X2 & in(X2,X0)))),
0.22/0.44	  inference(rectify,[],[f4])).
0.22/0.44	tff(f4,axiom,(
0.22/0.44	  ! [X6 : collection,X7 : $int,X5 : $int] : (in(X5,remove(X7,X6)) <=> (in(X5,X6) & X5 != X7))),
0.22/0.44	  file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown)).
0.22/0.44	tff(f124,plain,(
0.22/0.44	  ~in(0,remove(sK0,sK1)) | spl2_7),
0.22/0.44	  inference(avatar_component_clause,[],[f123])).
0.22/0.44	tff(f123,plain,(
0.22/0.44	  spl2_7 <=> in(0,remove(sK0,sK1))),
0.22/0.44	  introduced(avatar_definition,[new_symbols(naming,[spl2_7])])).
0.22/0.44	tff(f134,plain,(
0.22/0.44	  ~in(sK0,sK1) | spl2_9),
0.22/0.44	  inference(avatar_component_clause,[],[f133])).
0.22/0.44	tff(f133,plain,(
0.22/0.44	  spl2_9 <=> in(sK0,sK1)),
0.22/0.44	  introduced(avatar_definition,[new_symbols(naming,[spl2_9])])).
0.22/0.44	tff(f266,plain,(
0.22/0.44	  ~spl2_1 | spl2_7 | ~spl2_12),
0.22/0.44	  inference(avatar_contradiction_clause,[],[f265])).
0.22/0.44	tff(f265,plain,(
0.22/0.44	  $false | (~spl2_1 | spl2_7 | ~spl2_12)),
0.22/0.44	  inference(subsumption_resolution,[],[f254,f62])).
0.22/0.44	tff(f62,plain,(
0.22/0.44	  ( ! [X0 : collection,X1 : $int] : (~in(X1,remove(X1,X0))) )),
0.22/0.44	  inference(cnf_transformation,[],[f43])).
0.22/0.44	tff(f43,plain,(
0.22/0.44	  ! [X0 : collection,X1 : $int] : ~in(X1,remove(X1,X0))),
0.22/0.44	  inference(rectify,[],[f37])).
0.22/0.44	tff(f37,plain,(
0.22/0.44	  ! [X1 : collection,X0 : $int] : ~in(X0,remove(X0,X1))),
0.22/0.44	  inference(rectify,[],[f3])).
0.22/0.44	tff(f3,axiom,(
0.22/0.44	  ! [X3 : $int,X4 : collection] : ~in(X3,remove(X3,X4))),
0.22/0.44	  file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown)).
0.22/0.44	tff(f254,plain,(
0.22/0.44	  in(0,remove(0,add(0,sK1))) | (~spl2_1 | spl2_7 | ~spl2_12)),
0.22/0.44	  inference(backward_demodulation,[],[f107,f251])).
0.22/0.44	tff(f107,plain,(
0.22/0.44	  in(0,remove(sK0,add(sK0,sK1))) | ~spl2_1),
0.22/0.44	  inference(avatar_component_clause,[],[f92])).
0.22/0.44	tff(f92,plain,(
0.22/0.44	  spl2_1 <=> in(0,remove(sK0,add(sK0,sK1)))),
0.22/0.44	  introduced(avatar_definition,[new_symbols(naming,[spl2_1])])).
0.22/0.44	tff(f248,plain,(
0.22/0.44	  spl2_9 | spl2_14),
0.22/0.44	  inference(avatar_contradiction_clause,[],[f247])).
0.22/0.44	tff(f247,plain,(
0.22/0.44	  $false | (spl2_9 | spl2_14)),
0.22/0.44	  inference(subsumption_resolution,[],[f246,f134])).
0.22/0.44	tff(f246,plain,(
0.22/0.44	  in(sK0,sK1) | spl2_14),
0.22/0.44	  inference(evaluation,[],[f245])).
0.22/0.44	tff(f245,plain,(
0.22/0.44	  in(sK0,sK1) | count(sK1) != $sum(-1,$sum(count(sK1),1)) | spl2_14),
0.22/0.44	  inference(superposition,[],[f238,f75])).
0.22/0.44	tff(f75,plain,(
0.22/0.44	  ( ! [X0 : $int,X1 : collection] : (count(add(X0,X1)) = $sum(count(X1),1) | in(X0,X1)) )),
0.22/0.44	  inference(cnf_transformation,[],[f55])).
0.22/0.44	tff(f55,plain,(
0.22/0.44	  ! [X0 : $int,X1 : collection] : ((count(add(X0,X1)) = $sum(count(X1),1) | in(X0,X1)) & (~in(X0,X1) | count(add(X0,X1)) != $sum(count(X1),1)))),
0.22/0.44	  inference(rectify,[],[f54])).
0.22/0.44	tff(f54,plain,(
0.22/0.44	  ! [X1 : $int,X0 : collection] : ((count(add(X1,X0)) = $sum(count(X0),1) | in(X1,X0)) & (~in(X1,X0) | count(add(X1,X0)) != $sum(count(X0),1)))),
0.22/0.44	  inference(nnf_transformation,[],[f30])).
0.22/0.44	tff(f30,plain,(
0.22/0.44	  ! [X1 : $int,X0 : collection] : (count(add(X1,X0)) = $sum(count(X0),1) <=> ~in(X1,X0))),
0.22/0.44	  inference(rectify,[],[f10])).
0.22/0.44	tff(f10,axiom,(
0.22/0.44	  ! [X20 : collection,X19 : $int] : (~in(X19,X20) <=> count(add(X19,X20)) = $sum(count(X20),1))),
0.22/0.44	  file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown)).
0.22/0.44	tff(f238,plain,(
0.22/0.44	  count(sK1) != $sum(-1,count(add(sK0,sK1))) | spl2_14),
0.22/0.44	  inference(avatar_component_clause,[],[f237])).
0.22/0.44	tff(f237,plain,(
0.22/0.44	  spl2_14 <=> count(sK1) = $sum(-1,count(add(sK0,sK1)))),
0.22/0.44	  introduced(avatar_definition,[new_symbols(naming,[spl2_14])])).
0.22/0.44	tff(f243,plain,(
0.22/0.44	  ~spl2_9 | spl2_13),
0.22/0.44	  inference(avatar_split_clause,[],[f235,f227,f133])).
0.22/0.44	tff(f227,plain,(
0.22/0.44	  spl2_13 <=> $sum(-1,count(sK1)) = $sum(-1,count(add(sK0,sK1)))),
0.22/0.44	  introduced(avatar_definition,[new_symbols(naming,[spl2_13])])).
0.22/0.44	tff(f235,plain,(
0.22/0.44	  ~in(sK0,sK1) | spl2_13),
0.22/0.44	  inference(trivial_inequality_removal,[],[f232])).
0.22/0.44	tff(f232,plain,(
0.22/0.44	  ~in(sK0,sK1) | $sum(-1,count(sK1)) != $sum(-1,count(sK1)) | spl2_13),
0.22/0.44	  inference(superposition,[],[f228,f80])).
0.22/0.44	tff(f80,plain,(
0.22/0.44	  ( ! [X0 : $int,X1 : collection] : (count(X1) = count(add(X0,X1)) | ~in(X0,X1)) )),
0.22/0.44	  inference(cnf_transformation,[],[f59])).
0.22/0.44	tff(f59,plain,(
0.22/0.44	  ! [X0 : $int,X1 : collection] : ((count(X1) = count(add(X0,X1)) | ~in(X0,X1)) & (in(X0,X1) | count(X1) != count(add(X0,X1))))),
0.22/0.44	  inference(nnf_transformation,[],[f31])).
0.22/0.44	tff(f31,plain,(
0.22/0.44	  ! [X0 : $int,X1 : collection] : (count(X1) = count(add(X0,X1)) <=> in(X0,X1))),
0.22/0.44	  inference(rectify,[],[f8])).
0.22/0.44	tff(f8,axiom,(
0.22/0.44	  ! [X15 : $int,X16 : collection] : (count(add(X15,X16)) = count(X16) <=> in(X15,X16))),
0.22/0.44	  file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown)).
0.22/0.44	tff(f228,plain,(
0.22/0.44	  $sum(-1,count(sK1)) != $sum(-1,count(add(sK0,sK1))) | spl2_13),
0.22/0.44	  inference(avatar_component_clause,[],[f227])).
0.22/0.44	tff(f240,plain,(
0.22/0.44	  ~spl2_14 | spl2_9 | spl2_2 | ~spl2_7),
0.22/0.44	  inference(avatar_split_clause,[],[f220,f123,f95,f133,f237])).
0.22/0.44	tff(f95,plain,(
0.22/0.44	  spl2_2 <=> count(add(0,remove(sK0,sK1))) = count(remove(sK0,add(sK0,sK1)))),
0.22/0.44	  introduced(avatar_definition,[new_symbols(naming,[spl2_2])])).
0.22/0.44	tff(f220,plain,(
0.22/0.44	  count(sK1) != $sum(-1,count(add(sK0,sK1))) | in(sK0,sK1) | (spl2_2 | ~spl2_7)),
0.22/0.44	  inference(superposition,[],[f212,f63])).
0.22/0.44	tff(f63,plain,(
0.22/0.44	  ( ! [X0 : $int,X1 : collection] : (count(remove(X0,X1)) = count(X1) | in(X0,X1)) )),
0.22/0.44	  inference(cnf_transformation,[],[f45])).
0.22/0.44	tff(f45,plain,(
0.22/0.44	  ! [X0 : $int,X1 : collection] : ((~in(X0,X1) | count(remove(X0,X1)) != count(X1)) & (count(remove(X0,X1)) = count(X1) | in(X0,X1)))),
0.22/0.44	  inference(rectify,[],[f44])).
0.22/0.44	tff(f44,plain,(
0.22/0.44	  ! [X1 : $int,X0 : collection] : ((~in(X1,X0) | count(X0) != count(remove(X1,X0))) & (count(X0) = count(remove(X1,X0)) | in(X1,X0)))),
0.22/0.44	  inference(nnf_transformation,[],[f39])).
0.22/0.44	tff(f39,plain,(
0.22/0.44	  ! [X1 : $int,X0 : collection] : (~in(X1,X0) <=> count(X0) = count(remove(X1,X0)))),
0.22/0.44	  inference(rectify,[],[f9])).
0.22/0.44	tff(f9,axiom,(
0.22/0.44	  ! [X18 : collection,X17 : $int] : (~in(X17,X18) <=> count(remove(X17,X18)) = count(X18))),
0.22/0.44	  file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown)).
0.22/0.44	tff(f212,plain,(
0.22/0.44	  count(remove(sK0,sK1)) != $sum(-1,count(add(sK0,sK1))) | (spl2_2 | ~spl2_7)),
0.22/0.44	  inference(subsumption_resolution,[],[f210,f143])).
0.22/0.44	tff(f143,plain,(
0.22/0.44	  in(0,remove(sK0,sK1)) | ~spl2_7),
0.22/0.44	  inference(avatar_component_clause,[],[f123])).
0.22/0.44	tff(f210,plain,(
0.22/0.44	  ~in(0,remove(sK0,sK1)) | count(remove(sK0,sK1)) != $sum(-1,count(add(sK0,sK1))) | spl2_2),
0.22/0.44	  inference(superposition,[],[f170,f80])).
0.22/0.44	tff(f170,plain,(
0.22/0.44	  count(add(0,remove(sK0,sK1))) != $sum(-1,count(add(sK0,sK1))) | spl2_2),
0.22/0.44	  inference(forward_demodulation,[],[f169,f17])).
0.22/0.44	tff(f17,plain,(
0.22/0.44	  ( ! [X0 : $int,X1 : $int] : ($sum(X0,X1) = $sum(X1,X0)) )),
0.22/0.44	  introduced(theory_axiom_143,[])).
0.22/0.44	tff(f169,plain,(
0.22/0.44	  count(add(0,remove(sK0,sK1))) != $sum(count(add(sK0,sK1)),-1) | spl2_2),
0.22/0.44	  inference(subsumption_resolution,[],[f168,f73])).
0.22/0.44	tff(f73,plain,(
0.22/0.44	  ( ! [X0 : $int,X1 : collection] : (in(X0,add(X0,X1))) )),
0.22/0.44	  inference(cnf_transformation,[],[f53])).
0.22/0.44	tff(f53,plain,(
0.22/0.44	  ! [X0 : $int,X1 : collection] : in(X0,add(X0,X1))),
0.22/0.44	  inference(rectify,[],[f40])).
0.22/0.44	tff(f40,plain,(
0.22/0.44	  ! [X1 : $int,X0 : collection] : in(X1,add(X1,X0))),
0.22/0.44	  inference(rectify,[],[f2])).
0.22/0.44	tff(f2,axiom,(
0.22/0.44	  ! [X2 : collection,X1 : $int] : in(X1,add(X1,X2))),
0.22/0.44	  file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown)).
0.22/0.44	tff(f168,plain,(
0.22/0.44	  ~in(sK0,add(sK0,sK1)) | count(add(0,remove(sK0,sK1))) != $sum(count(add(sK0,sK1)),-1) | spl2_2),
0.22/0.44	  inference(superposition,[],[f96,f86])).
0.22/0.44	tff(f86,plain,(
0.22/0.44	  ( ! [X0 : collection,X1 : $int] : (count(remove(X1,X0)) = $sum(count(X0),-1) | ~in(X1,X0)) )),
0.22/0.44	  inference(evaluation,[],[f69])).
0.22/0.44	tff(f69,plain,(
0.22/0.44	  ( ! [X0 : collection,X1 : $int] : (~in(X1,X0) | count(remove(X1,X0)) = $sum(count(X0),$uminus(1))) )),
0.22/0.44	  inference(cnf_transformation,[],[f50])).
0.22/0.44	tff(f50,plain,(
0.22/0.44	  ! [X0 : collection,X1 : $int] : ((in(X1,X0) | count(remove(X1,X0)) != $sum(count(X0),$uminus(1))) & (count(remove(X1,X0)) = $sum(count(X0),$uminus(1)) | ~in(X1,X0)))),
0.22/0.44	  inference(rectify,[],[f49])).
0.22/0.44	tff(f49,plain,(
0.22/0.44	  ! [X1 : collection,X0 : $int] : ((in(X0,X1) | count(remove(X0,X1)) != $sum(count(X1),$uminus(1))) & (count(remove(X0,X1)) = $sum(count(X1),$uminus(1)) | ~in(X0,X1)))),
0.22/0.44	  inference(nnf_transformation,[],[f29])).
0.22/0.44	tff(f29,plain,(
0.22/0.44	  ! [X1 : collection,X0 : $int] : (in(X0,X1) <=> count(remove(X0,X1)) = $sum(count(X1),$uminus(1)))),
0.22/0.44	  inference(rectify,[],[f15])).
0.22/0.44	tff(f15,plain,(
0.22/0.44	  ! [X11 : $int,X12 : collection] : (in(X11,X12) <=> count(remove(X11,X12)) = $sum(count(X12),$uminus(1)))),
0.22/0.44	  inference(theory_normalization,[],[f6])).
0.22/0.44	tff(f6,axiom,(
0.22/0.44	  ! [X11 : $int,X12 : collection] : (in(X11,X12) <=> count(remove(X11,X12)) = $difference(count(X12),1))),
0.22/0.44	  file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown)).
0.22/0.44	tff(f96,plain,(
0.22/0.44	  count(add(0,remove(sK0,sK1))) != count(remove(sK0,add(sK0,sK1))) | spl2_2),
0.22/0.44	  inference(avatar_component_clause,[],[f95])).
0.22/0.44	tff(f229,plain,(
0.22/0.44	  ~spl2_9 | ~spl2_13 | spl2_2 | ~spl2_7),
0.22/0.44	  inference(avatar_split_clause,[],[f222,f123,f95,f227,f133])).
0.22/0.44	tff(f222,plain,(
0.22/0.44	  $sum(-1,count(sK1)) != $sum(-1,count(add(sK0,sK1))) | ~in(sK0,sK1) | (spl2_2 | ~spl2_7)),
0.22/0.44	  inference(forward_demodulation,[],[f221,f17])).
0.22/0.44	tff(f221,plain,(
0.22/0.44	  $sum(count(sK1),-1) != $sum(-1,count(add(sK0,sK1))) | ~in(sK0,sK1) | (spl2_2 | ~spl2_7)),
0.22/0.44	  inference(superposition,[],[f212,f86])).
0.22/0.44	tff(f219,plain,(
0.22/0.44	  spl2_12 | ~spl2_7),
0.22/0.44	  inference(avatar_split_clause,[],[f213,f123,f172])).
0.22/0.44	tff(f213,plain,(
0.22/0.44	  in(0,sK1) | ~spl2_7),
0.22/0.44	  inference(resolution,[],[f143,f76])).
0.22/0.44	tff(f76,plain,(
0.22/0.44	  ( ! [X2 : collection,X0 : $int,X1 : $int] : (~in(X0,remove(X1,X2)) | in(X0,X2)) )),
0.22/0.44	  inference(cnf_transformation,[],[f58])).
0.22/0.44	tff(f215,plain,(
0.22/0.44	  spl2_3 | ~spl2_7),
0.22/0.44	  inference(avatar_contradiction_clause,[],[f214])).
0.22/0.44	tff(f214,plain,(
0.22/0.44	  $false | (spl2_3 | ~spl2_7)),
0.22/0.44	  inference(subsumption_resolution,[],[f213,f198])).
0.22/0.44	tff(f198,plain,(
0.22/0.44	  ~in(0,sK1) | spl2_3),
0.22/0.44	  inference(resolution,[],[f101,f65])).
0.22/0.44	tff(f65,plain,(
0.22/0.44	  ( ! [X2 : $int,X0 : collection,X1 : $int] : (in(X1,add(X2,X0)) | ~in(X1,X0)) )),
0.22/0.44	  inference(cnf_transformation,[],[f48])).
0.22/0.44	tff(f48,plain,(
0.22/0.44	  ! [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))))),
0.22/0.44	  inference(rectify,[],[f47])).
0.22/0.44	tff(f47,plain,(
0.22/0.44	  ! [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))))),
0.22/0.44	  inference(flattening,[],[f46])).
0.22/0.44	tff(f46,plain,(
0.22/0.44	  ! [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))))),
0.22/0.44	  inference(nnf_transformation,[],[f36])).
0.22/0.44	tff(f36,plain,(
0.22/0.44	  ! [X1 : collection,X2 : $int,X0 : $int] : ((X0 = X2 | in(X2,X1)) <=> in(X2,add(X0,X1)))),
0.22/0.44	  inference(rectify,[],[f5])).
0.22/0.44	tff(f5,axiom,(
0.22/0.44	  ! [X10 : $int,X9 : collection,X8 : $int] : (in(X8,add(X10,X9)) <=> (X8 = X10 | in(X8,X9)))),
0.22/0.44	  file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown)).
0.22/0.44	tff(f101,plain,(
0.22/0.44	  ~in(0,add(sK0,sK1)) | spl2_3),
0.22/0.44	  inference(avatar_component_clause,[],[f100])).
0.22/0.44	tff(f100,plain,(
0.22/0.44	  spl2_3 <=> in(0,add(sK0,sK1))),
0.22/0.44	  introduced(avatar_definition,[new_symbols(naming,[spl2_3])])).
0.22/0.44	tff(f187,plain,(
0.22/0.44	  ~spl2_4 | ~spl2_7),
0.22/0.44	  inference(avatar_contradiction_clause,[],[f186])).
0.22/0.44	tff(f186,plain,(
0.22/0.44	  $false | (~spl2_4 | ~spl2_7)),
0.22/0.44	  inference(subsumption_resolution,[],[f185,f62])).
0.22/0.44	tff(f185,plain,(
0.22/0.44	  in(0,remove(0,sK1)) | (~spl2_4 | ~spl2_7)),
0.22/0.44	  inference(forward_demodulation,[],[f143,f104])).
0.22/0.44	tff(f104,plain,(
0.22/0.44	  0 = sK0 | ~spl2_4),
0.22/0.44	  inference(avatar_component_clause,[],[f103])).
0.22/0.44	tff(f103,plain,(
0.22/0.44	  spl2_4 <=> 0 = sK0),
0.22/0.44	  introduced(avatar_definition,[new_symbols(naming,[spl2_4])])).
0.22/0.44	tff(f184,plain,(
0.22/0.44	  ~spl2_1 | ~spl2_4),
0.22/0.44	  inference(avatar_contradiction_clause,[],[f183])).
0.22/0.44	tff(f183,plain,(
0.22/0.44	  $false | (~spl2_1 | ~spl2_4)),
0.22/0.44	  inference(subsumption_resolution,[],[f177,f62])).
0.22/0.44	tff(f177,plain,(
0.22/0.44	  in(0,remove(0,add(0,sK1))) | (~spl2_1 | ~spl2_4)),
0.22/0.44	  inference(backward_demodulation,[],[f107,f104])).
0.22/0.44	tff(f174,plain,(
0.22/0.44	  spl2_12 | spl2_4 | ~spl2_1),
0.22/0.44	  inference(avatar_split_clause,[],[f166,f92,f103,f172])).
0.22/0.44	tff(f166,plain,(
0.22/0.44	  0 = sK0 | in(0,sK1) | ~spl2_1),
0.22/0.44	  inference(resolution,[],[f163,f67])).
0.22/0.44	tff(f67,plain,(
0.22/0.44	  ( ! [X2 : $int,X0 : collection,X1 : $int] : (~in(X1,add(X2,X0)) | in(X1,X0) | X1 = X2) )),
0.22/0.44	  inference(cnf_transformation,[],[f48])).
0.22/0.44	tff(f163,plain,(
0.22/0.44	  in(0,add(sK0,sK1)) | ~spl2_1),
0.22/0.44	  inference(resolution,[],[f107,f76])).
0.22/0.44	tff(f162,plain,(
0.22/0.44	  ~spl2_9 | spl2_11),
0.22/0.44	  inference(avatar_split_clause,[],[f160,f145,f133])).
0.22/0.44	tff(f145,plain,(
0.22/0.44	  spl2_11 <=> count(add(sK0,sK1)) = $sum(1,count(remove(sK0,sK1)))),
0.22/0.44	  introduced(avatar_definition,[new_symbols(naming,[spl2_11])])).
0.22/0.44	tff(f160,plain,(
0.22/0.44	  ~in(sK0,sK1) | spl2_11),
0.22/0.44	  inference(trivial_inequality_removal,[],[f158])).
0.22/0.44	tff(f158,plain,(
0.22/0.44	  ~in(sK0,sK1) | count(sK1) != count(sK1) | spl2_11),
0.22/0.44	  inference(superposition,[],[f157,f80])).
0.22/0.44	tff(f157,plain,(
0.22/0.44	  count(add(sK0,sK1)) != count(sK1) | spl2_11),
0.22/0.44	  inference(subsumption_resolution,[],[f150,f79])).
0.22/0.44	tff(f79,plain,(
0.22/0.44	  ( ! [X0 : $int,X1 : collection] : (count(X1) != count(add(X0,X1)) | in(X0,X1)) )),
0.22/0.44	  inference(cnf_transformation,[],[f59])).
0.22/0.44	tff(f150,plain,(
0.22/0.44	  ~in(sK0,sK1) | count(add(sK0,sK1)) != count(sK1) | spl2_11),
0.22/0.44	  inference(evaluation,[],[f149])).
0.22/0.44	tff(f149,plain,(
0.22/0.44	  ~in(sK0,sK1) | count(add(sK0,sK1)) != $sum(1,$sum(count(sK1),-1)) | spl2_11),
0.22/0.44	  inference(superposition,[],[f146,f86])).
0.22/0.44	tff(f146,plain,(
0.22/0.44	  count(add(sK0,sK1)) != $sum(1,count(remove(sK0,sK1))) | spl2_11),
0.22/0.44	  inference(avatar_component_clause,[],[f145])).
0.22/0.44	tff(f156,plain,(
0.22/0.44	  spl2_9 | spl2_11),
0.22/0.44	  inference(avatar_contradiction_clause,[],[f155])).
0.22/0.44	tff(f155,plain,(
0.22/0.44	  $false | (spl2_9 | spl2_11)),
0.22/0.44	  inference(subsumption_resolution,[],[f154,f17])).
0.22/0.44	tff(f154,plain,(
0.22/0.44	  $sum(count(sK1),1) != $sum(1,count(sK1)) | (spl2_9 | spl2_11)),
0.22/0.44	  inference(subsumption_resolution,[],[f153,f134])).
0.22/0.44	tff(f153,plain,(
0.22/0.44	  in(sK0,sK1) | $sum(count(sK1),1) != $sum(1,count(sK1)) | (spl2_9 | spl2_11)),
0.22/0.44	  inference(superposition,[],[f151,f75])).
0.22/0.44	tff(f151,plain,(
0.22/0.44	  count(add(sK0,sK1)) != $sum(1,count(sK1)) | (spl2_9 | spl2_11)),
0.22/0.44	  inference(subsumption_resolution,[],[f148,f134])).
0.22/0.44	tff(f148,plain,(
0.22/0.44	  count(add(sK0,sK1)) != $sum(1,count(sK1)) | in(sK0,sK1) | spl2_11),
0.22/0.44	  inference(superposition,[],[f146,f63])).
0.22/0.44	tff(f147,plain,(
0.22/0.44	  spl2_7 | ~spl2_11 | spl2_5),
0.22/0.44	  inference(avatar_split_clause,[],[f118,f109,f145,f123])).
0.22/0.44	tff(f109,plain,(
0.22/0.44	  spl2_5 <=> count(add(0,remove(sK0,sK1))) = $sum(1,count(remove(sK0,add(sK0,sK1))))),
0.22/0.44	  introduced(avatar_definition,[new_symbols(naming,[spl2_5])])).
0.22/0.44	tff(f118,plain,(
0.22/0.44	  in(0,remove(sK0,sK1)) | count(add(sK0,sK1)) != $sum(1,count(remove(sK0,sK1))) | spl2_5),
0.22/0.44	  inference(forward_demodulation,[],[f117,f17])).
0.22/0.44	tff(f117,plain,(
0.22/0.44	  in(0,remove(sK0,sK1)) | count(add(sK0,sK1)) != $sum(count(remove(sK0,sK1)),1) | spl2_5),
0.22/0.44	  inference(superposition,[],[f115,f75])).
0.22/0.44	tff(f115,plain,(
0.22/0.44	  count(add(0,remove(sK0,sK1))) != count(add(sK0,sK1)) | spl2_5),
0.22/0.44	  inference(subsumption_resolution,[],[f114,f73])).
0.22/0.44	tff(f114,plain,(
0.22/0.44	  count(add(0,remove(sK0,sK1))) != count(add(sK0,sK1)) | ~in(sK0,add(sK0,sK1)) | spl2_5),
0.22/0.44	  inference(evaluation,[],[f113])).
0.22/0.44	tff(f113,plain,(
0.22/0.44	  ~in(sK0,add(sK0,sK1)) | count(add(0,remove(sK0,sK1))) != $sum(1,$sum(count(add(sK0,sK1)),-1)) | spl2_5),
0.22/0.44	  inference(superposition,[],[f110,f86])).
0.22/0.44	tff(f110,plain,(
0.22/0.44	  count(add(0,remove(sK0,sK1))) != $sum(1,count(remove(sK0,add(sK0,sK1)))) | spl2_5),
0.22/0.44	  inference(avatar_component_clause,[],[f109])).
0.22/0.44	tff(f111,plain,(
0.22/0.44	  spl2_1 | ~spl2_5),
0.22/0.44	  inference(avatar_split_clause,[],[f90,f109,f92])).
0.22/0.44	tff(f90,plain,(
0.22/0.44	  in(0,remove(sK0,add(sK0,sK1))) | count(add(0,remove(sK0,sK1))) != $sum(1,count(remove(sK0,add(sK0,sK1))))),
0.22/0.44	  inference(forward_demodulation,[],[f89,f17])).
0.22/0.44	tff(f89,plain,(
0.22/0.44	  in(0,remove(sK0,add(sK0,sK1))) | count(add(0,remove(sK0,sK1))) != $sum(count(remove(sK0,add(sK0,sK1))),1)),
0.22/0.44	  inference(superposition,[],[f71,f75])).
0.22/0.44	tff(f71,plain,(
0.22/0.44	  count(add(0,remove(sK0,add(sK0,sK1)))) != count(add(0,remove(sK0,sK1)))),
0.22/0.44	  inference(cnf_transformation,[],[f52])).
0.22/0.44	tff(f52,plain,(
0.22/0.44	  count(add(0,remove(sK0,add(sK0,sK1)))) != count(add(0,remove(sK0,sK1)))),
0.22/0.44	  inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f42,f51])).
0.22/0.44	tff(f51,plain,(
0.22/0.44	  ? [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)))),
0.22/0.44	  introduced(choice_axiom,[])).
0.22/0.44	tff(f42,plain,(
0.22/0.44	  ? [X0 : $int,X1 : collection] : count(add(0,remove(X0,add(X0,X1)))) != count(add(0,remove(X0,X1)))),
0.22/0.44	  inference(ennf_transformation,[],[f33])).
0.22/0.44	tff(f33,plain,(
0.22/0.44	  ~! [X1 : collection,X0 : $int] : count(add(0,remove(X0,add(X0,X1)))) = count(add(0,remove(X0,X1)))),
0.22/0.44	  inference(rectify,[],[f14])).
0.22/0.44	tff(f14,negated_conjecture,(
0.22/0.44	  ~! [X1 : $int,X0 : collection] : count(add(0,remove(X1,add(X1,X0)))) = count(add(0,remove(X1,X0)))),
0.22/0.44	  inference(negated_conjecture,[],[f13])).
0.22/0.44	tff(f13,conjecture,(
0.22/0.44	  ! [X1 : $int,X0 : collection] : count(add(0,remove(X1,add(X1,X0)))) = count(add(0,remove(X1,X0)))),
0.22/0.44	  file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown)).
0.22/0.44	tff(f105,plain,(
0.22/0.44	  ~spl2_3 | spl2_4 | spl2_1),
0.22/0.44	  inference(avatar_split_clause,[],[f98,f92,f103,f100])).
0.22/0.44	tff(f98,plain,(
0.22/0.44	  0 = sK0 | ~in(0,add(sK0,sK1)) | spl2_1),
0.22/0.44	  inference(resolution,[],[f93,f78])).
0.22/0.44	tff(f93,plain,(
0.22/0.44	  ~in(0,remove(sK0,add(sK0,sK1))) | spl2_1),
0.22/0.44	  inference(avatar_component_clause,[],[f92])).
0.22/0.44	tff(f97,plain,(
0.22/0.44	  ~spl2_1 | ~spl2_2),
0.22/0.44	  inference(avatar_split_clause,[],[f88,f95,f92])).
0.22/0.44	tff(f88,plain,(
0.22/0.44	  ~in(0,remove(sK0,add(sK0,sK1))) | count(add(0,remove(sK0,sK1))) != count(remove(sK0,add(sK0,sK1)))),
0.22/0.44	  inference(superposition,[],[f71,f80])).
0.22/0.44	% SZS output end Proof for theBenchmark
0.22/0.44	% (31315)------------------------------
0.22/0.44	% (31315)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
0.22/0.44	% (31315)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
0.22/0.44	% (31315)Termination reason: Refutation
0.22/0.44	
0.22/0.44	% (31315)Memory used [KB]: 907
0.22/0.44	% (31315)Time elapsed: 0.014 s
0.22/0.44	% (31315)Instructions burned: 18 (million)
0.22/0.44	% (31315)------------------------------
0.22/0.44	% (31315)------------------------------
0.22/0.44	% (31313)Success in time 0.073 s
0.22/0.44	EOF