%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT021_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 : n020.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 09:47:58 AM UTC 2026
% Result : Theorem 0.20s 0.31s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT021_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.18 % Computer : n020.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 00:06:34 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.21 Running first-order model finding
% 0.07/0.21 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
% 0.20/0.31 % (697250)Will run a generic schedule for satisfiability detection.
% 0.20/0.31 % (697257)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3519035441:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.31 % (697256)% WARNING: option uhcvi not known.
% 0.20/0.31 % (697255)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1765207457_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.31 % (697258)dis+10_1_sil=32000:sp=arity:random_seed=3036104445:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.31 % (697256)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1602516527:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.31 % (697259)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4082625590:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.31 % (697255)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.20/0.31 % (697261)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=678157655:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.31 % (697255)Terminated due to inappropriate strategy.
% 0.20/0.31 % (697255)------------------------------
% 0.20/0.31 % (697255)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.31 % (697255)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.31 % (697255)CaDiCaL version: 2.1.3
% 0.20/0.31 % (697255)Termination reason: Inappropriate
% 0.20/0.31 % (697255)Time elapsed: 0.001 s
% 0.20/0.31 % (697260)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2213648943:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.31 % (697255)Peak memory usage: 10 MB
% 0.20/0.31 % (697255)------------------------------
% 0.20/0.31 % (697255)------------------------------
% 0.20/0.31 % (697269)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=827981175:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.20/0.31 % (697269)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.20/0.31 % (697269)Terminated due to inappropriate strategy.
% 0.20/0.31 % (697269)------------------------------
% 0.20/0.31 % (697269)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.31 % (697269)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.31 % (697269)CaDiCaL version: 2.1.3
% 0.20/0.31 % (697269)Termination reason: Inappropriate
% 0.20/0.31 % (697269)Time elapsed: 0.0000 s
% 0.20/0.31 % (697269)Peak memory usage: 10 MB
% 0.20/0.31 % (697269)------------------------------
% 0.20/0.31 % (697269)------------------------------
% 0.20/0.31 % (697271)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2648074448:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.31 % (697260) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-697250-697260"...
% 0.20/0.31 % (697260)...printing done.
% 0.20/0.31 % (697260)Refutation found. Thanks to Tanya!
% 0.20/0.31 % SZS status Theorem for theBenchmark
% 0.20/0.31 % SZS output start Proof for theBenchmark
% 0.20/0.31 tff(type_def_5, type, collection: $tType).
% 0.20/0.31 tff(func_def_0, type, empty: collection).
% 0.20/0.31 tff(func_def_1, type, add: ($int * collection) > collection).
% 0.20/0.31 tff(func_def_2, type, remove: ($int * collection) > collection).
% 0.20/0.31 tff(func_def_10, type, sK0: collection).
% 0.20/0.31 tff(func_def_11, type, sK1: $int).
% 0.20/0.31 tff(func_def_12, type, sK2: $int).
% 0.20/0.31 tff(pred_def_1, type, in: ($int * collection) > $o).
% 0.20/0.31 tff(f1,axiom,(
% 0.20/0.31 ! [X0 : $int] : ~in(X0,empty)),
% 0.20/0.31 file('/export/starexec/sandbox/benchmark/Axioms/DAT002_0.ax',ax1)).
% 0.20/0.31 tff(f4,axiom,(
% 0.20/0.31 ! [X0 : $int,X1 : collection,X2 : $int] : ((in(X0,X1) | X0 = X2) <=> in(X0,add(X2,X1)))),
% 0.20/0.31 file('/export/starexec/sandbox/benchmark/Axioms/DAT002_0.ax',ax4)).
% 0.20/0.31 tff(f6,conjecture,(
% 0.20/0.31 ! [X0 : collection,X1 : $int,X2 : $int] : ((X0 = add(5,add(3,add(1,empty))) & in(X1,X0) & in(X2,X0) & X1 != X2) => $less($sum(X1,X2),9))),
% 0.20/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1)).
% 0.20/0.31 tff(f7,negated_conjecture,(
% 0.20/0.31 ~ ! [X0 : collection,X1 : $int,X2 : $int] : ((X0 = add(5,add(3,add(1,empty))) & in(X1,X0) & in(X2,X0) & X1 != X2) => $less($sum(X1,X2),9))),
% 0.20/0.31 inference(negated_conjecture,[status(cth)],[f6])).
% 0.20/0.31 tff(f8,definition,(
% 0.20/0.31 ( ! [X0 : $int,X1 : $int] : ($sum(X0,X1) = $sum(X1,X0)) )),
% 0.20/0.31 introduced(theory,[tha_commutativity])).
% 0.20/0.31 tff(f9,definition,(
% 0.20/0.31 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2)) )),
% 0.20/0.31 introduced(theory,[tha_associativity])).
% 0.20/0.31 tff(f11,definition,(
% 0.20/0.31 ( ! [X0 : $int,X1 : $int] : ($uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0))) )),
% 0.20/0.31 introduced(theory,[tha_inverse_op_op_inverses])).
% 0.20/0.31 tff(f12,definition,(
% 0.20/0.31 ( ! [X0 : $int] : (0 = $sum(X0,$uminus(X0))) )),
% 0.20/0.31 introduced(theory,[tha_inverse_op_unit])).
% 0.20/0.31 tff(f15,definition,(
% 0.20/0.31 ( ! [X0 : $int,X1 : $int] : ($less(X0,X1) | $less(X1,X0) | X0 = X1) )),
% 0.20/0.31 introduced(theory,[tha_order_totality])).
% 0.20/0.31 tff(f17,definition,(
% 0.20/0.31 ( ! [X0 : $int,X1 : $int] : ($less(X0,X1) | $less(X1,$sum(X0,1))) )),
% 0.20/0.31 introduced(theory,[tha_order_plus_one_dichotomy])).
% 0.20/0.31 tff(f19,definition,(
% 0.20/0.31 ( ! [X0 : $int,X1 : $int] : (~$less(X0,X1) | ~$less(X1,$sum(X0,1))) )),
% 0.20/0.31 introduced(theory,[tha_extra_integer_ordering])).
% 0.20/0.31 tff(f20,plain,(
% 0.20/0.31 ? [X0 : collection,X1 : $int,X2 : $int] : (~$less($sum(X1,X2),9) & (X0 = add(5,add(3,add(1,empty))) & in(X1,X0) & in(X2,X0) & X1 != X2))),
% 0.20/0.31 inference(ennf_transformation,[],[f7])).
% 0.20/0.31 tff(f21,plain,(
% 0.20/0.31 ? [X0 : collection,X1 : $int,X2 : $int] : (~$less($sum(X1,X2),9) & X0 = add(5,add(3,add(1,empty))) & in(X1,X0) & in(X2,X0) & X1 != X2)),
% 0.20/0.31 inference(flattening,[],[f20])).
% 0.20/0.31 tff(f22,plain,(
% 0.20/0.31 ! [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)))),
% 0.20/0.31 inference(nnf_transformation,[],[f4])).
% 0.20/0.31 tff(f23,plain,(
% 0.20/0.31 ! [X0 : $int,X1 : collection,X2 : $int] : ((in(X0,X1) | X0 = X2 | ~in(X0,add(X2,X1))) & (in(X0,add(X2,X1)) | (~in(X0,X1) & X0 != X2)))),
% 0.20/0.31 inference(flattening,[],[f22])).
% 0.20/0.31 tff(f26,plain,(
% 0.20/0.31 ~$less($sum(sK1,sK2),9) & add(5,add(3,add(1,empty))) = sK0 & in(sK1,sK0) & in(sK2,sK0) & sK1 != sK2),
% 0.20/0.31 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f21])).
% 0.20/0.31 tff(f27,plain,(
% 0.20/0.31 ( ! [X0 : $int] : (~in(X0,empty)) )),
% 0.20/0.31 inference(cnf_transformation,[],[f1])).
% 0.20/0.31 tff(f32,plain,(
% 0.20/0.31 ( ! [X2 : $int,X0 : $int,X1 : collection] : (~in(X0,add(X2,X1)) | X0 = X2 | in(X0,X1)) )),
% 0.20/0.31 inference(cnf_transformation,[],[f23])).
% 0.20/0.31 tff(f36,plain,(
% 0.20/0.31 sK1 != sK2),
% 0.20/0.31 inference(cnf_transformation,[],[f26])).
% 0.20/0.31 tff(f37,plain,(
% 0.20/0.31 in(sK2,sK0)),
% 0.20/0.31 inference(cnf_transformation,[],[f26])).
% 0.20/0.31 tff(f38,plain,(
% 0.20/0.31 in(sK1,sK0)),
% 0.20/0.31 inference(cnf_transformation,[],[f26])).
% 0.20/0.31 tff(f39,plain,(
% 0.20/0.31 add(5,add(3,add(1,empty))) = sK0),
% 0.20/0.31 inference(cnf_transformation,[],[f26])).
% 0.20/0.31 tff(f40,plain,(
% 0.20/0.31 ~$less($sum(sK1,sK2),9)),
% 0.20/0.31 inference(cnf_transformation,[],[f26])).
% 0.20/0.31 tff(f41,plain,(
% 0.20/0.31 in(sK1,add(5,add(3,add(1,empty))))),
% 0.20/0.31 inference(superposition,[],[f38,f39])).
% 0.20/0.31 tff(f42,plain,(
% 0.20/0.31 in(sK2,add(5,add(3,add(1,empty))))),
% 0.20/0.31 inference(superposition,[],[f37,f39])).
% 0.20/0.31 tff(f49,plain,(
% 0.20/0.31 $less(9,$sum($sum(sK1,sK2),1))),
% 0.20/0.31 inference(resolution,[],[f17,f40])).
% 0.20/0.31 tff(f53,plain,(
% 0.20/0.31 $less(9,$sum(1,$sum(sK1,sK2)))),
% 0.20/0.31 inference(forward_demodulation,[],[f49,f8])).
% 0.20/0.31 tff(f56,plain,(
% 0.20/0.31 ~$less($sum(1,$sum(sK1,sK2)),$sum(9,1))),
% 0.20/0.31 inference(resolution,[],[f19,f53])).
% 0.20/0.31 tff(f57,plain,(
% 0.20/0.31 ~$less($sum(1,$sum(sK1,sK2)),10)),
% 0.20/0.31 inference(evaluation,[],[f56])).
% 0.20/0.31 tff(f58,plain,(
% 0.20/0.31 $less(10,$sum($sum(1,$sum(sK1,sK2)),1))),
% 0.20/0.31 inference(resolution,[],[f57,f17])).
% 0.20/0.31 tff(f59,plain,(
% 0.20/0.31 $less(10,$sum(1,$sum(1,$sum(sK1,sK2))))),
% 0.20/0.31 inference(forward_demodulation,[],[f58,f8])).
% 0.20/0.31 tff(f82,plain,(
% 0.20/0.31 $less(9,$sum(sK1,sK2)) | 9 = $sum(sK1,sK2)),
% 0.20/0.31 inference(resolution,[],[f15,f40])).
% 0.20/0.31 tff(f113,definition,(
% 0.20/0.31 spl3_5 <=> 9 = $sum(sK1,sK2)),
% 0.20/0.31 introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition])).
% 0.20/0.31 tff(f115,plain,(
% 0.20/0.31 9 = $sum(sK1,sK2) | ~spl3_5),
% 0.20/0.31 inference(avatar_component_clause,[],[f113])).
% 0.20/0.31 tff(f117,definition,(
% 0.20/0.31 spl3_6 <=> $less(9,$sum(sK1,sK2))),
% 0.20/0.31 introduced(definition,[new_symbols(definition,[spl3_6])],[avatar_definition])).
% 0.20/0.31 tff(f119,plain,(
% 0.20/0.31 $less(9,$sum(sK1,sK2)) | ~spl3_6),
% 0.20/0.31 inference(avatar_component_clause,[],[f117])).
% 0.20/0.31 tff(f123,plain,(
% 0.20/0.31 spl3_5 | spl3_6),
% 0.20/0.31 inference(avatar_split_clause,[],[f82,f117,f113])).
% 0.20/0.31 tff(f135,plain,(
% 0.20/0.31 $sum($uminus(sK2),$uminus(sK1)) = $uminus(9) | ~spl3_5),
% 0.20/0.31 inference(superposition,[],[f11,f115])).
% 0.20/0.31 tff(f138,plain,(
% 0.20/0.31 $sum($uminus(sK2),$uminus(sK1)) = -9 | ~spl3_5),
% 0.20/0.31 inference(evaluation,[],[f135])).
% 0.20/0.31 tff(f142,plain,(
% 0.20/0.31 -9 = $sum($uminus(sK1),$uminus(sK2)) | ~spl3_5),
% 0.20/0.31 inference(forward_demodulation,[],[f138,f8])).
% 0.20/0.31 tff(f175,plain,(
% 0.20/0.31 ( ! [X0 : $int,X1 : $int] : ($sum(0,X1) = $sum(X0,$sum($uminus(X0),X1))) )),
% 0.20/0.31 inference(superposition,[],[f9,f12])).
% 0.20/0.31 tff(f177,plain,(
% 0.20/0.31 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($sum($sum(X0,X1),X2) = $sum(X1,$sum(X0,X2))) )),
% 0.20/0.31 inference(superposition,[],[f9,f8])).
% 0.20/0.31 tff(f186,plain,(
% 0.20/0.31 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($sum(X0,$sum(X1,X2)) = $sum(X2,$sum(X0,X1))) )),
% 0.20/0.31 inference(superposition,[],[f8,f9])).
% 0.20/0.31 tff(f190,plain,(
% 0.20/0.31 ( ! [X0 : $int,X1 : $int] : ($sum(X0,$sum($uminus(X0),X1)) = X1) )),
% 0.20/0.31 inference(evaluation,[],[f175])).
% 0.20/0.31 tff(f201,plain,(
% 0.20/0.31 5 = sK1 | in(sK1,add(3,add(1,empty)))),
% 0.20/0.31 inference(resolution,[],[f32,f41])).
% 0.20/0.31 tff(f202,plain,(
% 0.20/0.31 5 = sK2 | in(sK2,add(3,add(1,empty)))),
% 0.20/0.31 inference(resolution,[],[f32,f42])).
% 0.20/0.31 tff(f207,definition,(
% 0.20/0.31 spl3_7 <=> in(sK2,add(3,add(1,empty)))),
% 0.20/0.31 introduced(definition,[new_symbols(definition,[spl3_7])],[avatar_definition])).
% 0.20/0.31 tff(f209,plain,(
% 0.20/0.31 in(sK2,add(3,add(1,empty))) | ~spl3_7),
% 0.20/0.31 inference(avatar_component_clause,[],[f207])).
% 0.20/0.31 tff(f211,definition,(
% 0.20/0.31 spl3_8 <=> 5 = sK2),
% 0.20/0.31 introduced(definition,[new_symbols(definition,[spl3_8])],[avatar_definition])).
% 0.20/0.31 tff(f213,plain,(
% 0.20/0.31 5 = sK2 | ~spl3_8),
% 0.20/0.31 inference(avatar_component_clause,[],[f211])).
% 0.20/0.31 tff(f214,plain,(
% 0.20/0.31 spl3_7 | spl3_8),
% 0.20/0.31 inference(avatar_split_clause,[],[f202,f211,f207])).
% 0.20/0.31 tff(f216,definition,(
% 0.20/0.31 spl3_9 <=> in(sK1,add(3,add(1,empty)))),
% 0.20/0.31 introduced(definition,[new_symbols(definition,[spl3_9])],[avatar_definition])).
% 0.20/0.31 tff(f218,plain,(
% 0.20/0.31 in(sK1,add(3,add(1,empty))) | ~spl3_9),
% 0.20/0.31 inference(avatar_component_clause,[],[f216])).
% 0.20/0.31 tff(f220,definition,(
% 0.20/0.31 spl3_10 <=> 5 = sK1),
% 0.20/0.31 introduced(definition,[new_symbols(definition,[spl3_10])],[avatar_definition])).
% 0.20/0.31 tff(f222,plain,(
% 0.20/0.31 5 = sK1 | ~spl3_10),
% 0.20/0.31 inference(avatar_component_clause,[],[f220])).
% 0.20/0.31 tff(f223,plain,(
% 0.20/0.31 spl3_9 | spl3_10),
% 0.20/0.31 inference(avatar_split_clause,[],[f201,f220,f216])).
% 0.20/0.31 tff(f237,plain,(
% 0.20/0.31 3 = sK2 | in(sK2,add(1,empty)) | ~spl3_7),
% 0.20/0.31 inference(resolution,[],[f209,f32])).
% 0.20/0.31 tff(f241,definition,(
% 0.20/0.31 spl3_11 <=> in(sK2,add(1,empty))),
% 0.20/0.31 introduced(definition,[new_symbols(definition,[spl3_11])],[avatar_definition])).
% 0.20/0.31 tff(f243,plain,(
% 0.20/0.31 in(sK2,add(1,empty)) | ~spl3_11),
% 0.20/0.31 inference(avatar_component_clause,[],[f241])).
% 0.20/0.31 tff(f245,definition,(
% 0.20/0.31 spl3_12 <=> 3 = sK2),
% 0.20/0.31 introduced(definition,[new_symbols(definition,[spl3_12])],[avatar_definition])).
% 0.20/0.31 tff(f247,plain,(
% 0.20/0.31 3 = sK2 | ~spl3_12),
% 0.20/0.31 inference(avatar_component_clause,[],[f245])).
% 0.20/0.31 tff(f248,plain,(
% 0.20/0.31 spl3_11 | spl3_12 | ~spl3_7),
% 0.20/0.31 inference(avatar_split_clause,[],[f237,f207,f245,f241])).
% 0.20/0.31 tff(f260,plain,(
% 0.20/0.31 5 != sK1 | ~spl3_8),
% 0.20/0.31 inference(superposition,[],[f36,f213])).
% 0.20/0.31 tff(f282,plain,(
% 0.20/0.31 ~spl3_10 | ~spl3_8),
% 0.20/0.31 inference(avatar_split_clause,[],[f260,f211,f220])).
% 0.20/0.31 tff(f316,plain,(
% 0.20/0.31 $uminus(sK2) = $sum(sK1,-9) | ~spl3_5),
% 0.20/0.31 inference(superposition,[],[f190,f142])).
% 0.20/0.31 tff(f332,plain,(
% 0.20/0.31 $uminus(sK2) = $sum(-9,sK1) | ~spl3_5),
% 0.20/0.31 inference(forward_demodulation,[],[f316,f8])).
% 0.20/0.31 tff(f429,plain,(
% 0.20/0.31 3 = sK1 | in(sK1,add(1,empty)) | ~spl3_9),
% 0.20/0.31 inference(resolution,[],[f218,f32])).
% 0.20/0.31 tff(f433,definition,(
% 0.20/0.31 spl3_13 <=> in(sK1,add(1,empty))),
% 0.20/0.31 introduced(definition,[new_symbols(definition,[spl3_13])],[avatar_definition])).
% 0.20/0.31 tff(f435,plain,(
% 0.20/0.31 in(sK1,add(1,empty)) | ~spl3_13),
% 0.20/0.31 inference(avatar_component_clause,[],[f433])).
% 0.20/0.31 tff(f437,definition,(
% 0.20/0.31 spl3_14 <=> 3 = sK1),
% 0.20/0.31 introduced(definition,[new_symbols(definition,[spl3_14])],[avatar_definition])).
% 0.20/0.31 tff(f439,plain,(
% 0.20/0.31 3 = sK1 | ~spl3_14),
% 0.20/0.31 inference(avatar_component_clause,[],[f437])).
% 0.20/0.31 tff(f440,plain,(
% 0.20/0.31 spl3_13 | spl3_14 | ~spl3_9),
% 0.20/0.31 inference(avatar_split_clause,[],[f429,f216,f437,f433])).
% 0.20/0.31 tff(f588,plain,(
% 0.20/0.31 ( ! [X2 : $int,X3 : $int,X0 : $int,X1 : $int] : ($sum($sum(X0,$sum(X1,X2)),X3) = $sum(X2,$sum($sum(X0,X1),X3))) )),
% 0.20/0.31 inference(superposition,[],[f177,f9])).
% 0.20/0.31 tff(f631,plain,(
% 0.20/0.31 ( ! [X2 : $int,X3 : $int,X0 : $int,X1 : $int] : ($sum($sum(X0,$sum(X1,X2)),X3) = $sum(X2,$sum(X0,$sum(X1,X3)))) )),
% 0.20/0.31 inference(forward_demodulation,[],[f588,f9])).
% 0.20/0.31 tff(f645,plain,(
% 0.20/0.31 ( ! [X2 : $int,X3 : $int,X0 : $int,X1 : $int] : ($sum(X0,$sum($sum(X1,X2),X3)) = $sum(X2,$sum(X0,$sum(X1,X3)))) )),
% 0.20/0.31 inference(forward_demodulation,[],[f631,f9])).
% 0.20/0.31 tff(f655,plain,(
% 0.20/0.31 ( ! [X2 : $int,X3 : $int,X0 : $int,X1 : $int] : ($sum(X0,$sum(X1,$sum(X2,X3))) = $sum(X2,$sum(X0,$sum(X1,X3)))) )),
% 0.20/0.31 inference(forward_demodulation,[],[f645,f9])).
% 0.20/0.31 tff(f710,plain,(
% 0.20/0.31 ( ! [X2 : $int,X3 : $int,X0 : $int,X1 : $int] : ($sum(X3,$sum(X0,$sum(X1,X2))) = $sum(X2,$sum(X3,$sum(X0,X1)))) )),
% 0.20/0.31 inference(superposition,[],[f186,f9])).
% 0.20/0.31 tff(f830,plain,(
% 0.20/0.31 1 = sK2 | in(sK2,empty) | ~spl3_11),
% 0.20/0.31 inference(resolution,[],[f243,f32])).
% 0.20/0.31 tff(f836,plain,(
% 0.20/0.31 1 = sK2 | ~spl3_11),
% 0.20/0.31 inference(forward_subsumption_resolution,[],[f830,f27])).
% 0.20/0.31 tff(f853,plain,(
% 0.20/0.31 1 != sK1 | ~spl3_11),
% 0.20/0.31 inference(superposition,[],[f36,f836])).
% 0.20/0.31 tff(f855,plain,(
% 0.20/0.31 ~$less($sum(sK1,1),9) | ~spl3_11),
% 0.20/0.31 inference(superposition,[],[f40,f836])).
% 0.20/0.31 tff(f883,plain,(
% 0.20/0.31 ~$less($sum(1,sK1),9) | ~spl3_11),
% 0.20/0.31 inference(forward_demodulation,[],[f855,f8])).
% 0.20/0.31 tff(f906,plain,(
% 0.20/0.31 ~$less($sum(1,5),9) | (~spl3_10 | ~spl3_11)),
% 0.20/0.31 inference(forward_demodulation,[],[f883,f222])).
% 0.20/0.31 tff(f907,plain,(
% 0.20/0.31 $false | (~spl3_10 | ~spl3_11)),
% 0.20/0.31 inference(evaluation,[],[f906])).
% 0.20/0.31 tff(f908,plain,(
% 0.20/0.31 ~spl3_10 | ~spl3_11),
% 0.20/0.31 inference(avatar_contradiction_clause,[],[f907])).
% 0.20/0.31 tff(f998,plain,(
% 0.20/0.31 $less(10,$sum(1,$sum(1,$sum(sK1,3)))) | ~spl3_12),
% 0.20/0.31 inference(superposition,[],[f59,f247])).
% 0.20/0.31 tff(f1018,plain,(
% 0.20/0.31 $less(10,$sum(3,$sum(1,$sum(1,sK1)))) | ~spl3_12),
% 0.20/0.31 inference(forward_demodulation,[],[f998,f710])).
% 0.20/0.31 tff(f1032,plain,(
% 0.20/0.31 $less(10,$sum(1,$sum(3,$sum(1,sK1)))) | ~spl3_12),
% 0.20/0.31 inference(forward_demodulation,[],[f1018,f655])).
% 0.20/0.31 tff(f1041,plain,(
% 0.20/0.31 $less(10,$sum(1,$sum(1,$sum(3,sK1)))) | ~spl3_12),
% 0.20/0.31 inference(forward_demodulation,[],[f1032,f655])).
% 0.20/0.31 tff(f1051,plain,(
% 0.20/0.31 $less(10,$sum(1,$sum(1,$sum(3,5)))) | (~spl3_10 | ~spl3_12)),
% 0.20/0.31 inference(forward_demodulation,[],[f1041,f222])).
% 0.20/0.31 tff(f1052,plain,(
% 0.20/0.31 $false | (~spl3_10 | ~spl3_12)),
% 0.20/0.31 inference(evaluation,[],[f1051])).
% 0.20/0.31 tff(f1053,plain,(
% 0.20/0.31 ~spl3_10 | ~spl3_12),
% 0.20/0.31 inference(avatar_contradiction_clause,[],[f1052])).
% 0.20/0.31 tff(f1382,plain,(
% 0.20/0.31 1 = sK1 | in(sK1,empty) | ~spl3_13),
% 0.20/0.31 inference(resolution,[],[f435,f32])).
% 0.20/0.31 tff(f1385,plain,(
% 0.20/0.31 in(sK1,empty) | (~spl3_11 | ~spl3_13)),
% 0.20/0.31 inference(forward_subsumption_resolution,[],[f1382,f853])).
% 0.20/0.31 tff(f1386,plain,(
% 0.20/0.31 $false | (~spl3_11 | ~spl3_13)),
% 0.20/0.31 inference(forward_subsumption_resolution,[],[f1385,f27])).
% 0.20/0.31 tff(f1387,plain,(
% 0.20/0.31 ~spl3_11 | ~spl3_13),
% 0.20/0.31 inference(avatar_contradiction_clause,[],[f1386])).
% 0.20/0.31 tff(f1395,plain,(
% 0.20/0.31 ~$less($sum(3,sK2),9) | ~spl3_14),
% 0.20/0.31 inference(superposition,[],[f40,f439])).
% 0.20/0.31 tff(f1429,plain,(
% 0.20/0.31 ~$less($sum(3,1),9) | (~spl3_11 | ~spl3_14)),
% 0.20/0.31 inference(forward_demodulation,[],[f1395,f836])).
% 0.20/0.31 tff(f1430,plain,(
% 0.20/0.31 $false | (~spl3_11 | ~spl3_14)),
% 0.20/0.31 inference(evaluation,[],[f1429])).
% 0.20/0.31 tff(f1431,plain,(
% 0.20/0.31 ~spl3_11 | ~spl3_14),
% 0.20/0.31 inference(avatar_contradiction_clause,[],[f1430])).
% 0.20/0.31 tff(f1440,plain,(
% 0.20/0.31 $uminus(sK2) = $sum(-9,3) | (~spl3_5 | ~spl3_14)),
% 0.20/0.31 inference(forward_demodulation,[],[f332,f439])).
% 0.20/0.31 tff(f1441,plain,(
% 0.20/0.31 $uminus(sK2) = -6 | (~spl3_5 | ~spl3_14)),
% 0.20/0.31 inference(evaluation,[],[f1440])).
% 0.20/0.31 tff(f1484,plain,(
% 0.20/0.31 ~$less($sum(3,5),9) | (~spl3_8 | ~spl3_14)),
% 0.20/0.31 inference(forward_demodulation,[],[f1395,f213])).
% 0.20/0.31 tff(f1485,plain,(
% 0.20/0.31 $false | (~spl3_8 | ~spl3_14)),
% 0.20/0.31 inference(evaluation,[],[f1484])).
% 0.20/0.31 tff(f1486,plain,(
% 0.20/0.31 ~spl3_8 | ~spl3_14),
% 0.20/0.31 inference(avatar_contradiction_clause,[],[f1485])).
% 0.20/0.31 tff(f1487,plain,(
% 0.20/0.31 $uminus(5) = -6 | (~spl3_5 | ~spl3_8 | ~spl3_14)),
% 0.20/0.31 inference(forward_demodulation,[],[f1441,f213])).
% 0.20/0.31 tff(f1488,plain,(
% 0.20/0.31 $false | (~spl3_5 | ~spl3_8 | ~spl3_14)),
% 0.20/0.31 inference(evaluation,[],[f1487])).
% 0.20/0.31 tff(f1489,plain,(
% 0.20/0.31 ~spl3_5 | ~spl3_8 | ~spl3_14),
% 0.20/0.31 inference(avatar_contradiction_clause,[],[f1488])).
% 0.20/0.31 tff(f1576,plain,(
% 0.20/0.31 ~$less($sum(3,3),9) | (~spl3_12 | ~spl3_14)),
% 0.20/0.31 inference(forward_demodulation,[],[f1395,f247])).
% 0.20/0.31 tff(f1577,plain,(
% 0.20/0.31 $false | (~spl3_12 | ~spl3_14)),
% 0.20/0.31 inference(evaluation,[],[f1576])).
% 0.20/0.31 tff(f1578,plain,(
% 0.20/0.31 ~spl3_12 | ~spl3_14),
% 0.20/0.31 inference(avatar_contradiction_clause,[],[f1577])).
% 0.20/0.31 tff(f1579,plain,(
% 0.20/0.31 -6 = $uminus(3) | (~spl3_5 | ~spl3_12 | ~spl3_14)),
% 0.20/0.31 inference(forward_demodulation,[],[f1441,f247])).
% 0.20/0.31 tff(f1580,plain,(
% 0.20/0.31 $false | (~spl3_5 | ~spl3_12 | ~spl3_14)),
% 0.20/0.31 inference(evaluation,[],[f1579])).
% 0.20/0.31 tff(f1581,plain,(
% 0.20/0.31 ~spl3_5 | ~spl3_12 | ~spl3_14),
% 0.20/0.31 inference(avatar_contradiction_clause,[],[f1580])).
% 0.20/0.31 tff(f1624,plain,(
% 0.20/0.31 $less(10,$sum(1,$sum(1,$sum(sK1,3)))) | ~spl3_12),
% 0.20/0.31 inference(superposition,[],[f59,f247])).
% 0.20/0.31 tff(f1636,plain,(
% 0.20/0.31 $less(10,$sum(3,$sum(1,$sum(1,sK1)))) | ~spl3_12),
% 0.20/0.31 inference(forward_demodulation,[],[f1624,f710])).
% 0.20/0.31 tff(f1643,plain,(
% 0.20/0.31 $less(10,$sum(1,$sum(3,$sum(1,sK1)))) | ~spl3_12),
% 0.20/0.31 inference(forward_demodulation,[],[f1636,f655])).
% 0.20/0.31 tff(f1650,plain,(
% 0.20/0.31 $less(10,$sum(1,$sum(1,$sum(3,sK1)))) | ~spl3_12),
% 0.20/0.31 inference(forward_demodulation,[],[f1643,f655])).
% 0.20/0.31 tff(f1686,plain,(
% 0.20/0.31 1 = sK1 | in(sK1,empty) | ~spl3_13),
% 0.20/0.31 inference(resolution,[],[f435,f32])).
% 0.20/0.31 tff(f1689,plain,(
% 0.20/0.31 1 = sK1 | ~spl3_13),
% 0.20/0.31 inference(forward_subsumption_resolution,[],[f1686,f27])).
% 0.20/0.31 tff(f1812,plain,(
% 0.20/0.31 $less(9,$sum(sK1,3)) | (~spl3_6 | ~spl3_12)),
% 0.20/0.31 inference(forward_demodulation,[],[f119,f247])).
% 0.20/0.31 tff(f1835,plain,(
% 0.20/0.31 $less(10,$sum(1,$sum(1,$sum(3,1)))) | (~spl3_12 | ~spl3_13)),
% 0.20/0.31 inference(forward_demodulation,[],[f1650,f1689])).
% 0.20/0.31 tff(f1836,plain,(
% 0.20/0.31 $false | (~spl3_12 | ~spl3_13)),
% 0.20/0.31 inference(evaluation,[],[f1835])).
% 0.20/0.31 tff(f1837,plain,(
% 0.20/0.31 ~spl3_12 | ~spl3_13),
% 0.20/0.31 inference(avatar_contradiction_clause,[],[f1836])).
% 0.20/0.31 tff(f1839,plain,(
% 0.20/0.31 $less(9,$sum(3,sK1)) | (~spl3_6 | ~spl3_12)),
% 0.20/0.31 inference(forward_demodulation,[],[f1812,f8])).
% 0.20/0.31 tff(f1849,plain,(
% 0.20/0.31 $less(9,$sum(3,1)) | (~spl3_6 | ~spl3_12 | ~spl3_13)),
% 0.20/0.31 inference(forward_demodulation,[],[f1839,f1689])).
% 0.20/0.31 tff(f1850,plain,(
% 0.20/0.31 $false | (~spl3_6 | ~spl3_12 | ~spl3_13)),
% 0.20/0.31 inference(evaluation,[],[f1849])).
% 0.20/0.31 tff(f1851,plain,(
% 0.20/0.31 ~spl3_6 | ~spl3_12 | ~spl3_13),
% 0.20/0.31 inference(avatar_contradiction_clause,[],[f1850])).
% 0.20/0.31 tff(f1883,plain,(
% 0.20/0.31 $less(9,$sum(sK1,5)) | (~spl3_6 | ~spl3_8)),
% 0.20/0.31 inference(forward_demodulation,[],[f119,f213])).
% 0.20/0.31 tff(f1893,plain,(
% 0.20/0.31 $less(9,$sum(5,sK1)) | (~spl3_6 | ~spl3_8)),
% 0.20/0.31 inference(forward_demodulation,[],[f1883,f8])).
% 0.20/0.31 tff(f1903,plain,(
% 0.20/0.31 $less(9,$sum(5,1)) | (~spl3_6 | ~spl3_8 | ~spl3_13)),
% 0.20/0.31 inference(forward_demodulation,[],[f1893,f1689])).
% 0.20/0.31 tff(f1904,plain,(
% 0.20/0.31 $false | (~spl3_6 | ~spl3_8 | ~spl3_13)),
% 0.20/0.31 inference(evaluation,[],[f1903])).
% 0.20/0.31 tff(f1905,plain,(
% 0.20/0.31 ~spl3_6 | ~spl3_8 | ~spl3_13),
% 0.20/0.31 inference(avatar_contradiction_clause,[],[f1904])).
% 0.20/0.31 tff(f1934,plain,(
% 0.20/0.31 9 = $sum(sK1,5) | (~spl3_5 | ~spl3_8)),
% 0.20/0.31 inference(forward_demodulation,[],[f115,f213])).
% 0.20/0.31 tff(f1942,plain,(
% 0.20/0.31 9 = $sum(5,sK1) | (~spl3_5 | ~spl3_8)),
% 0.20/0.31 inference(forward_demodulation,[],[f1934,f8])).
% 0.20/0.31 tff(f1944,plain,(
% 0.20/0.31 9 = $sum(5,1) | (~spl3_5 | ~spl3_8 | ~spl3_13)),
% 0.20/0.31 inference(forward_demodulation,[],[f1942,f1689])).
% 0.20/0.31 tff(f1945,plain,(
% 0.20/0.31 $false | (~spl3_5 | ~spl3_8 | ~spl3_13)),
% 0.20/0.31 inference(evaluation,[],[f1944])).
% 0.20/0.31 tff(f1946,plain,(
% 0.20/0.31 ~spl3_5 | ~spl3_8 | ~spl3_13),
% 0.20/0.31 inference(avatar_contradiction_clause,[],[f1945])).
% 0.20/0.31 cnf(s6, plain, spl3_5 | spl3_6, inference(sat_conversion,[],[f123])).
% 0.20/0.31 cnf(s7, plain, spl3_7 | spl3_8, inference(sat_conversion,[],[f214])).
% 0.20/0.31 cnf(s8, plain, spl3_9 | spl3_10, inference(sat_conversion,[],[f223])).
% 0.20/0.31 cnf(s9, plain, ~spl3_7 | spl3_11 | spl3_12, inference(sat_conversion,[],[f248])).
% 0.20/0.31 cnf(s10, plain, ~spl3_8 | ~spl3_10, inference(sat_conversion,[],[f282])).
% 0.20/0.31 cnf(s11, plain, ~spl3_9 | spl3_13 | spl3_14, inference(sat_conversion,[],[f440])).
% 0.20/0.31 cnf(s21, plain, ~spl3_10 | ~spl3_11, inference(sat_conversion,[],[f908])).
% 0.20/0.31 cnf(s31, plain, ~spl3_10 | ~spl3_12, inference(sat_conversion,[],[f1053])).
% 0.20/0.31 cnf(s32, plain, ~spl3_11 | ~spl3_13, inference(sat_conversion,[],[f1387])).
% 0.20/0.31 cnf(s39, plain, ~spl3_11 | ~spl3_14, inference(sat_conversion,[],[f1431])).
% 0.20/0.31 cnf(s48, plain, ~spl3_8 | ~spl3_14, inference(sat_conversion,[],[f1486])).
% 0.20/0.31 cnf(s49, plain, ~spl3_5 | ~spl3_8 | ~spl3_14, inference(sat_conversion,[],[f1489])).
% 0.20/0.31 cnf(s58, plain, ~spl3_12 | ~spl3_14, inference(sat_conversion,[],[f1578])).
% 0.20/0.31 cnf(s59, plain, ~spl3_5 | ~spl3_12 | ~spl3_14, inference(sat_conversion,[],[f1581])).
% 0.20/0.31 cnf(s66, plain, ~spl3_12 | ~spl3_13, inference(sat_conversion,[],[f1837])).
% 0.20/0.31 cnf(s67, plain, ~spl3_6 | ~spl3_12 | ~spl3_13, inference(sat_conversion,[],[f1851])).
% 0.20/0.31 cnf(s68, plain, ~spl3_6 | ~spl3_8 | ~spl3_13, inference(sat_conversion,[],[f1905])).
% 0.20/0.31 cnf(s71, plain, ~spl3_5 | ~spl3_8 | ~spl3_13, inference(sat_conversion,[],[f1946])).
% 0.20/0.31 cnf(s72, plain, ~spl3_8 | ~spl3_6, inference(rat,[],[s8,s11,s10,s48,s68])).
% 0.20/0.31 cnf(s73, plain, ~spl3_10 | ~spl3_7, inference(rat,[],[s9,s21,s31])).
% 0.20/0.31 cnf(s74, plain, ~spl3_12 | ~spl3_6, inference(rat,[],[s11,s58,s67,s8,s73,s7,s72])).
% 0.20/0.31 cnf(s75, plain, ~spl3_6, inference(rat,[],[s11,s32,s39,s9,s74,s8,s73,s7,s72])).
% 0.20/0.31 cnf(s76, plain, spl3_5, inference(rat,[],[s6,s75])).
% 0.20/0.31 cnf(s77, plain, ~spl3_12 | ~spl3_9, inference(rat,[],[s11,s59,s66,s76])).
% 0.20/0.31 cnf(s78, plain, ~spl3_7, inference(rat,[],[s11,s32,s39,s9,s77,s8,s73])).
% 0.20/0.31 cnf(s79, plain, spl3_8, inference(rat,[],[s7,s78])).
% 0.20/0.31 cnf(s80, plain, ~spl3_13, inference(rat,[],[s71,s76,s79])).
% 0.20/0.31 cnf(s81, plain, ~spl3_14, inference(rat,[],[s49,s76,s79])).
% 0.20/0.31 cnf(s82, plain, ~spl3_10, inference(rat,[],[s10,s79])).
% 0.20/0.31 cnf(s83, plain, ~spl3_9, inference(rat,[],[s11,s80,s81])).
% 0.20/0.31 cnf(s84, plain, $false, inference(rat,[],[s8,s82,s83])).
% 0.20/0.31 tff(f1948,plain,(
% 0.20/0.31 $false),
% 0.20/0.31 inference(avatar_sat_refutation,[],[s84])).
% 0.20/0.31 % SZS output end Proof for theBenchmark
% 0.20/0.31 % (697260)------------------------------
% 0.20/0.31 % (697260)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.31 % (697260)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.31 % (697260)CaDiCaL version: 2.1.3
% 0.20/0.31 % (697260)Termination reason: Refutation
% 0.20/0.31 % (697260)Time elapsed: 0.049 s
% 0.20/0.31 % (697260)Peak memory usage: 13 MB
% 0.20/0.31 % (697260)Instructions burned: 79 (million)
% 0.20/0.31 % (697250)Success in time 0.087 s
% 0.20/0.31 % Vampire exiting
%------------------------------------------------------------------------------