%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT030_1 : TPTP v9.3.1. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n012.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 09:47:59 AM UTC 2026
% Result : Theorem 0.09s 0.20s
% Output : Refutation 0.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : DAT030_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Tue Sep 29 00:05:34 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.13 Running first-order model finding
% 0.09/0.13 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.20 % (3914940)Will run a generic schedule for satisfiability detection.
% 0.09/0.20 % (3914946)% WARNING: option uhcvi not known.
% 0.09/0.20 % (3914951)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3289603418:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.09/0.20 % (3914946)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2586983407:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.09/0.20 % (3914947)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2393069351:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.09/0.20 % (3914945)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3042865259_2999 on theBenchmark for (2999ds/0Mi)
% 0.09/0.20 % (3914949)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3375750861:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.09/0.20 % (3914950)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2406383331:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.09/0.20 % (3914945)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.09/0.20 % (3914945)Terminated due to inappropriate strategy.
% 0.09/0.20 % (3914945)------------------------------
% 0.09/0.20 % (3914945)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.20 % (3914945)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.20 % (3914945)CaDiCaL version: 2.1.3
% 0.09/0.20 % (3914945)Termination reason: Inappropriate
% 0.09/0.20 % (3914945)Time elapsed: 0.0000 s
% 0.09/0.20 % (3914945)Peak memory usage: 10 MB
% 0.09/0.20 % (3914948)dis+10_1_sil=32000:sp=arity:random_seed=1224298078:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.09/0.20 % (3914945)------------------------------
% 0.09/0.20 % (3914945)------------------------------
% 0.09/0.20 % (3914959)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1492438197:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.09/0.20 % (3914959)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.09/0.20 % (3914959)Terminated due to inappropriate strategy.
% 0.09/0.20 % (3914959)------------------------------
% 0.09/0.20 % (3914959)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.20 % (3914959)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.20 % (3914959)CaDiCaL version: 2.1.3
% 0.09/0.20 % (3914959)Termination reason: Inappropriate
% 0.09/0.20 % (3914959)Time elapsed: 0.0000 s
% 0.09/0.20 % (3914959)Peak memory usage: 10 MB
% 0.09/0.20 % (3914959)------------------------------
% 0.09/0.20 % (3914959)------------------------------
% 0.09/0.20 % (3914961)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1647385840:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.09/0.20 % (3914948) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3914940-3914948"...
% 0.09/0.20 % (3914948)...printing done.
% 0.09/0.20 % (3914948)Refutation found. Thanks to Tanya!
% 0.09/0.20 % SZS status Theorem for theBenchmark
% 0.09/0.20 % SZS output start Proof for theBenchmark
% 0.09/0.20 tff(type_def_5, type, collection: $tType).
% 0.09/0.20 tff(func_def_0, type, empty: collection).
% 0.09/0.20 tff(func_def_1, type, add: ($int * collection) > collection).
% 0.09/0.20 tff(func_def_2, type, remove: ($int * collection) > collection).
% 0.09/0.20 tff(func_def_7, type, sK0: collection).
% 0.09/0.20 tff(func_def_8, type, sK1: collection).
% 0.09/0.20 tff(func_def_9, type, sK2: $int).
% 0.09/0.20 tff(func_def_10, type, sK3: $int > $int).
% 0.09/0.20 tff(func_def_11, type, sK4: $int > $int).
% 0.09/0.20 tff(pred_def_1, type, in: ($int * collection) > $o).
% 0.09/0.20 tff(f6,conjecture,(
% 0.09/0.20 ! [X0 : collection,X1 : collection] : ((! [X2 : $int] : (in(X2,X1) => $greater(X2,0)) & ! [X3 : $int] : (in(X3,X0) => ? [X4 : $int,X5 : $int] : (in(X4,X1) & in(X5,X1) & X3 = $sum(X4,X5)))) => ! [X6 : $int] : (in(X6,X0) => $greater(X6,1)))),
% 0.09/0.20 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1)).
% 0.09/0.20 tff(f7,negated_conjecture,(
% 0.09/0.20 ~ ! [X0 : collection,X1 : collection] : ((! [X2 : $int] : (in(X2,X1) => $greater(X2,0)) & ! [X3 : $int] : (in(X3,X0) => ? [X4 : $int,X5 : $int] : (in(X4,X1) & in(X5,X1) & X3 = $sum(X4,X5)))) => ! [X6 : $int] : (in(X6,X0) => $greater(X6,1)))),
% 0.09/0.20 inference(negated_conjecture,[status(cth)],[f6])).
% 0.09/0.20 tff(f8,plain,(
% 0.09/0.20 ~ ! [X0 : collection,X1 : collection] : ((! [X2 : $int] : (in(X2,X1) => $less(0,X2)) & ! [X3 : $int] : (in(X3,X0) => ? [X4 : $int,X5 : $int] : (in(X4,X1) & in(X5,X1) & X3 = $sum(X4,X5)))) => ! [X6 : $int] : (in(X6,X0) => $less(1,X6)))),
% 0.09/0.20 inference(theory_normalization,[],[f7])).
% 0.09/0.20 tff(f9,definition,(
% 0.09/0.20 ( ! [X0 : $int,X1 : $int] : ($sum(X0,X1) = $sum(X1,X0)) )),
% 0.09/0.20 introduced(theory,[tha_commutativity])).
% 0.09/0.20 tff(f11,definition,(
% 0.09/0.20 ( ! [X0 : $int] : ($sum(X0,0) = X0) )),
% 0.09/0.20 introduced(theory,[tha_right_identity])).
% 0.09/0.20 tff(f15,definition,(
% 0.09/0.20 ( ! [X2 : $int,X0 : $int,X1 : $int] : (~$less(X1,X2) | ~$less(X0,X1) | $less(X0,X2)) )),
% 0.09/0.20 introduced(theory,[tha_transitivity])).
% 0.09/0.20 tff(f16,definition,(
% 0.09/0.20 ( ! [X0 : $int,X1 : $int] : ($less(X1,X0) | $less(X0,X1) | X0 = X1) )),
% 0.09/0.20 introduced(theory,[tha_order_totality])).
% 0.09/0.20 tff(f17,definition,(
% 0.09/0.20 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($less($sum(X0,X2),$sum(X1,X2)) | ~$less(X0,X1)) )),
% 0.09/0.20 introduced(theory,[tha_order_monotonicity])).
% 0.09/0.20 tff(f20,definition,(
% 0.09/0.20 ( ! [X0 : $int,X1 : $int] : (~$less(X1,$sum(X0,1)) | ~$less(X0,X1)) )),
% 0.09/0.20 introduced(theory,[tha_extra_integer_ordering])).
% 0.09/0.20 tff(f21,plain,(
% 0.09/0.20 ? [X0 : collection,X1 : collection] : (? [X6 : $int] : (~$less(1,X6) & in(X6,X0)) & (! [X2 : $int] : ($less(0,X2) | ~in(X2,X1)) & ! [X3 : $int] : (? [X4 : $int,X5 : $int] : (in(X4,X1) & in(X5,X1) & X3 = $sum(X4,X5)) | ~in(X3,X0))))),
% 0.09/0.20 inference(ennf_transformation,[],[f8])).
% 0.09/0.20 tff(f22,plain,(
% 0.09/0.20 ? [X0 : collection,X1 : collection] : (? [X6 : $int] : (~$less(1,X6) & in(X6,X0)) & ! [X2 : $int] : ($less(0,X2) | ~in(X2,X1)) & ! [X3 : $int] : (? [X4 : $int,X5 : $int] : (in(X4,X1) & in(X5,X1) & X3 = $sum(X4,X5)) | ~in(X3,X0)))),
% 0.09/0.20 inference(flattening,[],[f21])).
% 0.09/0.20 tff(f27,plain,(
% 0.09/0.20 ? [X0 : collection,X1 : collection] : (? [X2 : $int] : (~$less(1,X2) & in(X2,X0)) & ! [X3 : $int] : ($less(0,X3) | ~in(X3,X1)) & ! [X4 : $int] : (? [X5 : $int,X6 : $int] : (in(X5,X1) & in(X6,X1) & $sum(X5,X6) = X4) | ~in(X4,X0)))),
% 0.09/0.20 inference(rectify,[],[f22])).
% 0.09/0.20 tff(f28,plain,(
% 0.09/0.20 (~$less(1,sK2) & in(sK2,sK0)) & ! [X3 : $int] : ($less(0,X3) | ~in(X3,sK1)) & ! [X4 : $int] : ((in(sK3(X4),sK1) & in(sK4(X4),sK1) & $sum(sK3(X4),sK4(X4)) = X4) | ~in(X4,sK0))),
% 0.09/0.20 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X5,sK3(X4)),skolemize(X6,sK4(X4))],[f27])).
% 0.09/0.20 tff(f38,plain,(
% 0.09/0.20 ( ! [X4 : $int] : (~in(X4,sK0) | $sum(sK3(X4),sK4(X4)) = X4) )),
% 0.09/0.20 inference(cnf_transformation,[],[f28])).
% 0.09/0.20 tff(f39,plain,(
% 0.09/0.20 ( ! [X4 : $int] : (in(sK4(X4),sK1) | ~in(X4,sK0)) )),
% 0.09/0.20 inference(cnf_transformation,[],[f28])).
% 0.09/0.20 tff(f40,plain,(
% 0.09/0.20 ( ! [X4 : $int] : (in(sK3(X4),sK1) | ~in(X4,sK0)) )),
% 0.09/0.20 inference(cnf_transformation,[],[f28])).
% 0.09/0.20 tff(f41,plain,(
% 0.09/0.20 ( ! [X3 : $int] : (~in(X3,sK1) | $less(0,X3)) )),
% 0.09/0.20 inference(cnf_transformation,[],[f28])).
% 0.09/0.20 tff(f42,plain,(
% 0.09/0.20 in(sK2,sK0)),
% 0.09/0.20 inference(cnf_transformation,[],[f28])).
% 0.09/0.20 tff(f43,plain,(
% 0.09/0.20 ~$less(1,sK2)),
% 0.09/0.20 inference(cnf_transformation,[],[f28])).
% 0.09/0.20 tff(f46,plain,(
% 0.09/0.20 ( ! [X0 : $int] : (~in(X0,sK0) | $less(0,sK4(X0))) )),
% 0.09/0.20 inference(resolution,[],[f39,f41])).
% 0.09/0.20 tff(f47,plain,(
% 0.09/0.20 ( ! [X0 : $int] : (~in(X0,sK0) | $less(0,sK3(X0))) )),
% 0.09/0.20 inference(resolution,[],[f40,f41])).
% 0.09/0.20 tff(f48,plain,(
% 0.09/0.20 sK2 = $sum(sK3(sK2),sK4(sK2))),
% 0.09/0.20 inference(resolution,[],[f38,f42])).
% 0.09/0.20 tff(f49,plain,(
% 0.09/0.20 $less(0,sK4(sK2))),
% 0.09/0.20 inference(resolution,[],[f46,f42])).
% 0.09/0.20 tff(f50,plain,(
% 0.09/0.20 $less(0,sK3(sK2))),
% 0.09/0.20 inference(resolution,[],[f47,f42])).
% 0.09/0.20 tff(f69,plain,(
% 0.09/0.20 ( ! [X0 : $int,X1 : $int] : (~$less(X1,$sum(1,X0)) | ~$less(X0,X1)) )),
% 0.09/0.20 inference(superposition,[],[f20,f9])).
% 0.09/0.20 tff(f119,plain,(
% 0.09/0.20 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($less($sum(X0,X1),$sum(X2,X0)) | ~$less(X1,X2)) )),
% 0.09/0.20 inference(superposition,[],[f17,f9])).
% 0.09/0.20 tff(f227,plain,(
% 0.09/0.20 ( ! [X0 : $int] : (~$less(0,X0) | ~$less(X0,1)) )),
% 0.09/0.20 inference(superposition,[],[f69,f11])).
% 0.09/0.20 tff(f237,definition,(
% 0.09/0.20 spl5_8 <=> $less(sK4(sK2),sK2)),
% 0.09/0.20 introduced(definition,[new_symbols(definition,[spl5_8])],[avatar_definition])).
% 0.09/0.20 tff(f238,plain,(
% 0.09/0.20 $less(sK4(sK2),sK2) | ~spl5_8),
% 0.09/0.20 inference(avatar_component_clause,[],[f237])).
% 0.09/0.20 tff(f311,plain,(
% 0.09/0.20 ( ! [X0 : $int] : (~$less(X0,sK4(sK2)) | $less(X0,sK2)) ) | ~spl5_8),
% 0.09/0.20 inference(resolution,[],[f238,f15])).
% 0.09/0.20 tff(f457,plain,(
% 0.09/0.20 ( ! [X0 : $int] : ($less($sum(sK4(sK2),X0),sK2) | ~$less(X0,sK3(sK2))) )),
% 0.09/0.20 inference(superposition,[],[f119,f48])).
% 0.09/0.20 tff(f833,definition,(
% 0.09/0.20 spl5_14 <=> $less(sK4(sK2),1)),
% 0.09/0.20 introduced(definition,[new_symbols(definition,[spl5_14])],[avatar_definition])).
% 0.09/0.20 tff(f834,plain,(
% 0.09/0.20 ~$less(sK4(sK2),1) | spl5_14),
% 0.09/0.20 inference(avatar_component_clause,[],[f833])).
% 0.09/0.20 tff(f835,plain,(
% 0.09/0.20 $less(sK4(sK2),1) | ~spl5_14),
% 0.09/0.20 inference(avatar_component_clause,[],[f833])).
% 0.09/0.20 tff(f1433,plain,(
% 0.09/0.20 $less(1,sK4(sK2)) | 1 = sK4(sK2) | spl5_14),
% 0.09/0.20 inference(resolution,[],[f834,f16])).
% 0.09/0.20 tff(f1436,definition,(
% 0.09/0.20 spl5_16 <=> 1 = sK4(sK2)),
% 0.09/0.20 introduced(definition,[new_symbols(definition,[spl5_16])],[avatar_definition])).
% 0.09/0.20 tff(f1438,plain,(
% 0.09/0.20 1 = sK4(sK2) | ~spl5_16),
% 0.09/0.20 inference(avatar_component_clause,[],[f1436])).
% 0.09/0.20 tff(f1440,definition,(
% 0.09/0.20 spl5_17 <=> $less(1,sK4(sK2))),
% 0.09/0.20 introduced(definition,[new_symbols(definition,[spl5_17])],[avatar_definition])).
% 0.09/0.20 tff(f1442,plain,(
% 0.09/0.20 $less(1,sK4(sK2)) | ~spl5_17),
% 0.09/0.20 inference(avatar_component_clause,[],[f1440])).
% 0.09/0.20 tff(f1444,plain,(
% 0.09/0.20 spl5_16 | spl5_17 | spl5_14),
% 0.09/0.20 inference(avatar_split_clause,[],[f1433,f833,f1440,f1436])).
% 0.09/0.20 tff(f1450,plain,(
% 0.09/0.20 $less(sK4(sK2),sK2) | ~$less(0,sK3(sK2))),
% 0.09/0.20 inference(superposition,[],[f457,f11])).
% 0.09/0.20 tff(f1469,plain,(
% 0.09/0.20 $less(1,sK2) | (~spl5_8 | ~spl5_16)),
% 0.09/0.20 inference(superposition,[],[f238,f1438])).
% 0.09/0.20 tff(f1482,plain,(
% 0.09/0.20 $false | (~spl5_8 | ~spl5_16)),
% 0.09/0.20 inference(forward_subsumption_resolution,[],[f1469,f43])).
% 0.09/0.20 tff(f1483,plain,(
% 0.09/0.20 ~spl5_8 | ~spl5_16),
% 0.09/0.20 inference(avatar_contradiction_clause,[],[f1482])).
% 0.09/0.20 tff(f1512,plain,(
% 0.09/0.20 $less(1,sK2) | (~spl5_8 | ~spl5_17)),
% 0.09/0.20 inference(resolution,[],[f1442,f311])).
% 0.09/0.20 tff(f1516,plain,(
% 0.09/0.20 $false | (~spl5_8 | ~spl5_17)),
% 0.09/0.20 inference(forward_subsumption_resolution,[],[f1512,f43])).
% 0.09/0.20 tff(f1517,plain,(
% 0.09/0.20 ~spl5_8 | ~spl5_17),
% 0.09/0.20 inference(avatar_contradiction_clause,[],[f1516])).
% 0.09/0.20 tff(f1518,plain,(
% 0.09/0.20 $less(sK4(sK2),sK2)),
% 0.09/0.20 inference(forward_subsumption_resolution,[],[f1450,f50])).
% 0.09/0.20 tff(f1519,plain,(
% 0.09/0.20 spl5_8),
% 0.09/0.20 inference(avatar_split_clause,[],[f1518,f237])).
% 0.09/0.20 tff(f2176,plain,(
% 0.09/0.20 ~$less(sK4(sK2),1)),
% 0.09/0.20 inference(resolution,[],[f227,f49])).
% 0.09/0.20 tff(f2191,plain,(
% 0.09/0.20 $false | ~spl5_14),
% 0.09/0.20 inference(forward_subsumption_resolution,[],[f2176,f835])).
% 0.09/0.20 tff(f2192,plain,(
% 0.09/0.20 ~spl5_14),
% 0.09/0.20 inference(avatar_contradiction_clause,[],[f2191])).
% 0.09/0.20 cnf(s21, plain, spl5_14 | spl5_16 | spl5_17, inference(sat_conversion,[],[f1444])).
% 0.09/0.20 cnf(s24, plain, ~spl5_8 | ~spl5_16, inference(sat_conversion,[],[f1483])).
% 0.09/0.20 cnf(s26, plain, ~spl5_8 | ~spl5_17, inference(sat_conversion,[],[f1517])).
% 0.09/0.20 cnf(s27, plain, spl5_8, inference(sat_conversion,[],[f1519])).
% 0.09/0.20 cnf(s52, plain, ~spl5_14, inference(sat_conversion,[],[f2192])).
% 0.09/0.20 cnf(s54, plain, ~spl5_17, inference(rat,[],[s26,s27])).
% 0.09/0.20 cnf(s55, plain, ~spl5_16, inference(rat,[],[s24,s27])).
% 0.09/0.20 cnf(s56, plain, $false, inference(rat,[],[s21,s54,s55,s52])).
% 0.09/0.20 tff(f2193,plain,(
% 0.09/0.20 $false),
% 0.09/0.20 inference(avatar_sat_refutation,[],[s56])).
% 0.09/0.20 % SZS output end Proof for theBenchmark
% 0.09/0.20 % (3914948)------------------------------
% 0.09/0.20 % (3914948)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.20 % (3914948)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.20 % (3914948)CaDiCaL version: 2.1.3
% 0.09/0.20 % (3914948)Termination reason: Refutation
% 0.09/0.20 % (3914948)Time elapsed: 0.042 s
% 0.09/0.20 % (3914948)Peak memory usage: 13 MB
% 0.09/0.20 % (3914948)Instructions burned: 86 (million)
% 0.09/0.20 % (3914940)Success in time 0.065 s
% 0.09/0.20 % Vampire exiting
%------------------------------------------------------------------------------