%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT332_1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 09:48:30 AM UTC 2026
% Result : Unsatisfiable 0.19s 0.31s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT332_1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n010.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 00:20:02 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.23 Running first-order model finding
% 0.08/0.23 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
% 0.19/0.31 % (2502326)Will run a generic schedule for satisfiability detection.
% 0.19/0.31 % (2502331)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1014509084_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.31 % (2502331)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.19/0.31 % (2502331)Terminated due to inappropriate strategy.
% 0.19/0.31 % (2502331)------------------------------
% 0.19/0.31 % (2502331)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.31 % (2502331)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.31 % (2502331)CaDiCaL version: 2.1.3
% 0.19/0.31 % (2502331)Termination reason: Inappropriate
% 0.19/0.31 % (2502331)Time elapsed: 0.0000 s
% 0.19/0.31 % (2502331)Peak memory usage: 10 MB
% 0.19/0.31 % (2502331)------------------------------
% 0.19/0.31 % (2502331)------------------------------
% 0.19/0.31 % (2502332)% WARNING: option uhcvi not known.
% 0.19/0.31 % (2502332)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3539723393:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.31 % (2502335)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3230026155:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.31 % (2502333)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4107821565:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.31 % (2502334)dis+10_1_sil=32000:sp=arity:random_seed=4271399724:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.31 % (2502339)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1013162025:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.19/0.31 % (2502339)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.19/0.31 % (2502339)Terminated due to inappropriate strategy.
% 0.19/0.31 % (2502339)------------------------------
% 0.19/0.31 % (2502339)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.31 % (2502339)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.31 % (2502339)CaDiCaL version: 2.1.3
% 0.19/0.31 % (2502339)Termination reason: Inappropriate
% 0.19/0.31 % (2502339)Time elapsed: 0.0000 s
% 0.19/0.31 % (2502339)Peak memory usage: 10 MB
% 0.19/0.31 % (2502339)------------------------------
% 0.19/0.31 % (2502339)------------------------------
% 0.19/0.31 % (2502336)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=612261402:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.31 % (2502337)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3238276250:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.31 % (2502345)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1847358747:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.31 % (2502332) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2502326-2502332"...
% 0.19/0.31 % (2502332)...printing done.
% 0.19/0.31 % (2502332)Refutation found. Thanks to Tanya!
% 0.19/0.31 % SZS status Unsatisfiable for theBenchmark
% 0.19/0.31 % SZS output start Proof for theBenchmark
% 0.19/0.31 tff(type_def_5, type, 'Set': $tType).
% 0.19/0.31 tff(type_def_6, type, 'Array[Int,Int]': $tType).
% 0.19/0.31 tff(func_def_0, type, sup: 'Set' > $int).
% 0.19/0.31 tff(func_def_1, type, arr: 'Array[Int,Int]').
% 0.19/0.31 tff(func_def_2, type, s1: 'Set').
% 0.19/0.31 tff(func_def_3, type, i1: $int).
% 0.19/0.31 tff(func_def_4, type, delete: ('Set' * $int) > 'Set').
% 0.19/0.31 tff(func_def_5, type, 'store:(Array[Int,Int]*Int*Int)>Array[Int,Int]': ('Array[Int,Int]' * $int * $int) > 'Array[Int,Int]').
% 0.19/0.31 tff(func_def_6, type, 'const:(Int)>Array[Int,Int]': $int > 'Array[Int,Int]').
% 0.19/0.31 tff(func_def_7, type, g: $int > $int).
% 0.19/0.31 tff(func_def_8, type, s0: 'Set').
% 0.19/0.31 tff(func_def_9, type, 'select:(Array[Int,Int]*Int)>Int': ('Array[Int,Int]' * $int) > $int).
% 0.19/0.31 tff(func_def_10, type, insert: ('Set' * $int) > 'Set').
% 0.19/0.31 tff(func_def_15, type, sK0: ('Array[Int,Int]' * 'Array[Int,Int]') > $int).
% 0.19/0.31 tff(pred_def_1, type, member: ($int * 'Set') > $o).
% 0.19/0.31 tff(f2,axiom,(
% 0.19/0.31 ! [X0 : $int,X1 : $int,X2 : 'Set'] : (X0 != X1 => (member(X0,insert(X2,X1)) <=> member(X0,X2)))),
% 0.19/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_2)).
% 0.19/0.31 tff(f6,axiom,(
% 0.19/0.31 ! [X0 : 'Set'] : member(sup(X0),X0)),
% 0.19/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_6)).
% 0.19/0.31 tff(f7,axiom,(
% 0.19/0.31 ! [X0 : 'Set',X1 : $int] : (member(X1,X0) => $lesseq(X1,sup(X0)))),
% 0.19/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_7)).
% 0.19/0.31 tff(f9,axiom,(
% 0.19/0.31 ! [X0 : $int] : ($greater(X0,0) => $less('select:(Array[Int,Int]*Int)>Int'(arr,X0),sup(s0)))),
% 0.19/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_9)).
% 0.19/0.31 tff(f10,axiom,(
% 0.19/0.31 ! [X0 : $int] : $greater(g(X0),0)),
% 0.19/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_10)).
% 0.19/0.31 tff(f11,axiom,(
% 0.19/0.31 s1 = insert(s0,'select:(Array[Int,Int]*Int)>Int'(arr,g(i1)))),
% 0.19/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_11)).
% 0.19/0.31 tff(f12,axiom,(
% 0.19/0.31 sup(s1) != sup(s0)),
% 0.19/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_12)).
% 0.19/0.31 tff(f17,plain,(
% 0.19/0.31 ! [X0 : 'Set',X1 : $int] : (member(X1,X0) => ~$less(sup(X0),X1))),
% 0.19/0.31 inference(theory_normalization,[],[f7])).
% 0.19/0.31 tff(f18,plain,(
% 0.19/0.31 ! [X0 : $int] : ($less(0,X0) => $less('select:(Array[Int,Int]*Int)>Int'(arr,X0),sup(s0)))),
% 0.19/0.31 inference(theory_normalization,[],[f9])).
% 0.19/0.31 tff(f19,plain,(
% 0.19/0.31 ! [X0 : $int] : $less(0,g(X0))),
% 0.19/0.31 inference(theory_normalization,[],[f10])).
% 0.19/0.31 tff(f25,definition,(
% 0.19/0.31 ( ! [X0 : $int] : (~$less(X0,X0)) )),
% 0.19/0.31 introduced(theory,[tha_non-reflexivity])).
% 0.19/0.31 tff(f27,definition,(
% 0.19/0.31 ( ! [X0 : $int,X1 : $int] : ($less(X0,X1) | $less(X1,X0) | X0 = X1) )),
% 0.19/0.31 introduced(theory,[tha_order_totality])).
% 0.19/0.31 tff(f32,plain,(
% 0.19/0.31 ! [X0 : $int,X1 : $int,X2 : 'Set'] : ((member(X0,insert(X2,X1)) <=> member(X0,X2)) | X0 = X1)),
% 0.19/0.31 inference(ennf_transformation,[],[f2])).
% 0.19/0.31 tff(f35,plain,(
% 0.19/0.31 ! [X0 : 'Set',X1 : $int] : (~$less(sup(X0),X1) | ~member(X1,X0))),
% 0.19/0.31 inference(ennf_transformation,[],[f17])).
% 0.19/0.31 tff(f37,plain,(
% 0.19/0.31 ! [X0 : $int] : ($less('select:(Array[Int,Int]*Int)>Int'(arr,X0),sup(s0)) | ~$less(0,X0))),
% 0.19/0.31 inference(ennf_transformation,[],[f18])).
% 0.19/0.31 tff(f41,plain,(
% 0.19/0.31 ( ! [X2 : 'Set',X0 : $int,X1 : $int] : (member(X0,insert(X2,X1)) | ~member(X0,X2) | X0 = X1) )),
% 0.19/0.31 inference(cnf_transformation,[],[f32])).
% 0.19/0.31 tff(f42,plain,(
% 0.19/0.31 ( ! [X2 : 'Set',X0 : $int,X1 : $int] : (~member(X0,insert(X2,X1)) | member(X0,X2) | X0 = X1) )),
% 0.19/0.31 inference(cnf_transformation,[],[f32])).
% 0.19/0.31 tff(f46,plain,(
% 0.19/0.31 ( ! [X0 : 'Set'] : (member(sup(X0),X0)) )),
% 0.19/0.31 inference(cnf_transformation,[],[f6])).
% 0.19/0.31 tff(f47,plain,(
% 0.19/0.31 ( ! [X0 : 'Set',X1 : $int] : (~$less(sup(X0),X1) | ~member(X1,X0)) )),
% 0.19/0.31 inference(cnf_transformation,[],[f35])).
% 0.19/0.31 tff(f49,plain,(
% 0.19/0.31 ( ! [X0 : $int] : ($less('select:(Array[Int,Int]*Int)>Int'(arr,X0),sup(s0)) | ~$less(0,X0)) )),
% 0.19/0.31 inference(cnf_transformation,[],[f37])).
% 0.19/0.31 tff(f50,plain,(
% 0.19/0.31 ( ! [X0 : $int] : ($less(0,g(X0))) )),
% 0.19/0.31 inference(cnf_transformation,[],[f19])).
% 0.19/0.31 tff(f51,plain,(
% 0.19/0.31 s1 = insert(s0,'select:(Array[Int,Int]*Int)>Int'(arr,g(i1)))),
% 0.19/0.31 inference(cnf_transformation,[],[f11])).
% 0.19/0.31 tff(f52,plain,(
% 0.19/0.31 sup(s0) != sup(s1)),
% 0.19/0.31 inference(cnf_transformation,[],[f12])).
% 0.19/0.31 tff(f107,plain,(
% 0.19/0.31 ( ! [X0 : 'Set',X1 : $int] : (~member(X1,X0) | sup(X0) = X1 | $less(X1,sup(X0))) )),
% 0.19/0.31 inference(resolution,[],[f27,f47])).
% 0.19/0.31 tff(f182,plain,(
% 0.19/0.31 ( ! [X0 : $int] : (~member(X0,s0) | member(X0,s1) | 'select:(Array[Int,Int]*Int)>Int'(arr,g(i1)) = X0) )),
% 0.19/0.31 inference(superposition,[],[f41,f51])).
% 0.19/0.31 tff(f203,plain,(
% 0.19/0.31 ( ! [X0 : $int] : (~member(X0,s1) | member(X0,s0) | 'select:(Array[Int,Int]*Int)>Int'(arr,g(i1)) = X0) )),
% 0.19/0.31 inference(superposition,[],[f42,f51])).
% 0.19/0.31 tff(f503,definition,(
% 0.19/0.31 spl1_2 <=> 'select:(Array[Int,Int]*Int)>Int'(arr,g(i1)) = sup(s1)),
% 0.19/0.31 introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition])).
% 0.19/0.31 tff(f505,plain,(
% 0.19/0.31 'select:(Array[Int,Int]*Int)>Int'(arr,g(i1)) = sup(s1) | ~spl1_2),
% 0.19/0.31 inference(avatar_component_clause,[],[f503])).
% 0.19/0.31 tff(f656,plain,(
% 0.19/0.31 $less(sup(s1),sup(s0)) | ~$less(0,g(i1)) | ~spl1_2),
% 0.19/0.31 inference(superposition,[],[f49,f505])).
% 0.19/0.31 tff(f657,plain,(
% 0.19/0.31 $less(sup(s1),sup(s0)) | ~spl1_2),
% 0.19/0.31 inference(forward_subsumption_resolution,[],[f656,f50])).
% 0.19/0.31 tff(f659,plain,(
% 0.19/0.31 ~member(sup(s0),s1) | ~spl1_2),
% 0.19/0.31 inference(resolution,[],[f657,f47])).
% 0.19/0.31 tff(f772,plain,(
% 0.19/0.31 ( ! [X0 : $int] : (~member(X0,s0) | member(X0,s1) | sup(s1) = X0) ) | ~spl1_2),
% 0.19/0.31 inference(forward_demodulation,[],[f182,f505])).
% 0.19/0.31 tff(f773,plain,(
% 0.19/0.31 member(sup(s0),s1) | sup(s0) = sup(s1) | ~spl1_2),
% 0.19/0.31 inference(resolution,[],[f772,f46])).
% 0.19/0.31 tff(f775,plain,(
% 0.19/0.31 sup(s0) = sup(s1) | ~spl1_2),
% 0.19/0.31 inference(forward_subsumption_resolution,[],[f773,f659])).
% 0.19/0.31 tff(f776,plain,(
% 0.19/0.31 $false | ~spl1_2),
% 0.19/0.31 inference(forward_subsumption_resolution,[],[f775,f52])).
% 0.19/0.31 tff(f777,plain,(
% 0.19/0.31 ~spl1_2),
% 0.19/0.31 inference(avatar_contradiction_clause,[],[f776])).
% 0.19/0.31 tff(f778,plain,(
% 0.19/0.31 member(sup(s0),s1) | sup(s0) = 'select:(Array[Int,Int]*Int)>Int'(arr,g(i1))),
% 0.19/0.31 inference(resolution,[],[f182,f46])).
% 0.19/0.31 tff(f781,definition,(
% 0.19/0.31 spl1_3 <=> sup(s0) = 'select:(Array[Int,Int]*Int)>Int'(arr,g(i1))),
% 0.19/0.31 introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition])).
% 0.19/0.31 tff(f783,plain,(
% 0.19/0.31 sup(s0) = 'select:(Array[Int,Int]*Int)>Int'(arr,g(i1)) | ~spl1_3),
% 0.19/0.31 inference(avatar_component_clause,[],[f781])).
% 0.19/0.31 tff(f785,definition,(
% 0.19/0.31 spl1_4 <=> member(sup(s0),s1)),
% 0.19/0.31 introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition])).
% 0.19/0.31 tff(f787,plain,(
% 0.19/0.31 member(sup(s0),s1) | ~spl1_4),
% 0.19/0.31 inference(avatar_component_clause,[],[f785])).
% 0.19/0.31 tff(f788,plain,(
% 0.19/0.31 spl1_3 | spl1_4),
% 0.19/0.31 inference(avatar_split_clause,[],[f778,f785,f781])).
% 0.19/0.31 tff(f789,plain,(
% 0.19/0.31 sup(s0) = sup(s1) | $less(sup(s0),sup(s1)) | ~spl1_4),
% 0.19/0.31 inference(resolution,[],[f787,f107])).
% 0.19/0.31 tff(f790,plain,(
% 0.19/0.31 $less(sup(s0),sup(s1)) | ~spl1_4),
% 0.19/0.31 inference(forward_subsumption_resolution,[],[f789,f52])).
% 0.19/0.31 tff(f796,definition,(
% 0.19/0.31 spl1_5 <=> member(sup(s1),s0)),
% 0.19/0.31 introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition])).
% 0.19/0.31 tff(f798,plain,(
% 0.19/0.31 member(sup(s1),s0) | ~spl1_5),
% 0.19/0.31 inference(avatar_component_clause,[],[f796])).
% 0.19/0.31 tff(f801,plain,(
% 0.19/0.31 member(sup(s1),s0) | 'select:(Array[Int,Int]*Int)>Int'(arr,g(i1)) = sup(s1)),
% 0.19/0.31 inference(resolution,[],[f203,f46])).
% 0.19/0.31 tff(f805,plain,(
% 0.19/0.31 spl1_2 | spl1_5),
% 0.19/0.31 inference(avatar_split_clause,[],[f801,f796,f503])).
% 0.19/0.31 tff(f814,plain,(
% 0.19/0.31 ~member(sup(s1),s0) | ~spl1_4),
% 0.19/0.31 inference(resolution,[],[f790,f47])).
% 0.19/0.31 tff(f819,plain,(
% 0.19/0.31 $false | (~spl1_4 | ~spl1_5)),
% 0.19/0.31 inference(forward_subsumption_resolution,[],[f814,f798])).
% 0.19/0.31 tff(f820,plain,(
% 0.19/0.31 ~spl1_4 | ~spl1_5),
% 0.19/0.31 inference(avatar_contradiction_clause,[],[f819])).
% 0.19/0.31 tff(f1086,plain,(
% 0.19/0.31 $less(sup(s0),sup(s0)) | ~$less(0,g(i1)) | ~spl1_3),
% 0.19/0.31 inference(superposition,[],[f49,f783])).
% 0.19/0.31 tff(f1087,plain,(
% 0.19/0.31 ~$less(0,g(i1)) | ~spl1_3),
% 0.19/0.31 inference(forward_subsumption_resolution,[],[f1086,f25])).
% 0.19/0.31 tff(f1091,plain,(
% 0.19/0.31 $false | ~spl1_3),
% 0.19/0.31 inference(forward_subsumption_resolution,[],[f1087,f50])).
% 0.19/0.31 tff(f1092,plain,(
% 0.19/0.31 ~spl1_3),
% 0.19/0.31 inference(avatar_contradiction_clause,[],[f1091])).
% 0.19/0.31 cnf(s2, plain, ~spl1_2, inference(sat_conversion,[],[f777])).
% 0.19/0.31 cnf(s3, plain, spl1_3 | spl1_4, inference(sat_conversion,[],[f788])).
% 0.19/0.31 cnf(s5, plain, spl1_2 | spl1_5, inference(sat_conversion,[],[f805])).
% 0.19/0.31 cnf(s6, plain, ~spl1_4 | ~spl1_5, inference(sat_conversion,[],[f820])).
% 0.19/0.31 cnf(s8, plain, ~spl1_3, inference(sat_conversion,[],[f1092])).
% 0.19/0.31 cnf(s9, plain, spl1_4, inference(rat,[],[s3,s8])).
% 0.19/0.31 cnf(s10, plain, ~spl1_5, inference(rat,[],[s6,s9])).
% 0.19/0.31 cnf(s11, plain, spl1_2, inference(rat,[],[s5,s10])).
% 0.19/0.31 cnf(s12, plain, $false, inference(rat,[],[s2,s11])).
% 0.19/0.31 tff(f1093,plain,(
% 0.19/0.31 $false),
% 0.19/0.31 inference(avatar_sat_refutation,[],[s12])).
% 0.19/0.31 % SZS output end Proof for theBenchmark
% 0.19/0.31 % (2502332)------------------------------
% 0.19/0.31 % (2502332)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.31 % (2502332)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.31 % (2502332)CaDiCaL version: 2.1.3
% 0.19/0.31 % (2502332)Termination reason: Refutation
% 0.19/0.31 % (2502332)Time elapsed: 0.033 s
% 0.19/0.31 % (2502332)Peak memory usage: 13 MB
% 0.19/0.31 % (2502332)Instructions burned: 48 (million)
% 0.19/0.31 % (2502326)Success in time 0.072 s
% 0.19/0.31 % Vampire exiting
%------------------------------------------------------------------------------