%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT105_1 : TPTP v9.3.1. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n016.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 09:48:08 AM UTC 2026
% Result : Theorem 0.22s 0.31s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT105_1 : TPTP v9.3.1. Released v6.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 % Computer : n016.cluster.edu
% 0.09/0.22 % Model : x86_64 x86_64
% 0.09/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.22 % Memory : 8046.5625MB
% 0.09/0.22 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Tue Sep 29 00:13:19 UTC 2026
% 0.09/0.23 % CPUTime :
% 0.09/0.23 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.27 Running first-order model finding
% 0.09/0.27 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
% 0.22/0.31 % (4173228)Will run a generic schedule for satisfiability detection.
% 0.22/0.31 % (4173234)% WARNING: option uhcvi not known.
% 0.22/0.31 % (4173234)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1055850404:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 0.22/0.31 % (4173233)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2164947700_3000 on theBenchmark for (3000ds/0Mi)
% 0.22/0.31 % (4173237)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2857983419:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 0.22/0.31 % (4173236)dis+10_1_sil=32000:sp=arity:random_seed=1709637959:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 0.22/0.31 % (4173235)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=48587563:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 0.22/0.31 % (4173233)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.22/0.31 % (4173233)Terminated due to inappropriate strategy.
% 0.22/0.31 % (4173233)------------------------------
% 0.22/0.31 % (4173233)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (4173233)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (4173233)CaDiCaL version: 2.1.3
% 0.22/0.31 % (4173233)Termination reason: Inappropriate
% 0.22/0.31 % (4173233)Time elapsed: 0.001 s
% 0.22/0.31 % (4173233)Peak memory usage: 10 MB
% 0.22/0.31 % (4173233)------------------------------
% 0.22/0.31 % (4173233)------------------------------
% 0.22/0.31 % (4173237) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4173228-4173237"...
% 0.22/0.31 % (4173237)...printing done.
% 0.22/0.31 % (4173237)Refutation found. Thanks to Tanya!
% 0.22/0.31 % SZS status Theorem for theBenchmark
% 0.22/0.31 % SZS output start Proof for theBenchmark
% 0.22/0.31 tff(type_def_5, type, list: $tType).
% 0.22/0.31 tff(func_def_0, type, nil: list).
% 0.22/0.31 tff(func_def_1, type, cons: ($int * list) > list).
% 0.22/0.31 tff(func_def_2, type, head: list > $int).
% 0.22/0.31 tff(func_def_3, type, tail: list > list).
% 0.22/0.31 tff(func_def_10, type, sK0: ($int * list) > $int).
% 0.22/0.31 tff(func_def_11, type, sK1: ($int * list) > list).
% 0.22/0.31 tff(pred_def_1, type, inRange: ($int * list) > $o).
% 0.22/0.31 tff(f1,axiom,(
% 0.22/0.31 ! [X0 : $int,X1 : list] : head(cons(X0,X1)) = X0),
% 0.22/0.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1)).
% 0.22/0.31 tff(f4,axiom,(
% 0.22/0.31 ! [X0 : $int,X1 : list] : cons(X0,X1) != nil),
% 0.22/0.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4)).
% 0.22/0.31 tff(f5,axiom,(
% 0.22/0.31 ! [X0 : $int,X1 : list] : (inRange(X0,X1) <=> (X1 = nil | ? [X2 : $int,X3 : list] : (X1 = cons(X2,X3) & $lesseq(0,X2) & $less(X2,X0) & inRange(X0,X3))))),
% 0.22/0.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inRange)).
% 0.22/0.31 tff(f6,conjecture,(
% 0.22/0.31 ~ ! [X0 : list,X1 : $int] : ((X0 != nil & inRange(X1,X0)) => $greatereq($difference(X1,head(X0)),2))),
% 0.22/0.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c)).
% 0.22/0.31 tff(f7,negated_conjecture,(
% 0.22/0.31 ~ ~ ! [X0 : list,X1 : $int] : ((X0 != nil & inRange(X1,X0)) => $greatereq($difference(X1,head(X0)),2))),
% 0.22/0.31 inference(negated_conjecture,[status(cth)],[f6])).
% 0.22/0.31 tff(f8,plain,(
% 0.22/0.31 ! [X0 : $int,X1 : list] : (inRange(X0,X1) <=> (X1 = nil | ? [X2 : $int,X3 : list] : (X1 = cons(X2,X3) & ~$less(X2,0) & $less(X2,X0) & inRange(X0,X3))))),
% 0.22/0.31 inference(theory_normalization,[],[f5])).
% 0.22/0.31 tff(f9,plain,(
% 0.22/0.31 ! [X0 : list,X1 : $int] : ((X0 != nil & inRange(X1,X0)) => ~$less($sum(X1,$uminus(head(X0))),2))),
% 0.22/0.31 inference(theory_normalization,[],[f7])).
% 0.22/0.31 tff(f10,definition,(
% 0.22/0.31 ( ! [X0 : $int,X1 : $int] : ($sum(X0,X1) = $sum(X1,X0)) )),
% 0.22/0.31 introduced(theory,[tha_commutativity])).
% 0.22/0.31 tff(f11,definition,(
% 0.22/0.31 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2)) )),
% 0.22/0.31 introduced(theory,[tha_associativity])).
% 0.22/0.31 tff(f14,definition,(
% 0.22/0.31 ( ! [X0 : $int] : (0 = $sum(X0,$uminus(X0))) )),
% 0.22/0.31 introduced(theory,[tha_inverse_op_unit])).
% 0.22/0.31 tff(f15,definition,(
% 0.22/0.31 ( ! [X0 : $int] : (~$less(X0,X0)) )),
% 0.22/0.31 introduced(theory,[tha_non-reflexivity])).
% 0.22/0.31 tff(f19,definition,(
% 0.22/0.31 ( ! [X0 : $int,X1 : $int] : ($less(X1,$sum(X0,1)) | $less(X0,X1)) )),
% 0.22/0.31 introduced(theory,[tha_order_plus_one_dichotomy])).
% 0.22/0.31 tff(f22,plain,(
% 0.22/0.31 ! [X0 : list,X1 : $int] : (~$less($sum(X1,$uminus(head(X0))),2) | (nil = X0 | ~inRange(X1,X0)))),
% 0.22/0.31 inference(ennf_transformation,[],[f9])).
% 0.22/0.31 tff(f23,plain,(
% 0.22/0.31 ! [X0 : list,X1 : $int] : (~$less($sum(X1,$uminus(head(X0))),2) | nil = X0 | ~inRange(X1,X0))),
% 0.22/0.31 inference(flattening,[],[f22])).
% 0.22/0.31 tff(f24,plain,(
% 0.22/0.31 ( ! [X0 : $int,X1 : list] : (head(cons(X0,X1)) = X0) )),
% 0.22/0.31 inference(cnf_transformation,[],[f1])).
% 0.22/0.31 tff(f27,plain,(
% 0.22/0.31 ( ! [X0 : $int,X1 : list] : (cons(X0,X1) != nil) )),
% 0.22/0.31 inference(cnf_transformation,[],[f4])).
% 0.22/0.31 tff(f28,plain,(
% 0.22/0.31 ( ! [X2 : $int,X3 : list,X0 : $int,X1 : list] : (~inRange(X0,X3) | ~$less(X2,X0) | $less(X2,0) | cons(X2,X3) != X1 | inRange(X0,X1)) )),
% 0.22/0.31 inference(cnf_transformation,[],[f8])).
% 0.22/0.31 tff(f33,plain,(
% 0.22/0.31 ( ! [X0 : $int,X1 : list] : (nil != X1 | inRange(X0,X1)) )),
% 0.22/0.31 inference(cnf_transformation,[],[f8])).
% 0.22/0.31 tff(f34,plain,(
% 0.22/0.31 ( ! [X0 : list,X1 : $int] : (~inRange(X1,X0) | nil = X0 | ~$less($sum(X1,$uminus(head(X0))),2)) )),
% 0.22/0.31 inference(cnf_transformation,[],[f23])).
% 0.22/0.31 tff(f35,plain,(
% 0.22/0.31 ( ! [X0 : $int] : (inRange(X0,nil)) )),
% 0.22/0.31 inference(equality_resolution,[],[f33])).
% 0.22/0.31 tff(f36,plain,(
% 0.22/0.31 ( ! [X2 : $int,X3 : list,X0 : $int] : (inRange(X0,cons(X2,X3)) | ~$less(X2,X0) | $less(X2,0) | ~inRange(X0,X3)) )),
% 0.22/0.31 inference(equality_resolution,[],[f28])).
% 0.22/0.31 tff(f44,plain,(
% 0.22/0.31 ( ! [X0 : $int] : ($less(X0,$sum(X0,1))) )),
% 0.22/0.31 inference(resolution,[],[f19,f15])).
% 0.22/0.31 tff(f52,plain,(
% 0.22/0.31 ( ! [X0 : $int] : ($less(X0,$sum(1,X0))) )),
% 0.22/0.31 inference(superposition,[],[f44,f10])).
% 0.22/0.31 tff(f150,plain,(
% 0.22/0.31 ( ! [X0 : $int,X1 : $int] : ($sum(0,X1) = $sum(X0,$sum($uminus(X0),X1))) )),
% 0.22/0.31 inference(superposition,[],[f11,f14])).
% 0.22/0.31 tff(f168,plain,(
% 0.22/0.31 ( ! [X0 : $int,X1 : $int] : ($sum(X0,$sum($uminus(X0),X1)) = X1) )),
% 0.22/0.31 inference(evaluation,[],[f150])).
% 0.22/0.31 tff(f196,plain,(
% 0.22/0.31 ( ! [X2 : list,X0 : $int,X1 : $int] : (~$less(X0,X1) | $less(X0,0) | ~inRange(X1,X2) | nil = cons(X0,X2) | ~$less($sum(X1,$uminus(head(cons(X0,X2)))),2)) )),
% 0.22/0.31 inference(resolution,[],[f36,f34])).
% 0.22/0.31 tff(f198,plain,(
% 0.22/0.31 ( ! [X2 : list,X0 : $int,X1 : $int] : (~$less(X0,X1) | $less(X0,0) | ~inRange(X1,X2) | ~$less($sum(X1,$uminus(head(cons(X0,X2)))),2)) )),
% 0.22/0.31 inference(forward_subsumption_resolution,[],[f196,f27])).
% 0.22/0.31 tff(f204,plain,(
% 0.22/0.31 ( ! [X2 : list,X0 : $int,X1 : $int] : (~inRange(X1,X2) | ~$less(X0,X1) | $less(X0,0) | ~$less($sum(X1,$uminus(X0)),2)) )),
% 0.22/0.31 inference(forward_demodulation,[],[f198,f24])).
% 0.22/0.31 tff(f205,plain,(
% 0.22/0.31 ( ! [X0 : $int,X1 : $int] : (~$less($sum(X1,$uminus(X0)),2) | $less(X0,0) | ~$less(X0,X1)) )),
% 0.22/0.31 inference(resolution,[],[f204,f35])).
% 0.22/0.31 tff(f218,plain,(
% 0.22/0.31 ( ! [X0 : $int,X1 : $int] : (~$less($sum($uminus(X0),X1),2) | $less(X0,0) | ~$less(X0,X1)) )),
% 0.22/0.31 inference(superposition,[],[f205,f10])).
% 0.22/0.31 tff(f257,plain,(
% 0.22/0.31 ( ! [X0 : $int,X1 : $int] : (~$less(X0,2) | $less(X1,0) | ~$less(X1,$sum($uminus($uminus(X1)),X0))) )),
% 0.22/0.31 inference(superposition,[],[f218,f168])).
% 0.22/0.31 tff(f264,plain,(
% 0.22/0.31 ( ! [X0 : $int,X1 : $int] : (~$less(X1,$sum(X1,X0)) | $less(X1,0) | ~$less(X0,2)) )),
% 0.22/0.31 inference(evaluation,[],[f257])).
% 0.22/0.31 tff(f269,plain,(
% 0.22/0.31 $less(1,0) | ~$less(1,2)),
% 0.22/0.31 inference(resolution,[],[f264,f52])).
% 0.22/0.31 tff(f282,plain,(
% 0.22/0.31 $false),
% 0.22/0.31 inference(evaluation,[],[f269])).
% 0.22/0.31 % SZS output end Proof for theBenchmark
% 0.22/0.31 % (4173237)------------------------------
% 0.22/0.31 % (4173237)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (4173237)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (4173237)CaDiCaL version: 2.1.3
% 0.22/0.31 % (4173237)Termination reason: Refutation
% 0.22/0.31 % (4173237)Time elapsed: 0.010 s
% 0.22/0.31 % (4173237)Peak memory usage: 12 MB
% 0.22/0.31 % (4173237)Instructions burned: 13 (million)
% 0.22/0.31 % (4173228)Success in time 0.033 s
% 0.22/0.31 % Vampire exiting
%------------------------------------------------------------------------------