%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT103_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 : n003.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 0.18s 0.30s
% Output : Refutation 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : DAT103_1 : TPTP v9.3.1. Released v6.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.19 % Computer : n003.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 00:10:13 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.22 Running first-order model finding
% 0.07/0.22 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
% 0.18/0.30 % (2156309)Will run a generic schedule for satisfiability detection.
% 0.18/0.30 % (2156317)dis+10_1_sil=32000:sp=arity:random_seed=527407954:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.30 % (2156315)% WARNING: option uhcvi not known.
% 0.18/0.30 % (2156314)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2881682015_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.30 % (2156315)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=322357710:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.30 % (2156316)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2034085866:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.30 % (2156314)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.18/0.30 % (2156314)Terminated due to inappropriate strategy.
% 0.18/0.30 % (2156314)------------------------------
% 0.18/0.30 % (2156314)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.30 % (2156314)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.30 % (2156314)CaDiCaL version: 2.1.3
% 0.18/0.30 % (2156314)Termination reason: Inappropriate
% 0.18/0.30 % (2156314)Time elapsed: 0.001 s
% 0.18/0.30 % (2156314)Peak memory usage: 10 MB
% 0.18/0.30 % (2156319)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=837512048:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.30 % (2156318)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2655348663:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.30 % (2156320)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=422637133:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.30 % (2156314)------------------------------
% 0.18/0.30 % (2156314)------------------------------
% 0.18/0.30 % (2156328)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=331233170:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.18/0.30 % (2156328)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.18/0.30 % (2156328)Terminated due to inappropriate strategy.
% 0.18/0.30 % (2156328)------------------------------
% 0.18/0.30 % (2156328)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.30 % (2156328)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.30 % (2156328)CaDiCaL version: 2.1.3
% 0.18/0.30 % (2156328)Termination reason: Inappropriate
% 0.18/0.30 % (2156328)Time elapsed: 0.001 s
% 0.18/0.30 % (2156328)Peak memory usage: 10 MB
% 0.18/0.30 % (2156328)------------------------------
% 0.18/0.30 % (2156328)------------------------------
% 0.18/0.30 % (2156315) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2156309-2156315"...
% 0.18/0.30 % (2156315)...printing done.
% 0.18/0.30 % (2156317)Instruction limit reached!
% 0.18/0.30 % (2156317)------------------------------
% 0.18/0.30 % (2156317)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.30 % (2156317)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.30 % (2156317)CaDiCaL version: 2.1.3
% 0.18/0.30 % (2156317)Termination reason: Instruction limit
% 0.18/0.30 % (2156317)Termination phase: Saturation
% 0.18/0.30 % (2156317)Time elapsed: 0.038 s
% 0.18/0.30 % (2156317)Peak memory usage: 12 MB
% 0.18/0.30 % (2156317)Instructions burned: 106 (million)
% 0.18/0.30 % (2156315)Refutation found. Thanks to Tanya!
% 0.18/0.30 % SZS status Theorem for theBenchmark
% 0.18/0.30 % SZS output start Proof for theBenchmark
% 0.18/0.30 tff(type_def_5, type, list: $tType).
% 0.18/0.30 tff(func_def_0, type, nil: list).
% 0.18/0.30 tff(func_def_1, type, cons: ($int * list) > list).
% 0.18/0.30 tff(func_def_2, type, head: list > $int).
% 0.18/0.30 tff(func_def_3, type, tail: list > list).
% 0.18/0.30 tff(func_def_9, type, sK0: ($int * list) > $int).
% 0.18/0.30 tff(func_def_10, type, sK1: ($int * list) > list).
% 0.18/0.30 tff(func_def_11, type, sK2: list).
% 0.18/0.30 tff(func_def_12, type, sK3: $int).
% 0.18/0.30 tff(pred_def_1, type, inRange: ($int * list) > $o).
% 0.18/0.30 tff(f1,axiom,(
% 0.18/0.30 ! [X0 : $int,X1 : list] : head(cons(X0,X1)) = X0),
% 0.18/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1)).
% 0.18/0.30 tff(f5,axiom,(
% 0.18/0.30 ! [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))))),
% 0.18/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inRange)).
% 0.18/0.30 tff(f6,conjecture,(
% 0.18/0.30 ~ ? [X0 : list,X1 : $int] : (X0 != nil & inRange(X1,X0) & $less($difference(X1,head(X0)),1))),
% 0.18/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c)).
% 0.18/0.30 tff(f7,negated_conjecture,(
% 0.18/0.30 ~ ~ ? [X0 : list,X1 : $int] : (X0 != nil & inRange(X1,X0) & $less($difference(X1,head(X0)),1))),
% 0.18/0.30 inference(negated_conjecture,[status(cth)],[f6])).
% 0.18/0.30 tff(f8,plain,(
% 0.18/0.30 ! [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))))),
% 0.18/0.30 inference(theory_normalization,[],[f5])).
% 0.18/0.30 tff(f9,plain,(
% 0.18/0.30 ? [X0 : list,X1 : $int] : (X0 != nil & inRange(X1,X0) & $less($sum(X1,$uminus(head(X0))),1))),
% 0.18/0.30 inference(theory_normalization,[],[f7])).
% 0.18/0.30 tff(f10,definition,(
% 0.18/0.30 ( ! [X0 : $int,X1 : $int] : ($sum(X0,X1) = $sum(X1,X0)) )),
% 0.18/0.30 introduced(theory,[tha_commutativity])).
% 0.18/0.30 tff(f11,definition,(
% 0.18/0.30 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2)) )),
% 0.18/0.30 introduced(theory,[tha_associativity])).
% 0.18/0.30 tff(f14,definition,(
% 0.18/0.30 ( ! [X0 : $int] : (0 = $sum(X0,$uminus(X0))) )),
% 0.18/0.30 introduced(theory,[tha_inverse_op_unit])).
% 0.18/0.30 tff(f18,definition,(
% 0.18/0.30 ( ! [X2 : $int,X0 : $int,X1 : $int] : (~$less(X0,X1) | $less($sum(X0,X2),$sum(X1,X2))) )),
% 0.18/0.30 introduced(theory,[tha_order_monotonicity])).
% 0.18/0.30 tff(f21,definition,(
% 0.18/0.30 ( ! [X0 : $int,X1 : $int] : (~$less(X1,$sum(X0,1)) | ~$less(X0,X1)) )),
% 0.18/0.30 introduced(theory,[tha_extra_integer_ordering])).
% 0.18/0.30 tff(f22,plain,(
% 0.18/0.30 ( ! [X0 : $int,X1 : list] : (head(cons(X0,X1)) = X0) )),
% 0.18/0.30 inference(cnf_transformation,[],[f1])).
% 0.18/0.30 tff(f28,plain,(
% 0.18/0.30 ( ! [X0 : $int,X1 : list] : (~inRange(X0,X1) | nil = X1 | $less(sK0(X0,X1),X0)) )),
% 0.18/0.30 inference(cnf_transformation,[],[f8])).
% 0.18/0.30 tff(f30,plain,(
% 0.18/0.30 ( ! [X0 : $int,X1 : list] : (~inRange(X0,X1) | nil = X1 | cons(sK0(X0,X1),sK1(X0,X1)) = X1) )),
% 0.18/0.30 inference(cnf_transformation,[],[f8])).
% 0.18/0.30 tff(f32,plain,(
% 0.18/0.30 $less($sum(sK3,$uminus(head(sK2))),1)),
% 0.18/0.30 inference(cnf_transformation,[],[f9])).
% 0.18/0.30 tff(f33,plain,(
% 0.18/0.30 inRange(sK3,sK2)),
% 0.18/0.30 inference(cnf_transformation,[],[f9])).
% 0.18/0.30 tff(f34,plain,(
% 0.18/0.30 nil != sK2),
% 0.18/0.30 inference(cnf_transformation,[],[f9])).
% 0.18/0.30 tff(f59,plain,(
% 0.18/0.30 ( ! [X0 : $int,X1 : $int] : (~$less(X0,X1) | ~$less(X1,$sum(1,X0))) )),
% 0.18/0.30 inference(superposition,[],[f21,f10])).
% 0.18/0.30 tff(f94,plain,(
% 0.18/0.30 ( ! [X0 : $int] : ($less($sum($sum(sK3,$uminus(head(sK2))),X0),$sum(1,X0))) )),
% 0.18/0.30 inference(resolution,[],[f18,f32])).
% 0.18/0.30 tff(f127,plain,(
% 0.18/0.30 nil = sK2 | $less(sK0(sK3,sK2),sK3)),
% 0.18/0.30 inference(resolution,[],[f28,f33])).
% 0.18/0.30 tff(f130,plain,(
% 0.18/0.30 $less(sK0(sK3,sK2),sK3)),
% 0.18/0.30 inference(forward_subsumption_resolution,[],[f127,f34])).
% 0.18/0.30 tff(f138,plain,(
% 0.18/0.30 nil = sK2 | sK2 = cons(sK0(sK3,sK2),sK1(sK3,sK2))),
% 0.18/0.30 inference(resolution,[],[f30,f33])).
% 0.18/0.30 tff(f143,plain,(
% 0.18/0.30 sK2 = cons(sK0(sK3,sK2),sK1(sK3,sK2))),
% 0.18/0.30 inference(forward_subsumption_resolution,[],[f138,f34])).
% 0.18/0.30 tff(f146,plain,(
% 0.18/0.30 head(sK2) = sK0(sK3,sK2)),
% 0.18/0.30 inference(superposition,[],[f22,f143])).
% 0.18/0.30 tff(f156,plain,(
% 0.18/0.30 ( ! [X0 : $int] : ($less($sum(sK3,$sum($uminus(head(sK2)),X0)),$sum(1,X0))) )),
% 0.18/0.30 inference(forward_demodulation,[],[f94,f11])).
% 0.18/0.30 tff(f167,plain,(
% 0.18/0.30 $less($sum(sK3,0),$sum(1,$uminus($uminus(head(sK2)))))),
% 0.18/0.30 inference(superposition,[],[f156,f14])).
% 0.18/0.30 tff(f176,plain,(
% 0.18/0.30 $less(sK3,$sum(1,head(sK2)))),
% 0.18/0.30 inference(evaluation,[],[f167])).
% 0.18/0.30 tff(f228,plain,(
% 0.18/0.30 ~$less(sK3,$sum(1,sK0(sK3,sK2)))),
% 0.18/0.30 inference(resolution,[],[f59,f130])).
% 0.18/0.30 tff(f229,plain,(
% 0.18/0.30 ~$less(sK3,$sum(1,head(sK2)))),
% 0.18/0.30 inference(forward_demodulation,[],[f228,f146])).
% 0.18/0.30 tff(f1080,plain,(
% 0.18/0.30 $false),
% 0.18/0.30 inference(forward_subsumption_resolution,[],[f229,f176])).
% 0.18/0.30 % SZS output end Proof for theBenchmark
% 0.18/0.30 % (2156315)------------------------------
% 0.18/0.30 % (2156315)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.30 % (2156315)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.30 % (2156315)CaDiCaL version: 2.1.3
% 0.18/0.30 % (2156315)Termination reason: Refutation
% 0.18/0.30 % (2156315)Time elapsed: 0.029 s
% 0.18/0.30 % (2156315)Peak memory usage: 12 MB
% 0.18/0.30 % (2156315)Instructions burned: 44 (million)
% 0.18/0.30 % (2156309)Success in time 0.07 s
% 0.18/0.30 % Vampire exiting
%------------------------------------------------------------------------------