%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT106_1 : TPTP v9.3.1. Released v6.1.0.
% 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 09:48:08 AM UTC 2026
% Result : Theorem 0.20s 0.36s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT106_1 : TPTP v9.3.1. Released v6.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.19 % Computer : n020.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 00:09:34 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.21 Running first-order model finding
% 0.10/0.21 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
% 0.20/0.36 % (703225)Will run a generic schedule for satisfiability detection.
% 0.20/0.36 % (703236)% WARNING: option uhcvi not known.
% 0.20/0.36 % (703236)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4189273011:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.36 % (703235)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=741018638_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.36 % (703238)dis+10_1_sil=32000:sp=arity:random_seed=773244275:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.36 % (703239)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1974594292:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.36 % (703240)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2834461467:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.36 % (703235)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.20/0.36 % (703235)Terminated due to inappropriate strategy.
% 0.20/0.36 % (703235)------------------------------
% 0.20/0.36 % (703235)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.36 % (703235)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.36 % (703235)CaDiCaL version: 2.1.3
% 0.20/0.36 % (703235)Termination reason: Inappropriate
% 0.20/0.36 % (703235)Time elapsed: 0.001 s
% 0.20/0.36 % (703235)Peak memory usage: 10 MB
% 0.20/0.36 % (703237)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2804258671:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.36 % (703235)------------------------------
% 0.20/0.36 % (703235)------------------------------
% 0.20/0.36 % (703241)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=529385230:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.36 % (703255)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=4211946144:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.20/0.36 % (703255)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.20/0.36 % (703255)Terminated due to inappropriate strategy.
% 0.20/0.36 % (703255)------------------------------
% 0.20/0.36 % (703255)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.36 % (703255)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.36 % (703255)CaDiCaL version: 2.1.3
% 0.20/0.36 % (703255)Termination reason: Inappropriate
% 0.20/0.36 % (703255)Time elapsed: 0.001 s
% 0.20/0.36 % (703255)Peak memory usage: 11 MB
% 0.20/0.36 % (703255)------------------------------
% 0.20/0.36 % (703255)------------------------------
% 0.20/0.36 % (703263)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3426237236:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.36 % (703240)Instruction limit reached!
% 0.20/0.36 % (703240)------------------------------
% 0.20/0.36 % (703240)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.36 % (703240)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.36 % (703240)CaDiCaL version: 2.1.3
% 0.20/0.36 % (703240)Termination reason: Instruction limit
% 0.20/0.36 % (703240)Termination phase: Saturation
% 0.20/0.36 % (703240)Time elapsed: 0.045 s
% 0.20/0.36 % (703240)Peak memory usage: 13 MB
% 0.20/0.36 % (703240)Instructions burned: 132 (million)
% 0.20/0.36 % (703265)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=2990931554:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.20/0.36 % (703238)Instruction limit reached!
% 0.20/0.36 % (703238)------------------------------
% 0.20/0.36 % (703238)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.36 % (703238)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.36 % (703238)CaDiCaL version: 2.1.3
% 0.20/0.36 % (703238)Termination reason: Instruction limit
% 0.20/0.36 % (703238)Termination phase: Saturation
% 0.20/0.36 % (703238)Time elapsed: 0.065 s
% 0.20/0.36 % (703238)Peak memory usage: 12 MB
% 0.20/0.36 % (703238)Instructions burned: 103 (million)
% 0.20/0.36 % (703239)Instruction limit reached!
% 0.20/0.36 % (703239)------------------------------
% 0.20/0.36 % (703239)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.36 % (703239)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.36 % (703239)CaDiCaL version: 2.1.3
% 0.20/0.36 % (703239)Termination reason: Instruction limit
% 0.20/0.36 % (703239)Termination phase: Saturation
% 0.20/0.36 % (703239)Time elapsed: 0.071 s
% 0.20/0.36 % (703239)Peak memory usage: 12 MB
% 0.20/0.36 % (703239)Instructions burned: 117 (million)
% 0.20/0.36 % (703267)ott-21_1_sil=16000:fs=off:random_seed=2395967417:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 0.20/0.36 % (703270)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2116921775:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 0.20/0.36 % (703265) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-703225-703265"...
% 0.20/0.36 % (703241)Instruction limit reached!
% 0.20/0.36 % (703241)------------------------------
% 0.20/0.36 % (703241)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.36 % (703241)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.36 % (703241)CaDiCaL version: 2.1.3
% 0.20/0.36 % (703241)Termination reason: Instruction limit
% 0.20/0.36 % (703241)Termination phase: Saturation
% 0.20/0.36 % (703241)Time elapsed: 0.101 s
% 0.20/0.36 % (703241)Peak memory usage: 13 MB
% 0.20/0.36 % (703241)Instructions burned: 159 (million)
% 0.20/0.36 % (703265)...printing done.
% 0.20/0.36 % (703265)Refutation found. Thanks to Tanya!
% 0.20/0.36 % SZS status Theorem for theBenchmark
% 0.20/0.36 % SZS output start Proof for theBenchmark
% 0.20/0.36 tff(type_def_5, type, list: $tType).
% 0.20/0.36 tff(func_def_0, type, nil: list).
% 0.20/0.36 tff(func_def_1, type, cons: ($int * list) > list).
% 0.20/0.36 tff(func_def_2, type, head: list > $int).
% 0.20/0.36 tff(func_def_3, type, tail: list > list).
% 0.20/0.36 tff(func_def_10, type, sK0: ($int * list) > $int).
% 0.20/0.36 tff(func_def_11, type, sK1: ($int * list) > list).
% 0.20/0.36 tff(pred_def_1, type, inRange: ($int * list) > $o).
% 0.20/0.36 tff(f1,axiom,(
% 0.20/0.36 ! [X0 : $int,X1 : list] : head(cons(X0,X1)) = X0),
% 0.20/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1)).
% 0.20/0.36 tff(f4,axiom,(
% 0.20/0.36 ! [X0 : $int,X1 : list] : cons(X0,X1) != nil),
% 0.20/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4)).
% 0.20/0.36 tff(f5,axiom,(
% 0.20/0.36 ! [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))))),
% 0.20/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',inRange)).
% 0.20/0.36 tff(f6,conjecture,(
% 0.20/0.36 ~ ! [X0 : $int,X1 : list,X2 : list] : (($greater(X0,0) & inRange(X0,X1) & X2 = cons($difference(X0,2),X1)) => inRange(X0,X2))),
% 0.20/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',c)).
% 0.20/0.36 tff(f7,negated_conjecture,(
% 0.20/0.36 ~ ~ ! [X0 : $int,X1 : list,X2 : list] : (($greater(X0,0) & inRange(X0,X1) & X2 = cons($difference(X0,2),X1)) => inRange(X0,X2))),
% 0.20/0.36 inference(negated_conjecture,[status(cth)],[f6])).
% 0.20/0.36 tff(f8,plain,(
% 0.20/0.36 ! [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))))),
% 0.20/0.36 inference(theory_normalization,[],[f5])).
% 0.20/0.36 tff(f9,plain,(
% 0.20/0.36 ! [X0 : $int,X1 : list,X2 : list] : (($less(0,X0) & inRange(X0,X1) & cons($sum(X0,$uminus(2)),X1) = X2) => inRange(X0,X2))),
% 0.20/0.36 inference(theory_normalization,[],[f7])).
% 0.20/0.36 tff(f10,definition,(
% 0.20/0.36 ( ! [X0 : $int,X1 : $int] : ($sum(X0,X1) = $sum(X1,X0)) )),
% 0.20/0.36 introduced(theory,[tha_commutativity])).
% 0.20/0.36 tff(f11,definition,(
% 0.20/0.36 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2)) )),
% 0.20/0.36 introduced(theory,[tha_associativity])).
% 0.20/0.36 tff(f12,definition,(
% 0.20/0.36 ( ! [X0 : $int] : ($sum(X0,0) = X0) )),
% 0.20/0.36 introduced(theory,[tha_right_identity])).
% 0.20/0.36 tff(f14,definition,(
% 0.20/0.36 ( ! [X0 : $int] : (0 = $sum(X0,$uminus(X0))) )),
% 0.20/0.36 introduced(theory,[tha_inverse_op_unit])).
% 0.20/0.36 tff(f17,definition,(
% 0.20/0.36 ( ! [X0 : $int,X1 : $int] : ($less(X1,X0) | $less(X0,X1) | X0 = X1) )),
% 0.20/0.36 introduced(theory,[tha_order_totality])).
% 0.20/0.36 tff(f18,definition,(
% 0.20/0.36 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($less($sum(X0,X2),$sum(X1,X2)) | ~$less(X0,X1)) )),
% 0.20/0.36 introduced(theory,[tha_order_monotonicity])).
% 0.20/0.36 tff(f19,definition,(
% 0.20/0.36 ( ! [X0 : $int,X1 : $int] : ($less(X1,$sum(X0,1)) | $less(X0,X1)) )),
% 0.20/0.36 introduced(theory,[tha_order_plus_one_dichotomy])).
% 0.20/0.36 tff(f20,definition,(
% 0.20/0.36 ( ! [X0 : $int] : ($uminus($uminus(X0)) = X0) )),
% 0.20/0.36 introduced(theory,[tha_minus_minus_x])).
% 0.20/0.36 tff(f21,definition,(
% 0.20/0.36 ( ! [X0 : $int,X1 : $int] : (~$less(X1,$sum(X0,1)) | ~$less(X0,X1)) )),
% 0.20/0.36 introduced(theory,[tha_extra_integer_ordering])).
% 0.20/0.36 tff(f22,plain,(
% 0.20/0.36 ! [X0 : $int,X1 : list,X2 : list] : (inRange(X0,X2) | (~$less(0,X0) | ~inRange(X0,X1) | cons($sum(X0,$uminus(2)),X1) != X2))),
% 0.20/0.36 inference(ennf_transformation,[],[f9])).
% 0.20/0.36 tff(f23,plain,(
% 0.20/0.36 ! [X0 : $int,X1 : list,X2 : list] : (inRange(X0,X2) | ~$less(0,X0) | ~inRange(X0,X1) | cons($sum(X0,$uminus(2)),X1) != X2)),
% 0.20/0.36 inference(flattening,[],[f22])).
% 0.20/0.36 tff(f24,plain,(
% 0.20/0.36 ( ! [X0 : $int,X1 : list] : (head(cons(X0,X1)) = X0) )),
% 0.20/0.36 inference(cnf_transformation,[],[f1])).
% 0.20/0.36 tff(f27,plain,(
% 0.20/0.36 ( ! [X0 : $int,X1 : list] : (cons(X0,X1) != nil) )),
% 0.20/0.36 inference(cnf_transformation,[],[f4])).
% 0.20/0.36 tff(f30,plain,(
% 0.20/0.36 ( ! [X0 : $int,X1 : list] : (~inRange(X0,X1) | nil = X1 | $less(sK0(X0,X1),X0)) )),
% 0.20/0.36 inference(cnf_transformation,[],[f8])).
% 0.20/0.36 tff(f31,plain,(
% 0.20/0.36 ( ! [X0 : $int,X1 : list] : (~$less(sK0(X0,X1),0) | nil = X1 | ~inRange(X0,X1)) )),
% 0.20/0.36 inference(cnf_transformation,[],[f8])).
% 0.20/0.36 tff(f32,plain,(
% 0.20/0.36 ( ! [X0 : $int,X1 : list] : (~inRange(X0,X1) | nil = X1 | cons(sK0(X0,X1),sK1(X0,X1)) = X1) )),
% 0.20/0.36 inference(cnf_transformation,[],[f8])).
% 0.20/0.36 tff(f33,plain,(
% 0.20/0.36 ( ! [X0 : $int,X1 : list] : (nil != X1 | inRange(X0,X1)) )),
% 0.20/0.36 inference(cnf_transformation,[],[f8])).
% 0.20/0.36 tff(f34,plain,(
% 0.20/0.36 ( ! [X2 : list,X0 : $int,X1 : list] : (cons($sum(X0,$uminus(2)),X1) != X2 | ~inRange(X0,X1) | ~$less(0,X0) | inRange(X0,X2)) )),
% 0.20/0.36 inference(cnf_transformation,[],[f23])).
% 0.20/0.36 tff(f35,plain,(
% 0.20/0.36 ( ! [X0 : $int] : (inRange(X0,nil)) )),
% 0.20/0.36 inference(equality_resolution,[],[f33])).
% 0.20/0.36 tff(f37,plain,(
% 0.20/0.36 ( ! [X0 : $int,X1 : list] : (~inRange(X0,X1) | ~$less(0,X0) | inRange(X0,cons($sum(X0,$uminus(2)),X1))) )),
% 0.20/0.36 inference(equality_resolution,[],[f34])).
% 0.20/0.36 tff(f38,plain,(
% 0.20/0.36 ( ! [X0 : $int,X1 : list] : (inRange(X0,cons($sum(X0,-2),X1)) | ~$less(0,X0) | ~inRange(X0,X1)) )),
% 0.20/0.36 inference(evaluation,[],[f37])).
% 0.20/0.36 tff(f39,plain,(
% 0.20/0.36 ( ! [X0 : $int] : (0 = $sum($uminus(X0),X0)) )),
% 0.20/0.36 inference(superposition,[],[f14,f20])).
% 0.20/0.36 tff(f61,plain,(
% 0.20/0.36 ( ! [X0 : $int,X1 : $int] : ($less(X1,$sum(1,X0)) | $less(X0,X1)) )),
% 0.20/0.36 inference(superposition,[],[f19,f10])).
% 0.20/0.36 tff(f78,plain,(
% 0.20/0.36 ( ! [X0 : $int,X1 : $int] : (~$less(X1,$sum(1,X0)) | ~$less(X0,X1)) )),
% 0.20/0.36 inference(superposition,[],[f21,f10])).
% 0.20/0.36 tff(f834,plain,(
% 0.20/0.36 ( ! [X0 : $int,X1 : $int] : (~$less(X0,1) | ~$less(X1,$sum(X0,X1))) )),
% 0.20/0.36 inference(resolution,[],[f18,f78])).
% 0.20/0.36 tff(f1290,plain,(
% 0.20/0.36 ( ! [X2 : list,X0 : $int,X1 : $int] : (~inRange($sum(X0,X1),X2) | ~$less(0,$sum(X0,X1)) | inRange($sum(X0,X1),cons($sum(X0,$sum(X1,-2)),X2))) )),
% 0.20/0.36 inference(superposition,[],[f38,f11])).
% 0.20/0.36 tff(f1306,plain,(
% 0.20/0.36 ( ! [X0 : $int,X1 : $int] : (inRange($sum(X0,X1),cons($sum(X0,$sum(X1,-2)),nil)) | ~$less(0,$sum(X0,X1))) )),
% 0.20/0.36 inference(resolution,[],[f1290,f35])).
% 0.20/0.36 tff(f1327,plain,(
% 0.20/0.36 ( ! [X0 : $int] : (inRange($sum(X0,$uminus(-2)),cons($sum(X0,0),nil)) | ~$less(0,$sum(X0,$uminus(-2)))) )),
% 0.20/0.36 inference(superposition,[],[f1306,f39])).
% 0.20/0.36 tff(f1333,plain,(
% 0.20/0.36 ( ! [X0 : $int] : (inRange($sum(X0,2),cons(X0,nil)) | ~$less(0,$sum(X0,2))) )),
% 0.20/0.36 inference(evaluation,[],[f1327])).
% 0.20/0.36 tff(f1366,plain,(
% 0.20/0.36 ( ! [X0 : $int,X1 : $int] : (~$less(0,$sum(X0,$sum(X1,2))) | inRange($sum(X0,$sum(X1,2)),cons($sum(X0,X1),nil))) )),
% 0.20/0.36 inference(superposition,[],[f1333,f11])).
% 0.20/0.36 tff(f1530,plain,(
% 0.20/0.36 ( ! [X0 : $int] : (inRange($sum(1,$sum(X0,2)),cons($sum(1,X0),nil)) | $less($sum(X0,2),0)) )),
% 0.20/0.36 inference(resolution,[],[f1366,f61])).
% 0.20/0.36 tff(f1565,plain,(
% 0.20/0.36 inRange($sum(1,0),cons($sum(1,$uminus(2)),nil)) | $less(0,0)),
% 0.20/0.36 inference(superposition,[],[f1530,f39])).
% 0.20/0.36 tff(f1573,plain,(
% 0.20/0.36 inRange(1,cons(-1,nil))),
% 0.20/0.36 inference(evaluation,[],[f1565])).
% 0.20/0.36 tff(f2042,plain,(
% 0.20/0.36 nil = cons(-1,nil) | $less(sK0(1,cons(-1,nil)),1)),
% 0.20/0.36 inference(resolution,[],[f30,f1573])).
% 0.20/0.36 tff(f2051,plain,(
% 0.20/0.36 $less(sK0(1,cons(-1,nil)),1)),
% 0.20/0.36 inference(forward_subsumption_resolution,[],[f2042,f27])).
% 0.20/0.36 tff(f2106,plain,(
% 0.20/0.36 ( ! [X0 : $int] : (~$less(X0,$sum(sK0(1,cons(-1,nil)),X0))) )),
% 0.20/0.36 inference(resolution,[],[f2051,f834])).
% 0.20/0.36 tff(f2131,plain,(
% 0.20/0.36 ~$less(0,sK0(1,cons(-1,nil)))),
% 0.20/0.36 inference(superposition,[],[f2106,f12])).
% 0.20/0.36 tff(f2141,plain,(
% 0.20/0.36 $less(sK0(1,cons(-1,nil)),0) | 0 = sK0(1,cons(-1,nil))),
% 0.20/0.36 inference(resolution,[],[f2131,f17])).
% 0.20/0.36 tff(f2144,definition,(
% 0.20/0.36 spl2_1 <=> 0 = sK0(1,cons(-1,nil))),
% 0.20/0.36 introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition])).
% 0.20/0.36 tff(f2146,plain,(
% 0.20/0.36 0 = sK0(1,cons(-1,nil)) | ~spl2_1),
% 0.20/0.36 inference(avatar_component_clause,[],[f2144])).
% 0.20/0.36 tff(f2148,definition,(
% 0.20/0.36 spl2_2 <=> $less(sK0(1,cons(-1,nil)),0)),
% 0.20/0.36 introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition])).
% 0.20/0.36 tff(f2150,plain,(
% 0.20/0.36 $less(sK0(1,cons(-1,nil)),0) | ~spl2_2),
% 0.20/0.36 inference(avatar_component_clause,[],[f2148])).
% 0.20/0.36 tff(f2152,plain,(
% 0.20/0.36 spl2_1 | spl2_2),
% 0.20/0.36 inference(avatar_split_clause,[],[f2141,f2148,f2144])).
% 0.20/0.36 tff(f3722,plain,(
% 0.20/0.36 nil = cons(-1,nil) | cons(-1,nil) = cons(sK0(1,cons(-1,nil)),sK1(1,cons(-1,nil)))),
% 0.20/0.36 inference(resolution,[],[f32,f1573])).
% 0.20/0.36 tff(f3731,plain,(
% 0.20/0.36 cons(-1,nil) = cons(sK0(1,cons(-1,nil)),sK1(1,cons(-1,nil)))),
% 0.20/0.36 inference(forward_subsumption_resolution,[],[f3722,f27])).
% 0.20/0.36 tff(f3779,plain,(
% 0.20/0.36 cons(-1,nil) = cons(0,sK1(1,cons(-1,nil))) | ~spl2_1),
% 0.20/0.36 inference(forward_demodulation,[],[f3731,f2146])).
% 0.20/0.36 tff(f3783,plain,(
% 0.20/0.36 0 = head(cons(-1,nil)) | ~spl2_1),
% 0.20/0.36 inference(superposition,[],[f24,f3779])).
% 0.20/0.36 tff(f3786,plain,(
% 0.20/0.36 0 = -1 | ~spl2_1),
% 0.20/0.36 inference(forward_demodulation,[],[f3783,f24])).
% 0.20/0.36 tff(f3787,plain,(
% 0.20/0.36 $false | ~spl2_1),
% 0.20/0.36 inference(evaluation,[],[f3786])).
% 0.20/0.36 tff(f3788,plain,(
% 0.20/0.36 ~spl2_1),
% 0.20/0.36 inference(avatar_contradiction_clause,[],[f3787])).
% 0.20/0.36 tff(f3799,plain,(
% 0.20/0.36 nil = cons(-1,nil) | ~inRange(1,cons(-1,nil)) | ~spl2_2),
% 0.20/0.36 inference(resolution,[],[f2150,f31])).
% 0.20/0.36 tff(f3804,plain,(
% 0.20/0.36 ~inRange(1,cons(-1,nil)) | ~spl2_2),
% 0.20/0.36 inference(forward_subsumption_resolution,[],[f3799,f27])).
% 0.20/0.36 tff(f3805,plain,(
% 0.20/0.36 $false | ~spl2_2),
% 0.20/0.36 inference(forward_subsumption_resolution,[],[f3804,f1573])).
% 0.20/0.36 tff(f3806,plain,(
% 0.20/0.36 ~spl2_2),
% 0.20/0.36 inference(avatar_contradiction_clause,[],[f3805])).
% 0.20/0.36 cnf(s2, plain, spl2_1 | spl2_2, inference(sat_conversion,[],[f2152])).
% 0.20/0.36 cnf(s73, plain, ~spl2_1, inference(sat_conversion,[],[f3788])).
% 0.20/0.36 cnf(s75, plain, ~spl2_2, inference(sat_conversion,[],[f3806])).
% 0.20/0.36 cnf(s76, plain, $false, inference(rat,[],[s2,s75,s73])).
% 0.20/0.36 tff(f3807,plain,(
% 0.20/0.36 $false),
% 0.20/0.36 inference(avatar_sat_refutation,[],[s76])).
% 0.20/0.36 % SZS output end Proof for theBenchmark
% 0.20/0.36 % (703265)------------------------------
% 0.20/0.36 % (703265)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.36 % (703265)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.36 % (703265)CaDiCaL version: 2.1.3
% 0.20/0.36 % (703265)Termination reason: Refutation
% 0.20/0.36 % (703265)Time elapsed: 0.047 s
% 0.20/0.36 % (703265)Peak memory usage: 14 MB
% 0.20/0.36 % (703265)Instructions burned: 149 (million)
% 0.20/0.36 % (703225)Success in time 0.137 s
% 0.20/0.36 % Vampire exiting
%------------------------------------------------------------------------------