%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT097_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 : n014.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 09:48:07 AM UTC 2026
% Result : Theorem 0.06s 0.26s
% Output : Refutation 0.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : DAT097_1 : TPTP v9.3.1. Released v6.1.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.06/0.18 % Computer : n014.cluster.edu
% 0.06/0.18 % Model : x86_64 x86_64
% 0.06/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.18 % Memory : 8046.5625MB
% 0.06/0.18 % OS : Linux 6.8.0-71-generic
% 0.06/0.18 % CPULimit : 300
% 0.06/0.18 % WCLimit : 300
% 0.06/0.18 % DateTime : Tue Sep 29 00:08:16 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.06/0.21 Running first-order model finding
% 0.06/0.21 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
% 0.06/0.26 % (2304912)Will run a generic schedule for satisfiability detection.
% 0.06/0.26 % (2304919)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1756746173:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.06/0.26 % (2304917)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3641752688_2999 on theBenchmark for (2999ds/0Mi)
% 0.06/0.26 % (2304920)dis+10_1_sil=32000:sp=arity:random_seed=1843415959:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.06/0.26 % (2304923)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2597865821:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.06/0.26 % (2304921)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3826343156:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.06/0.26 % (2304922)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2562963467:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.06/0.26 % (2304917)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.06/0.26 % (2304917)Terminated due to inappropriate strategy.
% 0.06/0.26 % (2304917)------------------------------
% 0.06/0.26 % (2304917)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.06/0.26 % (2304917)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.06/0.26 % (2304917)CaDiCaL version: 2.1.3
% 0.06/0.26 % (2304917)Termination reason: Inappropriate
% 0.06/0.26 % (2304917)Time elapsed: 0.001 s
% 0.06/0.26 % (2304917)Peak memory usage: 10 MB
% 0.06/0.26 % (2304917)Instructions burned: 1 (million)
% 0.06/0.26 % (2304917)------------------------------
% 0.06/0.26 % (2304917)------------------------------
% 0.06/0.26 % (2304918)% WARNING: option uhcvi not known.
% 0.06/0.26 % (2304918)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2435968049:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.06/0.26 % (2304920) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2304912-2304920"...
% 0.06/0.26 % (2304920)...printing done.
% 0.06/0.26 % (2304920)Refutation found. Thanks to Tanya!
% 0.06/0.26 % SZS status Theorem for theBenchmark
% 0.06/0.26 % SZS output start Proof for theBenchmark
% 0.06/0.26 tff(type_def_5, type, list: $tType).
% 0.06/0.26 tff(func_def_0, type, nil: list).
% 0.06/0.26 tff(func_def_1, type, cons: ($int * list) > list).
% 0.06/0.26 tff(func_def_2, type, head: list > $int).
% 0.06/0.26 tff(func_def_3, type, tail: list > list).
% 0.06/0.26 tff(func_def_5, type, length: list > $int).
% 0.06/0.26 tff(func_def_8, type, count: ($int * list) > $int).
% 0.06/0.26 tff(func_def_9, type, append: (list * list) > list).
% 0.06/0.26 tff(func_def_11, type, sK0: ($int * list) > $int).
% 0.06/0.26 tff(func_def_12, type, sK1: ($int * list) > list).
% 0.06/0.26 tff(func_def_13, type, sK2: ($int * list) > $int).
% 0.06/0.26 tff(func_def_14, type, sK3: ($int * list) > list).
% 0.06/0.26 tff(func_def_15, type, sK4: ($int * list) > $int).
% 0.06/0.26 tff(func_def_16, type, sK5: ($int * list) > list).
% 0.06/0.26 tff(pred_def_1, type, in: ($int * list) > $o).
% 0.06/0.26 tff(pred_def_2, type, inRange: ($int * list) > $o).
% 0.06/0.26 tff(f5,axiom,(
% 0.06/0.26 ! [X0 : $int,X1 : list] : (in(X0,X1) <=> (? [X2 : $int,X3 : list] : (X1 = cons(X2,X3) & X0 = X2) | ? [X2 : $int,X3 : list] : (X1 = cons(X2,X3) & in(X0,X3))))),
% 0.06/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p',in_conv)).
% 0.06/0.26 tff(f9,axiom,(
% 0.06/0.26 ! [X0 : $int] : count(X0,nil) = 0),
% 0.06/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p',a)).
% 0.06/0.26 tff(f11,axiom,(
% 0.06/0.26 ! [X0 : $int,X1 : $int,X2 : list,X3 : $int] : (X0 = X1 => count(X0,cons(X1,X2)) = $sum(count(X0,X2),1))),
% 0.06/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_4)).
% 0.06/0.26 tff(f12,axiom,(
% 0.06/0.26 ! [X0 : list] : append(nil,X0) = X0),
% 0.06/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p',l_6)).
% 0.06/0.26 tff(f13,axiom,(
% 0.06/0.26 ! [X0 : $int,X1 : list,X2 : list] : append(cons(X0,X1),X2) = cons(X0,append(X1,X2))),
% 0.06/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p',l_7)).
% 0.06/0.26 tff(f14,axiom,(
% 0.06/0.26 ! [X0 : $int,X1 : list] : (in(X0,X1) <=> $greater(count(X0,X1),0))),
% 0.06/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_8)).
% 0.06/0.26 tff(f15,conjecture,(
% 0.06/0.26 ~ ! [X0 : $int,X1 : $int,X2 : list,X3 : list,X4 : list] : ((in(X1,X3) & ~in(X0,X2) & X4 = append(X3,cons(X0,X2))) => count(X1,X4) = count(X1,X3))),
% 0.06/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p',c)).
% 0.06/0.26 tff(f16,negated_conjecture,(
% 0.06/0.26 ~ ~ ! [X0 : $int,X1 : $int,X2 : list,X3 : list,X4 : list] : ((in(X1,X3) & ~in(X0,X2) & X4 = append(X3,cons(X0,X2))) => count(X1,X4) = count(X1,X3))),
% 0.06/0.26 inference(negated_conjecture,[status(cth)],[f15])).
% 0.06/0.26 tff(f18,plain,(
% 0.06/0.26 ! [X0 : $int,X1 : list] : (in(X0,X1) <=> $less(0,count(X0,X1)))),
% 0.06/0.26 inference(theory_normalization,[],[f14])).
% 0.06/0.26 tff(f19,definition,(
% 0.06/0.26 ( ! [X0 : $int,X1 : $int] : ($sum(X0,X1) = $sum(X1,X0)) )),
% 0.06/0.26 introduced(theory,[tha_commutativity])).
% 0.06/0.26 tff(f31,plain,(
% 0.06/0.26 ! [X0 : $int,X1 : list] : (in(X0,X1) <=> (? [X2 : $int,X3 : list] : (X1 = cons(X2,X3) & X0 = X2) | ? [X4 : $int,X5 : list] : (cons(X4,X5) = X1 & in(X0,X5))))),
% 0.06/0.26 inference(rectify,[],[f5])).
% 0.06/0.26 tff(f33,plain,(
% 0.06/0.26 ! [X0 : $int,X1 : $int,X2 : list] : (X0 = X1 => count(X0,cons(X1,X2)) = $sum(count(X0,X2),1))),
% 0.06/0.26 inference(rectify,[],[f11])).
% 0.06/0.26 tff(f34,plain,(
% 0.06/0.26 ! [X0 : $int,X1 : $int,X2 : list,X3 : list,X4 : list] : ((in(X1,X3) & ~in(X0,X2) & X4 = append(X3,cons(X0,X2))) => count(X1,X4) = count(X1,X3))),
% 0.06/0.26 inference(flattening,[],[f16])).
% 0.06/0.26 tff(f36,plain,(
% 0.06/0.26 ! [X0 : $int,X1 : $int,X2 : list] : (count(X0,cons(X1,X2)) = $sum(count(X0,X2),1) | X0 != X1)),
% 0.06/0.26 inference(ennf_transformation,[],[f33])).
% 0.06/0.26 tff(f37,plain,(
% 0.06/0.26 ! [X0 : $int,X1 : $int,X2 : list,X3 : list,X4 : list] : (count(X1,X4) = count(X1,X3) | (~in(X1,X3) | in(X0,X2) | append(X3,cons(X0,X2)) != X4))),
% 0.06/0.26 inference(ennf_transformation,[],[f34])).
% 0.06/0.26 tff(f38,plain,(
% 0.06/0.26 ! [X0 : $int,X1 : $int,X2 : list,X3 : list,X4 : list] : (count(X1,X4) = count(X1,X3) | ~in(X1,X3) | in(X0,X2) | append(X3,cons(X0,X2)) != X4)),
% 0.06/0.26 inference(flattening,[],[f37])).
% 0.06/0.26 tff(f39,plain,(
% 0.06/0.26 ! [X0 : $int,X1 : list] : ((in(X0,X1) | (! [X2 : $int,X3 : list] : (cons(X2,X3) != X1 | X0 != X2) & ! [X4 : $int,X5 : list] : (cons(X4,X5) != X1 | ~in(X0,X5)))) & ((? [X2 : $int,X3 : list] : (X1 = cons(X2,X3) & X0 = X2) | ? [X4 : $int,X5 : list] : (cons(X4,X5) = X1 & in(X0,X5))) | ~in(X0,X1)))),
% 0.06/0.26 inference(nnf_transformation,[],[f31])).
% 0.06/0.26 tff(f40,plain,(
% 0.06/0.26 ! [X0 : $int,X1 : list] : ((in(X0,X1) | (! [X2 : $int,X3 : list] : (cons(X2,X3) != X1 | X0 != X2) & ! [X4 : $int,X5 : list] : (cons(X4,X5) != X1 | ~in(X0,X5)))) & (? [X2 : $int,X3 : list] : (X1 = cons(X2,X3) & X0 = X2) | ? [X4 : $int,X5 : list] : (cons(X4,X5) = X1 & in(X0,X5)) | ~in(X0,X1)))),
% 0.06/0.26 inference(flattening,[],[f39])).
% 0.06/0.26 tff(f41,plain,(
% 0.06/0.26 ! [X0 : $int,X1 : list] : ((in(X0,X1) | (! [X2 : $int,X3 : list] : (cons(X2,X3) != X1 | X0 != X2) & ! [X4 : $int,X5 : list] : (cons(X4,X5) != X1 | ~in(X0,X5)))) & (? [X6 : $int,X7 : list] : (cons(X6,X7) = X1 & X0 = X6) | ? [X8 : $int,X9 : list] : (cons(X8,X9) = X1 & in(X0,X9)) | ~in(X0,X1)))),
% 0.06/0.26 inference(rectify,[],[f40])).
% 0.06/0.26 tff(f42,plain,(
% 0.06/0.26 ! [X0 : $int,X1 : list] : ((in(X0,X1) | (! [X2 : $int,X3 : list] : (cons(X2,X3) != X1 | X0 != X2) & ! [X4 : $int,X5 : list] : (cons(X4,X5) != X1 | ~in(X0,X5)))) & ((cons(sK0(X0,X1),sK1(X0,X1)) = X1 & sK0(X0,X1) = X0) | (cons(sK2(X0,X1),sK3(X0,X1)) = X1 & in(X0,sK3(X0,X1))) | ~in(X0,X1)))),
% 0.06/0.26 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X6,sK0(X0,X1)),skolemize(X7,sK1(X0,X1)),skolemize(X8,sK2(X0,X1)),skolemize(X9,sK3(X0,X1))],[f41])).
% 0.06/0.26 tff(f47,plain,(
% 0.06/0.26 ! [X0 : $int,X1 : list] : ((in(X0,X1) | ~$less(0,count(X0,X1))) & ($less(0,count(X0,X1)) | ~in(X0,X1)))),
% 0.06/0.26 inference(nnf_transformation,[],[f18])).
% 0.06/0.26 tff(f57,plain,(
% 0.06/0.26 ( ! [X2 : $int,X3 : list,X0 : $int,X1 : list] : (in(X0,X1) | cons(X2,X3) != X1 | X0 != X2) )),
% 0.06/0.26 inference(cnf_transformation,[],[f42])).
% 0.06/0.26 tff(f66,plain,(
% 0.06/0.26 ( ! [X0 : $int] : (0 = count(X0,nil)) )),
% 0.06/0.26 inference(cnf_transformation,[],[f9])).
% 0.06/0.26 tff(f68,plain,(
% 0.06/0.26 ( ! [X2 : list,X0 : $int,X1 : $int] : (count(X0,cons(X1,X2)) = $sum(count(X0,X2),1) | X0 != X1) )),
% 0.06/0.26 inference(cnf_transformation,[],[f36])).
% 0.06/0.26 tff(f69,plain,(
% 0.06/0.26 ( ! [X0 : list] : (append(nil,X0) = X0) )),
% 0.06/0.26 inference(cnf_transformation,[],[f12])).
% 0.06/0.26 tff(f70,plain,(
% 0.06/0.26 ( ! [X2 : list,X0 : $int,X1 : list] : (append(cons(X0,X1),X2) = cons(X0,append(X1,X2))) )),
% 0.06/0.26 inference(cnf_transformation,[],[f13])).
% 0.06/0.26 tff(f71,plain,(
% 0.06/0.26 ( ! [X0 : $int,X1 : list] : (~in(X0,X1) | $less(0,count(X0,X1))) )),
% 0.06/0.26 inference(cnf_transformation,[],[f47])).
% 0.06/0.26 tff(f73,plain,(
% 0.06/0.26 ( ! [X2 : list,X3 : list,X0 : $int,X1 : $int,X4 : list] : (count(X1,X4) = count(X1,X3) | ~in(X1,X3) | in(X0,X2) | append(X3,cons(X0,X2)) != X4) )),
% 0.06/0.26 inference(cnf_transformation,[],[f38])).
% 0.06/0.26 tff(f74,plain,(
% 0.06/0.26 ( ! [X2 : $int,X3 : list,X0 : $int] : (in(X0,cons(X2,X3)) | X0 != X2) )),
% 0.06/0.26 inference(equality_resolution,[],[f57])).
% 0.06/0.26 tff(f75,plain,(
% 0.06/0.26 ( ! [X2 : $int,X3 : list] : (in(X2,cons(X2,X3))) )),
% 0.06/0.26 inference(equality_resolution,[],[f74])).
% 0.06/0.26 tff(f79,plain,(
% 0.06/0.26 ( ! [X2 : list,X1 : $int] : (count(X1,cons(X1,X2)) = $sum(count(X1,X2),1)) )),
% 0.06/0.26 inference(equality_resolution,[],[f68])).
% 0.06/0.26 tff(f80,plain,(
% 0.06/0.26 ( ! [X2 : list,X3 : list,X0 : $int,X1 : $int] : (~in(X1,X3) | count(X1,X3) = count(X1,append(X3,cons(X0,X2))) | in(X0,X2)) )),
% 0.06/0.26 inference(equality_resolution,[],[f73])).
% 0.06/0.26 tff(f81,plain,(
% 0.06/0.26 ( ! [X2 : $int,X3 : list,X0 : $int,X1 : list] : (in(X2,X3) | count(X0,cons(X0,X1)) = count(X0,append(cons(X0,X1),cons(X2,X3)))) )),
% 0.06/0.26 inference(resolution,[],[f75,f80])).
% 0.06/0.26 tff(f110,plain,(
% 0.06/0.26 ( ! [X2 : $int,X3 : list,X0 : $int,X1 : list] : ($less(0,count(X0,X1)) | count(X2,cons(X2,X3)) = count(X2,append(cons(X2,X3),cons(X0,X1)))) )),
% 0.06/0.26 inference(resolution,[],[f71,f81])).
% 0.06/0.26 tff(f111,plain,(
% 0.06/0.26 ( ! [X2 : list,X0 : $int,X1 : $int] : ($less(0,0) | count(X1,cons(X1,X2)) = count(X1,append(cons(X1,X2),cons(X0,nil)))) )),
% 0.06/0.26 inference(superposition,[],[f110,f66])).
% 0.06/0.26 tff(f112,plain,(
% 0.06/0.26 ( ! [X2 : list,X0 : $int,X1 : $int] : (count(X1,cons(X1,X2)) = count(X1,append(cons(X1,X2),cons(X0,nil)))) )),
% 0.06/0.26 inference(evaluation,[],[f111])).
% 0.06/0.26 tff(f244,plain,(
% 0.06/0.26 ( ! [X2 : $int,X0 : $int,X1 : list] : (count(X0,cons(X0,X1)) = count(X0,cons(X0,append(X1,cons(X2,nil))))) )),
% 0.06/0.26 inference(superposition,[],[f112,f70])).
% 0.06/0.26 tff(f257,plain,(
% 0.06/0.26 ( ! [X0 : $int,X1 : $int] : (count(X1,cons(X1,nil)) = count(X1,cons(X1,cons(X0,nil)))) )),
% 0.06/0.26 inference(superposition,[],[f244,f69])).
% 0.06/0.26 tff(f269,plain,(
% 0.06/0.26 ( ! [X2 : list,X1 : $int] : (count(X1,cons(X1,X2)) = $sum(1,count(X1,X2))) )),
% 0.06/0.26 inference(forward_demodulation,[],[f79,f19])).
% 0.06/0.26 tff(f284,plain,(
% 0.06/0.26 ( ! [X0 : $int,X1 : $int] : (count(X0,cons(X0,nil)) = $sum(1,count(X0,cons(X1,nil)))) )),
% 0.06/0.26 inference(superposition,[],[f257,f269])).
% 0.06/0.26 tff(f294,plain,(
% 0.06/0.26 ( ! [X0 : $int,X1 : $int] : ($sum(1,count(X0,cons(X1,nil))) = $sum(1,count(X0,nil))) )),
% 0.06/0.26 inference(forward_demodulation,[],[f284,f269])).
% 0.06/0.26 tff(f302,plain,(
% 0.06/0.26 ( ! [X0 : $int,X1 : $int] : ($sum(1,0) = $sum(1,count(X0,cons(X1,nil)))) )),
% 0.06/0.26 inference(forward_demodulation,[],[f294,f66])).
% 0.06/0.26 tff(f303,plain,(
% 0.06/0.26 ( ! [X0 : $int,X1 : $int] : (1 = $sum(1,count(X0,cons(X1,nil)))) )),
% 0.06/0.26 inference(evaluation,[],[f302])).
% 0.06/0.26 tff(f309,plain,(
% 0.06/0.26 ( ! [X0 : $int] : (1 = $sum(1,$sum(1,count(X0,nil)))) )),
% 0.06/0.26 inference(superposition,[],[f303,f269])).
% 0.06/0.26 tff(f314,plain,(
% 0.06/0.26 1 = $sum(1,$sum(1,0))),
% 0.06/0.26 inference(forward_demodulation,[],[f309,f66])).
% 0.06/0.26 tff(f315,plain,(
% 0.06/0.26 $false),
% 0.06/0.26 inference(evaluation,[],[f314])).
% 0.06/0.26 % SZS output end Proof for theBenchmark
% 0.06/0.26 % (2304920)------------------------------
% 0.06/0.26 % (2304920)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.06/0.26 % (2304920)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.06/0.26 % (2304920)CaDiCaL version: 2.1.3
% 0.06/0.26 % (2304920)Termination reason: Refutation
% 0.06/0.26 % (2304920)Time elapsed: 0.013 s
% 0.06/0.26 % (2304920)Peak memory usage: 12 MB
% 0.06/0.26 % (2304920)Instructions burned: 19 (million)
% 0.06/0.26 % (2304912)Success in time 0.045 s
% 0.06/0.26 % Vampire exiting
%------------------------------------------------------------------------------