%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT095_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 : n017.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 0.20s 0.27s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT095_1 : TPTP v9.3.1. Released v6.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.18 % Computer : n017.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 00:03:51 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 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
% 0.20/0.27 % (4152068)Will run a generic schedule for satisfiability detection.
% 0.20/0.27 % (4152079)dis+10_1_sil=32000:sp=arity:random_seed=2142543591:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.27 % (4152076)% WARNING: option uhcvi not known.
% 0.20/0.27 % (4152079) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4152068-4152079"...
% 0.20/0.27 % (4152080)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1799160408:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.27 % (4152077)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=362392129:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.27 % (4152076)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1647389564:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.27 % (4152075)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2594523376_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.27 % (4152081)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1914175069:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.27 % (4152079)...printing done.
% 0.20/0.27 % (4152082)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=428276603:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.27 % (4152079)Refutation found. Thanks to Tanya!
% 0.20/0.27 % SZS status Theorem for theBenchmark
% 0.20/0.27 % SZS output start Proof for theBenchmark
% 0.20/0.27 tff(type_def_5, type, list: $tType).
% 0.20/0.27 tff(func_def_0, type, nil: list).
% 0.20/0.27 tff(func_def_1, type, cons: ($int * list) > list).
% 0.20/0.27 tff(func_def_2, type, head: list > $int).
% 0.20/0.27 tff(func_def_3, type, tail: list > list).
% 0.20/0.27 tff(func_def_5, type, length: list > $int).
% 0.20/0.27 tff(func_def_8, type, count: ($int * list) > $int).
% 0.20/0.27 tff(func_def_9, type, append: (list * list) > list).
% 0.20/0.27 tff(func_def_11, type, sK0: ($int * list) > $int).
% 0.20/0.27 tff(func_def_12, type, sK1: ($int * list) > list).
% 0.20/0.27 tff(func_def_13, type, sK2: ($int * list) > $int).
% 0.20/0.27 tff(func_def_14, type, sK3: ($int * list) > list).
% 0.20/0.27 tff(func_def_15, type, sK4: ($int * list) > $int).
% 0.20/0.27 tff(func_def_16, type, sK5: ($int * list) > list).
% 0.20/0.27 tff(pred_def_1, type, in: ($int * list) > $o).
% 0.20/0.27 tff(pred_def_2, type, inRange: ($int * list) > $o).
% 0.20/0.27 tff(f5,axiom,(
% 0.20/0.27 ! [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))))),
% 0.20/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',in_conv)).
% 0.20/0.27 tff(f9,axiom,(
% 0.20/0.27 ! [X0 : $int] : count(X0,nil) = 0),
% 0.20/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a)).
% 0.20/0.27 tff(f11,axiom,(
% 0.20/0.27 ! [X0 : $int,X1 : $int,X2 : list,X3 : $int] : (X0 = X1 => count(X0,cons(X1,X2)) = $sum(count(X0,X2),1))),
% 0.20/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_4)).
% 0.20/0.27 tff(f15,conjecture,(
% 0.20/0.27 ~ ! [X0 : $int,X1 : $int,X2 : list,X3 : list] : ((in(X1,X2) & X3 = cons(X0,X2)) => count(X1,X3) = count(X1,X2))),
% 0.20/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c)).
% 0.20/0.27 tff(f16,negated_conjecture,(
% 0.20/0.27 ~ ~ ! [X0 : $int,X1 : $int,X2 : list,X3 : list] : ((in(X1,X2) & X3 = cons(X0,X2)) => count(X1,X3) = count(X1,X2))),
% 0.20/0.27 inference(negated_conjecture,[status(cth)],[f15])).
% 0.20/0.27 tff(f19,definition,(
% 0.20/0.27 ( ! [X0 : $int,X1 : $int] : ($sum(X0,X1) = $sum(X1,X0)) )),
% 0.20/0.27 introduced(theory,[tha_commutativity])).
% 0.20/0.27 tff(f31,plain,(
% 0.20/0.27 ! [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))))),
% 0.20/0.27 inference(rectify,[],[f5])).
% 0.20/0.27 tff(f33,plain,(
% 0.20/0.27 ! [X0 : $int,X1 : $int,X2 : list] : (X0 = X1 => count(X0,cons(X1,X2)) = $sum(count(X0,X2),1))),
% 0.20/0.27 inference(rectify,[],[f11])).
% 0.20/0.27 tff(f34,plain,(
% 0.20/0.27 ! [X0 : $int,X1 : $int,X2 : list,X3 : list] : ((in(X1,X2) & X3 = cons(X0,X2)) => count(X1,X3) = count(X1,X2))),
% 0.20/0.27 inference(flattening,[],[f16])).
% 0.20/0.27 tff(f36,plain,(
% 0.20/0.27 ! [X0 : $int,X1 : $int,X2 : list] : (count(X0,cons(X1,X2)) = $sum(count(X0,X2),1) | X0 != X1)),
% 0.20/0.27 inference(ennf_transformation,[],[f33])).
% 0.20/0.27 tff(f37,plain,(
% 0.20/0.27 ! [X0 : $int,X1 : $int,X2 : list,X3 : list] : (count(X1,X3) = count(X1,X2) | (~in(X1,X2) | cons(X0,X2) != X3))),
% 0.20/0.27 inference(ennf_transformation,[],[f34])).
% 0.20/0.27 tff(f38,plain,(
% 0.20/0.27 ! [X0 : $int,X1 : $int,X2 : list,X3 : list] : (count(X1,X3) = count(X1,X2) | ~in(X1,X2) | cons(X0,X2) != X3)),
% 0.20/0.27 inference(flattening,[],[f37])).
% 0.20/0.27 tff(f39,plain,(
% 0.20/0.27 ! [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)))),
% 0.20/0.27 inference(nnf_transformation,[],[f31])).
% 0.20/0.27 tff(f40,plain,(
% 0.20/0.27 ! [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)))),
% 0.20/0.27 inference(flattening,[],[f39])).
% 0.20/0.27 tff(f41,plain,(
% 0.20/0.27 ! [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)))),
% 0.20/0.27 inference(rectify,[],[f40])).
% 0.20/0.27 tff(f42,plain,(
% 0.20/0.27 ! [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)))),
% 0.20/0.27 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])).
% 0.20/0.27 tff(f57,plain,(
% 0.20/0.27 ( ! [X2 : $int,X3 : list,X0 : $int,X1 : list] : (in(X0,X1) | cons(X2,X3) != X1 | X0 != X2) )),
% 0.20/0.27 inference(cnf_transformation,[],[f42])).
% 0.20/0.27 tff(f66,plain,(
% 0.20/0.27 ( ! [X0 : $int] : (0 = count(X0,nil)) )),
% 0.20/0.27 inference(cnf_transformation,[],[f9])).
% 0.20/0.27 tff(f68,plain,(
% 0.20/0.27 ( ! [X2 : list,X0 : $int,X1 : $int] : (count(X0,cons(X1,X2)) = $sum(count(X0,X2),1) | X0 != X1) )),
% 0.20/0.27 inference(cnf_transformation,[],[f36])).
% 0.20/0.27 tff(f73,plain,(
% 0.20/0.27 ( ! [X2 : list,X3 : list,X0 : $int,X1 : $int] : (count(X1,X3) = count(X1,X2) | ~in(X1,X2) | cons(X0,X2) != X3) )),
% 0.20/0.27 inference(cnf_transformation,[],[f38])).
% 0.20/0.27 tff(f74,plain,(
% 0.20/0.27 ( ! [X2 : $int,X3 : list,X0 : $int] : (in(X0,cons(X2,X3)) | X0 != X2) )),
% 0.20/0.27 inference(equality_resolution,[],[f57])).
% 0.20/0.27 tff(f75,plain,(
% 0.20/0.27 ( ! [X2 : $int,X3 : list] : (in(X2,cons(X2,X3))) )),
% 0.20/0.27 inference(equality_resolution,[],[f74])).
% 0.20/0.27 tff(f79,plain,(
% 0.20/0.27 ( ! [X2 : list,X1 : $int] : (count(X1,cons(X1,X2)) = $sum(count(X1,X2),1)) )),
% 0.20/0.27 inference(equality_resolution,[],[f68])).
% 0.20/0.27 tff(f80,plain,(
% 0.20/0.27 ( ! [X2 : list,X0 : $int,X1 : $int] : (~in(X1,X2) | count(X1,X2) = count(X1,cons(X0,X2))) )),
% 0.20/0.27 inference(equality_resolution,[],[f73])).
% 0.20/0.27 tff(f81,plain,(
% 0.20/0.27 ( ! [X2 : $int,X0 : $int,X1 : list] : (count(X0,cons(X0,X1)) = count(X0,cons(X2,cons(X0,X1)))) )),
% 0.20/0.27 inference(resolution,[],[f75,f80])).
% 0.20/0.27 tff(f261,plain,(
% 0.20/0.27 ( ! [X2 : list,X1 : $int] : (count(X1,cons(X1,X2)) = $sum(1,count(X1,X2))) )),
% 0.20/0.27 inference(forward_demodulation,[],[f79,f19])).
% 0.20/0.27 tff(f268,plain,(
% 0.20/0.27 ( ! [X0 : $int,X1 : list] : (count(X0,cons(X0,X1)) = $sum(1,count(X0,cons(X0,X1)))) )),
% 0.20/0.27 inference(superposition,[],[f81,f261])).
% 0.20/0.27 tff(f277,plain,(
% 0.20/0.27 ( ! [X0 : $int,X1 : list] : ($sum(1,count(X0,X1)) = $sum(1,$sum(1,count(X0,X1)))) )),
% 0.20/0.27 inference(forward_demodulation,[],[f268,f261])).
% 0.20/0.27 tff(f285,plain,(
% 0.20/0.27 $sum(1,0) = $sum(1,$sum(1,0))),
% 0.20/0.27 inference(superposition,[],[f277,f66])).
% 0.20/0.27 tff(f296,plain,(
% 0.20/0.27 $false),
% 0.20/0.27 inference(evaluation,[],[f285])).
% 0.20/0.27 % SZS output end Proof for theBenchmark
% 0.20/0.27 % (4152079)------------------------------
% 0.20/0.27 % (4152079)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (4152079)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (4152079)CaDiCaL version: 2.1.3
% 0.20/0.27 % (4152079)Termination reason: Refutation
% 0.20/0.27 % (4152079)Time elapsed: 0.007 s
% 0.20/0.27 % (4152079)Peak memory usage: 12 MB
% 0.20/0.27 % (4152079)Instructions burned: 15 (million)
% 0.20/0.27 % (4152068)Success in time 0.041 s
% 0.20/0.27 % Vampire exiting
%------------------------------------------------------------------------------