%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT037_1 : TPTP v9.3.1. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n013.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 09:48:00 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 : DAT037_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n013.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 00:05:37 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 % (1710068)Will run a generic schedule for satisfiability detection.
% 0.20/0.27 % (1710076)dis+10_1_sil=32000:sp=arity:random_seed=1114673681:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.27 % (1710074)% WARNING: option uhcvi not known.
% 0.20/0.27 % (1710076) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1710068-1710076"...
% 0.20/0.27 % (1710076)...printing done.
% 0.20/0.27 % (1710075)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3797946544:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.27 % (1710073)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2915437902_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.27 % (1710074)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3004794841:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.27 % (1710078)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1880424992:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.27 % (1710076)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, collection: $tType).
% 0.20/0.27 tff(func_def_0, type, empty: collection).
% 0.20/0.27 tff(func_def_1, type, add: ($int * collection) > collection).
% 0.20/0.27 tff(func_def_2, type, remove: ($int * collection) > collection).
% 0.20/0.27 tff(func_def_3, type, count: collection > $int).
% 0.20/0.27 tff(func_def_11, type, sK0: collection).
% 0.20/0.27 tff(pred_def_1, type, in: ($int * collection) > $o).
% 0.20/0.27 tff(f1,axiom,(
% 0.20/0.27 ! [X0 : $int] : ~in(X0,empty)),
% 0.20/0.27 file('/export/starexec/sandbox2/benchmark/Axioms/DAT002_0.ax',ax1)).
% 0.20/0.27 tff(f5,axiom,(
% 0.20/0.27 ! [X0 : $int,X1 : collection,X2 : $int] : ((in(X0,X1) & X0 != X2) <=> in(X0,remove(X2,X1)))),
% 0.20/0.27 file('/export/starexec/sandbox2/benchmark/Axioms/DAT002_0.ax',ax5)).
% 0.20/0.27 tff(f7,axiom,(
% 0.20/0.27 ! [X0 : collection] : (X0 = empty <=> count(X0) = 0)),
% 0.20/0.27 file('/export/starexec/sandbox2/benchmark/Axioms/DAT002=1.ax',ax2)).
% 0.20/0.27 tff(f10,axiom,(
% 0.20/0.27 ! [X0 : $int,X1 : collection] : (in(X0,X1) <=> count(remove(X0,X1)) = $difference(count(X1),1))),
% 0.20/0.27 file('/export/starexec/sandbox2/benchmark/Axioms/DAT002=1.ax',ax5)).
% 0.20/0.27 tff(f13,conjecture,(
% 0.20/0.27 ! [X0 : collection] : ((in(2,X0) & count(X0) = 1) => ~in(5,X0))),
% 0.20/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1)).
% 0.20/0.27 tff(f14,negated_conjecture,(
% 0.20/0.27 ~ ! [X0 : collection] : ((in(2,X0) & count(X0) = 1) => ~in(5,X0))),
% 0.20/0.27 inference(negated_conjecture,[status(cth)],[f13])).
% 0.20/0.27 tff(f16,plain,(
% 0.20/0.27 ! [X0 : $int,X1 : collection] : (in(X0,X1) <=> count(remove(X0,X1)) = $sum(count(X1),$uminus(1)))),
% 0.20/0.27 inference(theory_normalization,[],[f10])).
% 0.20/0.27 tff(f17,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(f30,plain,(
% 0.20/0.27 ? [X0 : collection] : (in(5,X0) & (in(2,X0) & count(X0) = 1))),
% 0.20/0.27 inference(ennf_transformation,[],[f14])).
% 0.20/0.27 tff(f31,plain,(
% 0.20/0.27 ? [X0 : collection] : (in(5,X0) & in(2,X0) & count(X0) = 1)),
% 0.20/0.27 inference(flattening,[],[f30])).
% 0.20/0.27 tff(f34,plain,(
% 0.20/0.27 ! [X0 : $int,X1 : collection,X2 : $int] : (((in(X0,X1) & X0 != X2) | ~in(X0,remove(X2,X1))) & (in(X0,remove(X2,X1)) | (~in(X0,X1) | X0 = X2)))),
% 0.20/0.27 inference(nnf_transformation,[],[f5])).
% 0.20/0.27 tff(f35,plain,(
% 0.20/0.27 ! [X0 : $int,X1 : collection,X2 : $int] : (((in(X0,X1) & X0 != X2) | ~in(X0,remove(X2,X1))) & (in(X0,remove(X2,X1)) | ~in(X0,X1) | X0 = X2))),
% 0.20/0.27 inference(flattening,[],[f34])).
% 0.20/0.27 tff(f36,plain,(
% 0.20/0.27 ! [X0 : collection] : ((X0 = empty | count(X0) != 0) & (count(X0) = 0 | empty != X0))),
% 0.20/0.27 inference(nnf_transformation,[],[f7])).
% 0.20/0.27 tff(f39,plain,(
% 0.20/0.27 ! [X0 : $int,X1 : collection] : ((in(X0,X1) | count(remove(X0,X1)) != $sum(count(X1),$uminus(1))) & (count(remove(X0,X1)) = $sum(count(X1),$uminus(1)) | ~in(X0,X1)))),
% 0.20/0.27 inference(nnf_transformation,[],[f16])).
% 0.20/0.27 tff(f41,plain,(
% 0.20/0.27 in(5,sK0) & in(2,sK0) & 1 = count(sK0)),
% 0.20/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f31])).
% 0.20/0.27 tff(f42,plain,(
% 0.20/0.27 ( ! [X0 : $int] : (~in(X0,empty)) )),
% 0.20/0.27 inference(cnf_transformation,[],[f1])).
% 0.20/0.27 tff(f48,plain,(
% 0.20/0.27 ( ! [X2 : $int,X0 : $int,X1 : collection] : (in(X0,remove(X2,X1)) | ~in(X0,X1) | X0 = X2) )),
% 0.20/0.27 inference(cnf_transformation,[],[f35])).
% 0.20/0.27 tff(f53,plain,(
% 0.20/0.27 ( ! [X0 : collection] : (count(X0) != 0 | empty = X0) )),
% 0.20/0.27 inference(cnf_transformation,[],[f36])).
% 0.20/0.27 tff(f58,plain,(
% 0.20/0.27 ( ! [X0 : $int,X1 : collection] : (count(remove(X0,X1)) = $sum(count(X1),$uminus(1)) | ~in(X0,X1)) )),
% 0.20/0.27 inference(cnf_transformation,[],[f39])).
% 0.20/0.27 tff(f63,plain,(
% 0.20/0.27 1 = count(sK0)),
% 0.20/0.27 inference(cnf_transformation,[],[f41])).
% 0.20/0.27 tff(f64,plain,(
% 0.20/0.27 in(2,sK0)),
% 0.20/0.27 inference(cnf_transformation,[],[f41])).
% 0.20/0.27 tff(f65,plain,(
% 0.20/0.27 in(5,sK0)),
% 0.20/0.27 inference(cnf_transformation,[],[f41])).
% 0.20/0.27 tff(f69,plain,(
% 0.20/0.27 ( ! [X0 : $int,X1 : collection] : (count(remove(X0,X1)) = $sum(count(X1),-1) | ~in(X0,X1)) )),
% 0.20/0.27 inference(evaluation,[],[f58])).
% 0.20/0.27 tff(f252,plain,(
% 0.20/0.27 ( ! [X0 : $int,X1 : collection] : (~in(X0,X1) | count(remove(X0,X1)) = $sum(-1,count(X1))) )),
% 0.20/0.27 inference(forward_demodulation,[],[f69,f17])).
% 0.20/0.27 tff(f300,plain,(
% 0.20/0.27 count(remove(5,sK0)) = $sum(-1,count(sK0))),
% 0.20/0.27 inference(resolution,[],[f252,f65])).
% 0.20/0.27 tff(f301,plain,(
% 0.20/0.27 $sum(-1,1) = count(remove(5,sK0))),
% 0.20/0.27 inference(forward_demodulation,[],[f300,f63])).
% 0.20/0.27 tff(f302,plain,(
% 0.20/0.27 0 = count(remove(5,sK0))),
% 0.20/0.27 inference(evaluation,[],[f301])).
% 0.20/0.27 tff(f309,plain,(
% 0.20/0.27 0 != 0 | empty = remove(5,sK0)),
% 0.20/0.27 inference(superposition,[],[f53,f302])).
% 0.20/0.27 tff(f311,plain,(
% 0.20/0.27 empty = remove(5,sK0)),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f309])).
% 0.20/0.27 tff(f319,plain,(
% 0.20/0.27 ( ! [X0 : $int] : (in(X0,empty) | ~in(X0,sK0) | 5 = X0) )),
% 0.20/0.27 inference(superposition,[],[f48,f311])).
% 0.20/0.27 tff(f324,plain,(
% 0.20/0.27 ( ! [X0 : $int] : (~in(X0,sK0) | 5 = X0) )),
% 0.20/0.27 inference(forward_subsumption_resolution,[],[f319,f42])).
% 0.20/0.27 tff(f398,plain,(
% 0.20/0.27 2 = 5),
% 0.20/0.27 inference(resolution,[],[f324,f64])).
% 0.20/0.27 tff(f402,plain,(
% 0.20/0.27 $false),
% 0.20/0.27 inference(evaluation,[],[f398])).
% 0.20/0.27 % SZS output end Proof for theBenchmark
% 0.20/0.27 % (1710076)------------------------------
% 0.20/0.27 % (1710076)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (1710076)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (1710076)CaDiCaL version: 2.1.3
% 0.20/0.27 % (1710076)Termination reason: Refutation
% 0.20/0.27 % (1710076)Time elapsed: 0.006 s
% 0.20/0.27 % (1710076)Peak memory usage: 12 MB
% 0.20/0.27 % (1710076)Instructions burned: 15 (million)
% 0.20/0.27 % (1710068)Success in time 0.037 s
% 0.20/0.27 % Vampire exiting
%------------------------------------------------------------------------------